Final Report. Study on Radiometric Requirements for Hyperspectral Applications. Prepared for ESTEC, Noordwijk, The Netherlands

Transcription

1 Sira Electro-Optics Limited, South Hill Chislehurst, Kent, BR7 5EH, England Telephone: +44 (0) Fax: +44 (0) Website: Registered in England No Final Report Study on Radiometric Requirements for Hyperspectral Applications Prepared for ESTEC, Noordwijk, The Netherlands Authorised by: Sira Reference J0028/FR1 Issue 1 Dr M A Cutter Technology & Developments Manager Date: 30 March 2001 Copyright Sira Ltd 2001 COMMERCIAL IN CONFIDENCE

2 This page is intentionally blank 30 March 2001 COMMERCIAL IN CONFIDENCE Page 2 of 245

3 ESA CONTRACT NO. ESA STUDY CONTRACT REPORT SUBJECT CONTRACTOR 13245/87/BK/GD Study on Radiometric Requirements for Hyperspectral Applications ESA CR( ) No STAR CODE No of Volumes 1 This is Volume No 1 Sira Electro-Optics Limited Contractor's Reference J0028 Abstract This is the final report on the study, performed for ESA under contract number 13245/98/NL/GD. The study examines the requirements, and the potential methods, for in-flight characterisation of hyperspectral Earthobservation instruments in low Earth orbit. The study has been based on the requirements defined for the ESA PRISM (Process Research by an Imaging Space Mission) instrument, which was intended for the Land Surface Processes and Interactions Mission (LSPIM). However, the study has general relevance to future space missions using hyperspectral radiometers in the visible, near infrared and short-wave infrared spectral regions. A key aim of the study is to determine whether the radiometric requirements placed on the PRISM instrument can reasonably be changed, such that the difficulty of in-flight characterisation is significantly reduced. The study therefore includes a detailed examination of the requirements that should be placed on the PRISM instrument, and its in-flight characterisation, in order to achieve reasonable results in terms of the accuracy of its data products. In a contract extension, a detailed review has been performed on the most significant problems for in-flight characterisation methods, related to calibration for: absolute response, flat-fielding and relative spectral response functions. The work described in this report was done under ESA Contract. Responsibility for the contents resides in the author or organisation that prepared it. Names of principal authors: Dan Lobb (Sira Electro-Optics Ltd) Robert Renton (Sira Electro-Optics Ltd) Dieter Scherer (MCR Lab., ) Christian Feigenwinter (MCR Lab., ) ESA study manager: U. Del Bello Division: Future Programmes and Technical Studies Directorate: Applications ESA budget heading: E6401/ /98.E52 30 March 2001 COMMERCIAL IN CONFIDENCE Page 3 of 245

4 DISTRIBUTION Name Organisation Number U Del Bello ESA 15 ESA Publications Division ESA 45 D Scherer MCR Lab 2 E Parlow MCR Lab 1 D R Lobb Sira Electro-Optics Ltd 1 M A Cutter Sira Electro-Optics Ltd 1 C&DM Sira Electro-Optics Ltd Electronic copy 30 March 2001 COMMERCIAL IN CONFIDENCE Page 4 of 245

5 Contents 1 INTRODUCTION Scope and objectives Study logic Instrument design and requirements review Effects of instrument and atmosphere errors Conclusions on radiometric requirements In-flight characterisation methods Arrangement of this report Reference documents Summary of conclusions Instrument performance and characterisation requirements Effects on higher-level data products In-flight characterisation of the space instrument 15 2 THE PRISM INSTRUMENT - SPECIFICATIONS AND REQUIREMENTS PRISM mission and instrument specification Instrument design form Pointing the instrument pointing/calibration mirror Telescope and spectral channel separation Imaging spectrometer Detectors In-flight characterisation hardware Instrument errors Pre-flight characterisation Gain and polarisation errors due to contamination Stray light effects Detection system errors Thermal background signals Movements due to vibration and temperature-change 36 3 IN-FLIGHT CHARACTERISATION METHODS Dark signal and other offset measurements Full-frame at zero radiance Dark signal and electronics offset drifts Background radiation, out-of-band stray light and smear Requirements for dark signal and offset corrections Absolute response and flat-fielding Sun-illuminated reflecting diffusers Other diffuser options On-board alternatives to diffusers Vicarious calibration Moon view March 2001 COMMERCIAL IN CONFIDENCE Page 5 of 245

6 3.3 Linearity measurements Wavelength and waveband measurements 50 4 SENSITIVITY ANALYSIS Structure of the sensitivity analysis Ranges of parameters for radiance computations Conversion of radiance data to PRISM spectral bands Additional data available Fixed atmosphere/observation parameters Reference data set Differentials with respect to ground reflectance variations for nadir pointing angle Differentials with respect to atmosphere parameter variations Differentials with respect to ground reflectance variations - 40 off-nadir Differentials with respect to atmosphere parameter variations - 40 off-nadir At-satellite radiance of cumulus cloud Linearity with respect to ground reflectance 65 5 EFFECTS OF CHARACTERISATION ERRORS Effects of instrument characterisation errors Modelling the effects of instrument errors Effects of gain errors Effects of dark level errors Effects of electronics offset errors Effects of stray light errors Effects of non-linearity errors Effects of wavelength and waveband errors Effects of atmosphere characterisation errors Modelling of atmosphere error effects Effects of height errors Effects of visibility errors Effects of water vapour errors CASE STUDY PLANT WATER Case study design Retrieval of plant water content from vegetation spectra Vegetation spectra Sensitivity analysis Results - Atmosphere characterization errors Water vapour Visibility Altitude March 2001 COMMERCIAL IN CONFIDENCE Page 6 of 245

7 6.3 Results - Space-instrument characterisation errors Simple gain error Relative spectral response Stray light Wavelength and waveband errors Overview of the case study results Conclusions from the case study CONCLUSIONS Comparison of contributions to ground-reflectance errors Instrument characterisation and qualification Atmosphere characterisation comparison Insights from the case study In-flight characterisation requirements and methods Dark level and offset errors drift and non-uniformity Absolute spectral response (gain) and relative spectral response Linearity Response non-uniformity Stray light Spectral response calibration - wavelengths Spectral response calibration - wavebands (spectral widths) 149 APPENDIX A - SELECTION OF DATA PRODUCTS FOR ANALYSIS OF EFFECTS OF INSTRUMENT AND ATMOSPHERE CHARACTERISATION ERRORS 150 A.1 INTRODUCTION 150 A.2 ATMOSPHERIC WATER VAPOUR 150 General remarks 150 Algorithmic approach 151 Literature 153 A.3 SNOW GRAIN SIZE 154 General remarks 154 Algorithmic approach 154 Literature 156 A.4 SOIL FRACTION 157 General remarks 157 Algorithmic approach 157 Literature 157 A.5 LEAF AREA INDEX 158 General remarks 158 Algorithmic approach 158 Literature March 2001 COMMERCIAL IN CONFIDENCE Page 7 of 245

8 A.6 PLANT WATER CONTENT 160 General remarks 160 Algorithmic approach 160 Literature 160 APPENDIX B - PRISM INSTRUMENT SPECTRAL BANDS 163 APPENDIX C - RATIOING METHODS FOR IN-FLIGHT CHARACTERISATION OF ABSOLUTE RESPONSE IN THE VNIR AND SWIR SPECTRAL BANDS 168 C.1 INTRODUCTION 168 C.1.1 The key problem absolute response 168 C.1.2 Scope of this investigation ratioing methods 169 C.1.3 Summary of conclusions 169 C.2 BASIC CONCEPT OF RATIOING METHODS 169 C.2.1 Use of the sun and an attenuator 169 C.2.2 Attenuators and their relevant properties 170 C.2.3 In-flight measurement of attenuator properties 170 C.2.4 Use of main instrument for ratio measurements 171 C.3 RATIOING WITH DIFFUSERS 172 C.3.1 Two full-aperture transmitting diffusers 172 C.3.2 Theory of two-diffuser systems 173 C Effects of changes in relative polar distributions of scatter 175 C Problems of multiple reflections 176 C Problems of stray light 176 C.3.3 Other transmitting diffuser configurations minimising movements 177 C Full aperture systems 178 C Full-aperture diffuser + part-aperture diffuser 179 C Elimination of movements 182 C.3.4 Reflecting diffuser options 182 C Example using flat reflecting diffusers 183 C Example using two spherical diffusers 184 C Geometry of transmitting and reflecting diffuser systems 185 C Selection between transmitting and reflecting diffusers 187 C.4 RATIOING WITH SPECULAR ATTENUATORS 187 C.4.1 Sieve plates and filters 188 C Sieve plates 188 C Sieve plate and 2 neutral-density filters March 2001 COMMERCIAL IN CONFIDENCE Page 8 of 245

9 C.4.2 Multiple-reflecting windows 190 C Ratioing system designs using fused quartz windows 190 C Movements for the reflecting window ratioing method 193 C Stray light errors in the reflecting-window ratioing method 193 C Other errors in the reflecting window method 194 C.4.3 Comparisons of diffusers and specular attenuators 194 C.5 MEASUREMENTS ON TRANSMITTING DIFFUSERS 195 APPENDIX D - IN-FLIGHT SPECTRAL CALIBRATION OF HYPERSPECTRAL SENSORS 202 D.1 INTRODUCTION 202 D.1.1 The need for Spectral characterisation of hyperspectral data 202 D.1.2 Scope of the investigation 203 D.1.3 Summary of conclusions 204 D.2 BASIC ELEMENTS OF SPECTRAL CALIBRATION 204 D.2.1 Source spectral features 206 D Shapes of spectral features 206 D Minimum number of spectral features required 206 D Advantage of multiple spectral features 206 D.2.2 Field coverage 207 D.2.3 Full and part-aperture coverage 207 D Effects of part-aperture illumination 207 D Limiting errors due to part-aperture illumination 208 D Use of part aperture illumination for checks on SRF widths 209 D Summary of full-aperture and part-aperture merits 209 D.3 USE OF EXTERNAL SOURCES 210 D.3.1 Absorption bands in the solar spectrum. 210 D.3.2 Use of atmosphere absorption bands 215 D.3.3 Analysis for CHRIS in-flight spectral calibration 217 D Linear regression method 219 D LUT method 220 D.3.4 Artificial ground targets 221 D.4 USE OF ON-BOARD SOURCES 222 D.4.1 Spectral lamps March 2001 COMMERCIAL IN CONFIDENCE Page 9 of 245

10 D.4.2 Low pressure lamps 223 D Space use of low pressure lamps 225 D Emission characteristics 226 D Output and life variations with current 226 D.4.3 Use of solid state laser diodes 227 D Output characteristics 227 D Use for laser diodes for spectral calibration 229 D.4.4 Tungsten lamp and filters 230 D.5 FILTERS AND COLOURED DIFFUSERS 231 D.5.1 Interference filters 231 D.5.2 Fabry-Perot etalons 232 D.5.3 Rare-earth glass filters and rare-earth doped diffusers 235 D.6 IMPLEMENTATIONS WAVELENGTH MEASUREMENT 236 D.6.1 Large diffuser options 236 D.6.2 Direct illumination of the full aperture 239 D.6.3 Direct illumination at the entrance slit 240 D.6.4 Part aperture illumination 242 D.7 IMPLEMENTATIONS WAVEBAND MEASUREMENT 243 D.7.1 Wavelength scanning 243 D.7.2 Digital wavelength scanning, using multiple lines 244 D.7.3 Spectrometer focus measurement March 2001 COMMERCIAL IN CONFIDENCE Page 10 of 245

11 1 INTRODUCTION This is the final report on the study Radiometric Requirements for Hyperspectral Applications, performed for ESA under contract number 13245/98/NL/GD. The study examines the requirements, and the potential methods, for in-flight characterisation of hyperspectral Earth-observation instruments in low Earth orbit, that provide moderate spectral resolution in the visible to short-wave IR spectral region. Requirements placed on the ESA PRISM (Process Research by an Imaging Space Mission) instrument have been used as a reference. (The PRISM instrument was specified for the ESA Land Surface Processes and Interactions Mission.) However, the study is intended to be relevant also to a range of similar hyperspectral radiometers. 1.1 SCOPE AND OBJECTIVES The study is concerned with passive hyperspectral radiometry from space, in the spectral region dominated by reflected solar radiation, at moderate spectral resolution in the order of 10nm. This spectral resolution is used typically for measurement of land surfaces and water bodies, with some limited applications also in studies on atmosphere. The study does not address hyperspectral systems used in other wavebands, or at substantially higher spectral resolution, which are used for example in measurement of atmosphere gas concentrations and temperatures. Hyperspectral instruments of moderate spectral resolution, exemplified by the ESA MERIS and PRISM instruments, will be required to provide data of high radiometric accuracy, after calibration for the response of the instrument and for effect of the Earth atmosphere. In-flight characterisation of the instrument response will be essential to provide coefficients for data calibration. At present, the task of in-flight characterisation appears difficult, and is likely to contribute substantially to the instrument and mission costs. A key aim of the study is to determine whether the radiometric requirements placed on the PRISM instrument can reasonably be changed, such that the difficulty of in-flight characterisation is significantly reduced. The study therefore includes work on both:! Examination of the requirements that should be placed on the PRISM instrument, and its in-flight characterisation, in order to achieve reasonable results in terms of the accuracy of its data products, and! Critical review of methods for in-flight characterisation, with special attention to the most significant problems, which relate to calibration for (a) absolute response and (b) wavelengths (i.e. peak-wavelengths and widths of the relative spectral response functions defined by the sensor. The study concentrates on radiometric requirements for the waveband 450nm to 2350nm, which is specified for the PRISM imaging spectrometer. (PRISM also includes imaging radiometry in thermal bands, which is not covered in the study.) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 11 of 245

12 1.2 STUDY LOGIC The study logic is illustrated in figure WP201 (MCR Lab) Select data products and algorithms WP202 (MCR Lab) Sensitivity analysis (reflectance, atmos.) WP203 (MCR Lab) Case study - effects on a data product WP101 (Sira) Update instrument requirements (Sira) WP403 (Sira) detailed study of ratioing methods for characterisation WP101 (Sira) Review instrument requirements and errors WP302 (Sira) Sensitivity analysis (instrument errors) WP402 (Sira) characterisation methods - detailed study wavelength WP301 (Sira) Review instrument characterisation methods WP303 (Sira) Instrument characterisation strategies:- recommendations Figure Study logic Instrument design and requirements review An initial review of the radiometric performance requirements placed on the PRISM instrument is performed in WP101. This work package also includes a review of hyperspectral radiometer design, and the likely uncertainties in its radiometric response, before in-flight characterisation. The reviews of requirements and uncertainties lead to a definition of the requirements for in-flight characterisation of instrument response Effects of instrument and atmosphere errors The validity of the instrument performance requirements is addressed in WPs 201, 202, 302 and 203. The original intention was to base this review on a study of the effects of instrument errors on higher-level data products for example, plant water content. WP201 is therefore a review of data products for this analysis. However, the study was redirected to reduce the emphasis on higher-level data products so that the effects of instrument and atmosphere characterisation errors were computed for only one selected higher-level data product, in a case study under WP 203. The effects of errors in characterisation of the space instrument are computed mainly in terms of errors in ground reflectance, in WP 302. For comparison, the effects of errors in characterisation of the atmosphere (visibility, water vapour content etc.) are also computed, again in terms of errors in ground reflectance data. The analysis in WP 302 makes use of a 30 March 2001 COMMERCIAL IN CONFIDENCE Page 12 of 245

13 large number of at-sensor radiance computations performed in WP 202, which relates specifically to a range of atmosphere effects, at different ground reflectance values Conclusions on radiometric requirements The results of WPs 203 and 302 are used as a basis for comments on the instrument performance requirements, and suggestions for some changes, in WP101a. WP 203 has limited weight, because it relates only to a single case study, but it provides some interesting insights. No accepted requirements have been specified for accuracy of ground reflectance data, so that conclusions from WP 302 are based mainly on a comparison of the various effects of instrument characterisation errors and the effects of typical uncertainties in atmosphere characterisation. In particular, it is tacitly assumed that the tolerated effects of instrument errors need not be much smaller than typical effects of imperfect atmosphere correction In-flight characterisation methods Known methods for in-flight characterisation of hyperspectral space instruments are reviewed in WP301. Together with the results of the updated requirements review in WP101a, this leads in WP 303 to recommendations for characterisation strategies to be considered for future hyperspectral space missions. In an extension to the initial contract, WPs 402 and 403 provide more detailed investigation and analysis, related to the most significant in-flight characterisation problems. WP402 reviews methods for in-flight characterisation of the wavelengths and resolved wavebands defined by the space hardware. WP403 investigates some of the most promising methods for in-flight characterisation of absolute response. 1.3 ARRANGEMENT OF THIS REPORT Hyperspectral instrument design, with particular reference to PRISM, and recent requirements placed on PRISM radiometric performance, are discussed in Chapter 2, which includes: a discussion of the design and operation of the space instrument, a review of the likely uncertainties in the radiometric response of the instrument in flight, and a set of requirements for in-flight characterisation, related to the current performance requirements, with notes on difficulty. A review of methods for in-flight characterisation of hyperspectral radiometers is presented in Chapter 3. The more detailed investigations from WPs 402 and 403 are presented in Appendices C and D. Chapter 4 presents the results of at-sensor radiance computations for a range of atmosphere characteristics and observation scenarios, with comments on the effects of uncertainties. These results provide the basis for sensitivity analysis in Chapter 5 computation of the 30 March 2001 COMMERCIAL IN CONFIDENCE Page 13 of 245

14 effects of errors in instrument and atmosphere characterisation on ground reflectance data deduced from space instrument data. Chapter 6 describes an analysis of the effects of instrument and atmosphere characterisation errors in terms of errors in a selected data product plant water content. A larger set of higher-level data products was initially selected for this analysis, as described in Appendix A. Conclusions of the study are briefly summarised in section 1.5, and discussed in greater detail in Chapter REFERENCE DOCUMENTS 1 ESA invitation to tender RFQ/s-9338/98/NL/GD. 2 Sira Proposal for a Study on Radiometric Requirements for Hyperspectral Applications, Sira reference A/1568/00, 14/10/98. 3 Aerospatiale document: Intermediate Class Mission Final Report, issue 1, 24/7/98. 4 ESA document EE-LSPIM-SRD-ESA-01, draft issue 3, 28/9/ SUMMARY OF CONCLUSIONS Instrument performance and characterisation requirements In general, the most recent requirements placed on the PRISM instrument performance appear reasonable on the basis of: comparison of the effects of different types of instrument errors (mainly on accuracy of measured ground reflectance), and comparison of the effects of instrument errors with the effects of typical errors in characterisation of the atmosphere. However, some minor changes in specification are justified by these comparisons: # Stray light specifications (performance over non-uniform scenes) may be relaxed by a small factor. It is suggested that the separation of the specified target area from an area of different radiance may be increased by a factor 2 (from 10 pixels to 20 pixel) to reduce the impact of simple diffraction on computed performance. # Wavelength calibration (location of the centre-wavelengths of spectral response functions) to ±0.5nm is desirable. This compares with ±1.0nm in the most recent PRISM specification. # Waveband calibration requirements (knowledge of the widths of spectral response functions) can reasonably be relaxed to ±2nm. This compares with ±1nm in the present PRISM specification. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 14 of 245

15 1.5.2 Effects on higher-level data products Computations on: ground-reflectance errors and errors in one higher-level data product - plant water content, show significant differences in ranking of the importance of different instrument and atmosphere characterisation errors. In particular, instrument errors that are spectrally uniform are less significant than errors with large spectral variations, in their effects on the example data product. There is a good case for work on a wider range of higher-level data products, which may provide further insights relevant to optimisation of future specifications. (These may for example include a relaxation of the requirement on absolute response error, balanced by an added specification on wavelength-variation of instrument response error.) In-flight characterisation of the space instrument Gain (absolute response) The most significant characterisation problem for the space instrument is in-flight characterisation of instrument gain often called absolute calibration. In previous developments, it has been found difficult to provide ±2% accuracy with high confidence. Current suggestions for PRISM involve fairly complex and bulky space hardware, but provide only moderate confidence levels. It will be desirable to investigate alternative schemes that may provide better compromises between mission costs and performance. Investigations are recommended particularly on: Ratioing methods for on-board hardware (discussed in detail in Appendix C), Vicarious calibration (including emphasis on relative spectral accuracy, and including cost estimates for comparison with likely costs of space hardware developments) Dark level and offsets Adequate dark level characterisation, and also characterisation of electronics offsets, are likely to be easy (but must be addressed in instrument design) Stray light (affecting performance over non-uniform scenes) An in-flight check on the instrument stray light function may be considered desirable and is likely to be possible, for instruments on agile satellites, by use of the sun as a out-of-field source. However, in-flight characterisation is not obviously needed. Good pre-flight characterisation is essential, and fairly low stray light must be achieved. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 15 of 245

16 Linearity Good pre-flight characterisation for detection system linearity is essential. It is not clear whether there will be significant changes in linearity after pre-flight characterisation. However, there are relatively easy methods to check for linearity changes in flight (see section 3.3 below), which may be preferred to extensive programs of work to prove that no significant changes will occur Relative spectral response functions (wavelengths and wavebands) In-flight calibration is likely to be considered necessary for the centre-wavelengths of the spectral response functions (SRFs) defined by the sensor hardware. There are many possible methods, discussed in Appendix D. Selection of preferred approaches will depend on overall sensor design considerations, related particularly to pointing methods (pointing mirror or platform rotation) and absolute response measurement. If the requirement on knowledge of SRF widths is relaxed to around ±2nm, it may be considered reasonable to avoid in-flight characterisation, by implementing a qualification programme to prove spectrometer stability. However, an in-flight check on SRF widths is in principle desirable, and should be considered. Possible methods are also discussed in Appendix D. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 16 of 245

17 2 THE PRISM INSTRUMENT - SPECIFICATIONS AND REQUIREMENTS The study relates particularly to the impact of radiometric requirements on the design and construction of the PRISM instrument. The instrument will be thoroughly characterised preflight, but some response characteristics will change after pre-flight measurements, so that inflight characterisation of the instrument will be required; data from in-flight characterisation procedures will provide coefficients for correction of image data for instrument-related errors. In-flight characterisation is one of the important cost drivers for the PRISM mission. In this chapter, we: review of the current requirements for radiometric performance of the PRISM instrument, consider the likely design form of the instrument and the radiometric errors that it is likely to produce (before data calibration), and derive requirements for in-flight characterisation of the PRISM instrument. 2.1 PRISM MISSION AND INSTRUMENT SPECIFICATION PRISM is a passive, spaceborne Earth-observing instrument. Its mission is scientific, aimed mainly at investigation of interaction processes between land and atmosphere. The instrument will be designed to provide 50m spatial resolution (i.e. 50m ground sampling interval) from a platform in low Earth orbit. The orbit will probably be high-inclination, sunsynchronous with hour descending node. The orbit will be near circular, at an altitude between 600km and 800km (provisionally 767km). The instrument will include an imaging spectrometer for the VNIR and SWIR (solar) bands, to provide spectral resolution in these bands of around 10nm. The instrument will also include two thermal IR bands. In the present study, we are not directly concerned with radiometric requirements for the thermal bands, but they may have some indirect relevance, because some common optics may be used for the solar and thermal bands. The instrument will have a swath width of 50km, provided by pushbroom imaging onto detector arrays having about 1000 elements per row. Area arrays will be used in the imaging spectrometer channels, with separate rows assigned to separate resolved wavebands. The instrument will typically be used to form images on target areas about 50km square at nadir (i.e. recording about 1000 frames of detector data in one recording interval). It is an important function of the PRISM instrument to form sets of images of selected target sites at a range of viewing angles, to provide scientists with directional data on Earth radiance. For this purpose, the instrument must be pointable across-track and along-track. These pointing functions may be achieved by using pointing optics on the instrument (typically rotatable mirrors), or by rotation of the platform, or both. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 17 of 245

18 The present specification for the PRISM instrument includes the requirements listed below. Solar waveband: 450nm to 2350nm, excluding bands of near-total atmospheric absorption. In practice, it is convenient to define two bands that require different detector types:! VNIR from 450nm to about 1000nm and! SWIR from about 1000nm to 2350nm. Spectral resolution: typically 10nm 15nm maximum Spectral response function calibration: ±1nm for knowledge of both centre wavelength and waveband (width of spectral response function) Scene radiances: maximum radiances: computed top-of-atmosphere radiances for ground reflectance value 1.1 at low latitude. Absolute radiometric accuracy * (Region 1): typical radiances: computed top-of-atmosphere radiances for ground reflectance values 0.2 (450nm to 600nm and 1900nm to 2350nm) and 0.4 (600nm to 1900nm), at high latitude (60 N). minimum radiances: computed top-of-atmosphere radiances for ground reflectance of mud (increasing linearly from 0.02 to 0.07 between 450nm and 1850nm 0.07 above 1850nm), at high latitude (60 N). typically 2% of the true radiance at all radiances in the defined ranges. Radiometric resolution *, computed for typical radiance conditions: to achieve noise-equivalent ground reflectance (NEδρ) < between 450nm and 910nm, NEδρ <0.01 between 920nm and 1060nm, and NEδρ <0.005 between 1060nm and 2350nm. * Radiometric accuracy, radiometric resolution, spatial radiometric accuracy and temporal radiometric stability are all defined for PRISM in terms of radiances at the top of atmosphere (although, except for absolute accuracy, computed from ground reflectance requirements). Radiometric resolution and spatial radiometric accuracy are defined respectively as the rms variations of recorded columns and rows of data points, in the image of scene which actually has uniform radiance (defined for PRISM only at the typical radiance levels). An image is 1000 x 1000 spatially-resolved pixels. Radiometric resolution includes temporal noise on each detector element, plus drifts in system response over the period required to record an image. Spatial radiometric accuracy includes temporal noise, errors in flat-fielding and differential drifts in detector element response over the image-taking period. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 18 of 245

19 Spatial radiometric accuracy* : as for radiometric resolution Temporal radiometric stability*, computed for typical radiance conditions: Performance over non-uniform scenes: Instrument polarisation: change in response, between first and last images in a set over one target, in one overpass, to produce ground reflectance errors < between 450nm and 910nm, <0.01 between 920nm and 1060nm, and <0.005 between 1060nm. the specified absolute accuracy to be achieved at all specified radiances, in these conditions: (a) (recovery) 5 seconds after observation of sun reflected from a smooth water surface, (b) (stray light) at 10 spatial sampling intervals from (i) a semi-infinite scene area at the specified maximum radiance and (ii) a TBD area at 10 x the maximum radiance at 450nm <0.03 at 700nm <0.1 >1000nm <0.3 Pointing capability with respect to nadir: across-track: to allow three-day revisit at the equator. {At least roll range is likely to be allowed, to enhance directional measurement capabilities.} along-track: to provide several view-angles, measured at ground level with respect to zenith, in the range -70 to +70 Note that this is not the complete specification, in particular: Requirements only for the solar spectral bands, called Region 1 in the PRISM specification, is detailed. Thermal bands (Region 2) are merely noted. Geometrical requirements are excluded. Temporal radiometric stability is defined as the maximum difference of absolute accuracies between a number of images of one scene recorded at different along-track pointing angles in a single orbit. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 19 of 245

20 Scene radiance data and detailed radiometric resolution requirements are very briefly summarised. 2.2 INSTRUMENT DESIGN FORM The PRISM instrument includes imaging spectrometer channels for the visible/near-ir (VNIR) and short-wave IR (SWIR) spectral bands, and also (most recently) two thermal IR bands. The present study concentrates on the VNIR and SWIR bands. cryostat cold shield LWIR/MWIR detectors pointing optics field stop relay optics spectrometer telescope channel separation optics entrance slit Figure Hyperspectral instrument schematic VNIR/SWIR detectors The space instrument design is likely to be of the general form indicated schematically in figure In optical order, the system will include pointing/calibration optics, a telescope, and channel-separation optics. After separation into beams assigned to solar and thermal channels, the solar beam will pass through spectrometer optics to VNIR and SWIR detectors. The beam assigned to thermal channels will be relayed through dichroics and filters to cryogenically cooled detectors Pointing the instrument pointing/calibration mirror The view-direction of the instrument can in principle be varied by platform rotation and/or by optics in front of the instrument (or even by rotation of a larger part of the instrument). If at least one pointing mirror is included, as indicated schematically in figure 2.2-1, it may be used both to adjust the view direction to ground and also to point at on-board calibration sources. On-board sources may for example include a sun-illuminated diffuser for the solar bands and a black body for the thermal bands. If a pointing/calibration mirror is not included, it becomes 30 March 2001 COMMERCIAL IN CONFIDENCE Page 20 of 245

21 necessary to move and on-board calibration sources with respect to the main body of the instrument (so that at least one movement is likely to be necessary in any case). A pointing mirror is therefore potentially useful for in-flight characterisation of the space instrument. However, a pointing mirror can also introduce significant errors if the mirror rotation introduces a significant variation in the angle of incidence (and reflection) of the received radiation. Such a change of angle will in general introduce a variation in transmission with pointing direction. The variation can be minimised by coating design, and calibrated on ground, but the variation may be altered by contamination after pre-flight characterisation. Use of a pointing mirror will also in general introduce some instrument polarisation, which will change with mirror rotation and may also change after pre-flight calibration. At the end of the pre-phase A studies on PRISM, both competing teams preferred to use large rotations of the platform to generate all or most of the required pointing ranges, in both acrosstrack and along-track directions. The Daimler-Benz team proposed no pointing mirror. The Alcatel team proposed to include a single rotatable flat mirror outside the main optics. The important function of this mirror was to provide views of several on-board calibration sources, although there was also an option to use it for small-amplitude (~4 ) corrections in the view of ground in the along-track direction. The mirror rotates on an axis parallel to the reflected beam direction. In this arrangement (called in-beam rotation ) the mean angle of incidence does not change with rotation of the mirror, so that the effective reflectance of the mirror will be almost identical for unpolarised Earth scenes and for unpolarised calibration sources (accessed at any convenient mirror rotations), at all rotational positions. The in-beam rotation provides a wide range of positions for in-flight calibration sources, in an arc subtending most of 360 about the telescope input beam axis. These pre-phase A schemes, making maximum use of platform rotations, avoid the potentially serious radiometric errors due to pointing/calibration optics. However, at the end of the Phase A study, Alcatel have preferred that a pointing mirror shall be used to generate across-track pointing, since platform roll introduces a large variation in the efficiency of the radiator that is used for passive cooling of SWIR detectors. They have made this change by altering the axis of rotation of the pointing/calibration mirror from in-beam to in-plane (an axis in the plane of the mirror itself). The reason for preferring an in-plane rotation to an in-beam rotation is not entirely clear. In-beam rotation would rotate the IFOV line with respect to the heading direction, but this image distortion is not obviously unacceptable. A switch to in-plane rotation may also have been preferred to avoid reorientation of the main optical bench, with impacts on thermal design. In-plane rotation of the pointing mirror, for across-track pointing at Earth, will vary the angle of incidence through a total range of about 35, and can potentially introduce significant errors due to variations in reflectance and polarisation with angle. The range of positions for onboard calibration sources is more restricted, and a range of mirror incidence-angles must also be used for these sources. The change of layout for Phase A therefore introduces some potentially significant uncertainties in system response, due to variations in reflectance, polarisation and thermal emission of the pointing mirror, with angle of incidence. These errors are difficult to characterise in flight, to the extent that they may not in fact be measured, since it would be necessary to make measurements at a range of different pointing angles. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 21 of 245

22 However, the proposed scheme retains platform rotation for along-track pointing. Only small adjustments will be necessary in across-track pointing angle during recording of each image set. For the present study, an important conclusion is that the pointing hardware will introduce no significant errors in temporal radiometric stability. The optical layout particularly the pointing/calibration scheme is the result of complex system trade-offs. Considering only radiometric performance, there is a good case either for no pointing mirror (relying entirely on platform rotations) or for a mirror rotated in-beam, which introduces minimal errors and gives flexibility in design of calibration sub-systems. A pointing mirror rotated in-plane is a worst case for radiometry, though it may of course be convenient from other points of view Telescope and spectral channel separation The very broad waveband of the PRISM instrument requires use of three different detector types for VNIR, SWIR and thermal IR bands. The optical system will therefore probably provide three separate focal planes. Some common optics may be used to provide these three focal planes, but beams must of course be separated before the detectors. There is a wide range of possible options on where and how the separations shall be made. If a pointing/calibration mirror is included, as in the phase A baseline, it is very likely that a common mirror and telescope will be used for the whole waveband, as indicated in figure 2.2-1, to limit overall system size and complexity. (If at any stage the pointing mirror is eliminated, it will be sensible to consider use of separate telescopes for the thermal and solar bands.) Preferred basic layouts have evolved, during the pre-phase A and phase A studies on PRISM, with developments in detailed optical designs. In particular, it has been found possible to design efficient and compact spectrometers, based on the Offner three-mirror relay and curved dispersing prisms, that can transmit the complete waveband between 450nm and 2350nm. It is therefore logical (as indicated schematically in figure 2.2-1) to design an imaging spectrometer with almost all optics common to VNIR and SWIR bands. In the phase A baseline, the output beam will be split between VNIR and SWIR detectors immediately before the detectors, by a dichroic mirror (not included in the schematic figure 2.2-1). There are stringent requirements (not included in the list given in section 2.1) on spatial registration over the solar band (Region 1). There is a tendency to justify use of common optics, for the SWIR and VNIR channels, as a means for achieving this registration. However, it would be risky to assume that common optics will alone ensure good registration between VNIR and SWIR bands, since relative movements of detectors may present significant problems. It would be possible to use refracting optics for the thermal IR bands alone, while the solar band alone could in principle use a catadioptric telescope. However, a telescope for all bands tends to demand all-mirror optics. The design form selected as phase A baseline for the telescope is a three-mirror anastigmat an arrangement of three off-axis aspherics. This selection raises no very serious concerns for the present study. The off-axis angles of the mirrors are probably too shallow to introduce significant polarisation. The only significant stray light due to the telescope will be introduced by surface scatter. It may be more difficult to achieve low scatter on aspheric surfaces, but good polish can of course be achieved with sufficient work and good quality control. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 22 of 245

23 2.2.3 Imaging spectrometer The spectrometer selected for PRISM is likely to be a system of three spherical mirrors, at least two dispersing prisms with curved surfaces, and a dichroic mirror splitting the VNIR and SWIR bands. Given its very broad spectral coverage, this type of system is well adapted to control of stray light: there is a minimum number of surfaces and all surfaces are spherical, so that stray light due to surface scatter can be minimised. Other stray light contributions can in principle be made trivial; stray reflections from refracting surfaces will generally be directed away from the detectors; it may be necessary to tilt detector windows, if windows are included. The spectrometer is likely to introduce some polarisation, due mainly to oblique incidence of beams on the dispersing prism surfaces and on the dichroic. Polarisation in the spectrometer may change after pre-flight calibration due to molecular contamination of the same surfaces. The geometry of the spectrometer determines the wavelength calibration of the instrument i.e. the detector-row addresses of wavelengths. It will be difficult to guarantee stability of wavelength calibration though launch and thermal changes in orbit, since movements of order mm will produce 0.5nm wavelength errors. The system is likely to require some wavelength calibration in flight Detectors The detectors used on PRISM are likely to be: VNIR area-array silicon CCD, thinned and back-illuminated, uncooled SWIR area-array CMT diodes, cooled to ~150K For purposes of the present study, we are concerned with radiometric errors that will be introduced by detectors and electronics, including: drifts in response with temperature, space-radiation and other ageing effects, dark-signal and response non-uniformities and non-linearities. Some of these characteristics have been measured by detector manufacturers. However, in general, available detectors are not intended for use in accurate radiometry, or for imaging over wide radiance ranges, or for use in space. Therefore some of the detector data required to assess detector-related errors is not available in satisfactory forms. We are particularly concerned with linearity errors:- non-linearities have not generally been measured with adequate accuracy even in laboratory conditions. the effects of ionising radiation on detector and electronics linearity (on average or pixel response) is not known from measurements. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 23 of 245

24 In general, VNIR detectors are expected to be linear through life, provided that maximum signal levels do not approach well-defined saturation levels. However space radiation is known to change dark-signal levels and charge transfer efficiencies. SWIR and thermal arrays tend to be non-linear at low signal levels, due to variations in injection efficiency with signal levels. Non-linearities may also be produced in analogue electronics chains and at ADCs. It is possible that a set of amplifiers will be used with each detector, providing gain switching to enhance the dynamic range provided by the ADCs. Differential changes in gain between channels may then introduce an overall system non-linearity. At present, it is not possible to identify a mechanism that will certainly produce significant changes in flight - either average linearities or pixel-to-pixel differences. It must be considered likely that pre-flight characterisation will provide adequate calibration data for the instrument life. However, it is not possible to rule out changes of linearity in flight, so that there is a case at least for limited in-flight checks. It may be desirable at least to provide a range of radiant signal levels that can be used to test each analogue gain stage In-flight characterisation hardware In-flight characterisation hardware at present proposed for PRISM includes a full-aperture reflecting diffuser, as indicated schematically in figure The pointing/calibration mirror is rotated to provide a view of the diffuser, which is illuminated directly by the sun, at a suitable point in the orbit. A large filter wheel is included in the path of sunlight to the diffuser. When the diffuser is not in use, the filter wheel acts as a shutter to protect the diffuser from solar UV radiation. This is important to limit polymerisation of organic materials outgassed from the diffuser. In the Phase A baseline, the filter wheel will also carry a sieve plate to reduce the average diffuser radiance to a level typical of Earth radiances. It may also carry a rare-earth filter to provide for calibration of the centre-wavelengths of spectral response functions. The baseline proposal for full-field dark level characterisation is a view of the diffuser when sunlight is blocked by an opaque region of the filter wheel. The pointing/calibration mirror can be rotated to provide views of other calibration sources. These will certainly include a black body for characterisation of the thermal IR channels (not considered in this report). The baseline proposal also includes a second diffuser, which will be exposed less frequently to sun radiation. The theory is that the second diffuser will suffer less degradation of reflectance in flight, so that it can be used to monitor the degradation of the more-frequently used diffuser. 2.3 INSTRUMENT ERRORS Uncertainties in space instrument radiometric response are discussed in sections to below. The more important uncertainties, and typical errors introduced, are summarised in Table Note that the error estimates are order-of-magnitude at best, since real performance will depend on detailed design features and on manufacturing methods and quality control. The following definitions are applied: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 24 of 245

25 Gain is the gradient of the signal/radiance calibration curve. Linearity refers to departures from uniform gradient in the signal/radiance calibration curve. Errors are estimated in terms of radiance, for any selected radiance in the specified range, as a proportion of that radiance. Stray light errors are due to radiation, usually from the scene, that reaches detectors by paths other than the nominal path that provides good spatial and spectral resolution. In this Chapter, the stray light is estimated as radiance error for a dark target point in a uniformlybright surrounding scene, as a proportion of the average scene radiance. Errors related to pointing optics are ignored, since it is considered unlikely that a substantial range will be assigned to mirror rotation (or other optics). Temporal radiometric stability errors are generated only by dark signal drift. Error source Error type Typical significant error at BOL, with pre-flight calibration Optics imperfections and contamination Ageing of detector and electronics Temperature changes in flight Launch vibration Typical change in flight before calibration Gain - 10% Stray light 0.2% Negligible? Instrument polarisation 2% at 450nm 1% Pointing mirror 0.1% 0.5% (variation with angle) Gain - 1% Linearity <1% Probably <1% Dark signal and nonuniformity - <0.2% Dark level drift - 0.1% Gain drift - Negligible? Wavelength calibration <0.5nm 1nm Waveband change - 1nm Wavelength calibration <0.5nm 1nm Waveband change - 1nm to 10nm Pre-flight characterisation Table Instrument errors It is assumed that the instrument will be characterised on ground at least for: absolute response (gain), 30 March 2001 COMMERCIAL IN CONFIDENCE Page 25 of 245

26 linearity, stray light, polarisation. Absolute response calibration on ground may be considered non-critical, since it will not be reasonable to assume that gain will remain constant through the instrument life. In-flight characterisation will be considered necessary, and in-flight measurements will be used for data calibration. However, it will be very important to achieve good pre-flight characterisation of any on-board hardware for example diffusers which are used for in-flight characterisation of absolute response. Linearity characterisation means measurement of response over a wide range of source radiances. These measurements, combined with a good absolute measurement of gain at any pair of radiance levels, extend the absolute characterisation to all relevant radiance levels. Changes in linearity through life are expected to be small, and detailed linearity measurements in space would probably be considered too expensive. Data calibration will therefore probably be based on detailed linearity measurements made pre-flight (though a relatively simple check may be made in-flight). The pre-flight measurements will therefore be critical. Stray light and polarisation errors are scene dependant, so that calibration of data for these errors is not possible unless the scene is characterised - respectively for the scene radiance distribution and the scene polarisation. However, accurate ground measurements of the instrument stray light and polarisation characteristics will be desirable at least (a) to determine whether the instrument meets requirements, and (b) to predict errors in data related to stray light and polarisation Gain and polarisation errors due to contamination Absolute response (gain) of the space instrument can be affected by ageing of detectors and electronics, and by through-life temperature changes. However, the major effects on absolute response are expected to be due to changes in optics transmission, due to molecular contamination of the optics after pre-flight calibration. Changes in instrument polarisation, also due to molecular contamination, may also be justsignificant. Polarisation changes will be produced by contamination of surfaces used at oblique angles, including: the pointing mirror, dispersing prism surfaces and the dichroic History of transmission loss Large degradations in instrument response have been documented. For example, Rao and Chen 1 used ground reference areas to quantify the degradation of AVHRR in channels 1 and 2 (589nm-680nm and 720nm to 1100nm). They recorded degradation rates for three instruments - NOAA-7, NOAA-9 and NOAA-11 of 3.6%, 5.9% and 1.2% per year in channel 1, and 4.3%, 3.5% and 2.0% for channel 2. Degradation of the SPOT instruments has been recorded using the on-board calibration lamp and ground reference areas. The changes 1 Calibration of the visible and near-infrared channels of the advanced very high resolution radiometer (AVHRR) after launch, C R N Rao and J Chen, Proc. SPIE Vol.1938, April March 2001 COMMERCIAL IN CONFIDENCE Page 26 of 245

27 measured by Gellman et al 2 for SPOT 2, over a period of 2.6 years are approximately 24% in channel Xs1 (green), 28% in Xs2 (red) and 17% in Xs3 (near IR). In the case of SPOT, the rate of degradation decreases with years in orbit, but this trend is not obvious from the NOAA results. These degradations are probably due mainly to molecular contamination of optical surfaces. In principle, it is possible to reduce contamination of optical surfaces by careful design and control of integration and test procedures, and by use of covers during and for some time after launch (e.g. as described by R Thomas 3 for SOHO). Materials will preferably be selected for low mass-loss in vacuum, and components may be space-conditioned by baking out before integration. However, it would not be reasonable at present to assume that the errors due to contamination will in practice be made negligible by planning and control. The effects of particulate contamination on transmission, averaged across the optical aperture, are generally very small, for instruments constructed in clean areas and sensibly covered during storage and through launch, so that the most significant concern is usually molecular contamination, which produces thin films on optical surfaces. Contamination of optical surfaces will be expected to change the optics transmission in all spectral bands. The effects are usually expected to be stronger at short wavelengths (but the AVHRR and SPOT results indicate some substantial departures from this pattern in the visible/near-ir region). There is relatively little data on degradations in the thermal IR. Slater 4 has measured the Thematic Mapper response in band 6 (10.4m to 12.4m) by vicarious calibration, and estimated that the degradation in flight is less than 5%, compared with the pre-flight calibration. This would indicate smaller losses than are typical in the visible-near-ir region. The most significant molecular contamination, for enclosed or semi-enclosed surfaces of the instrument, is expected to be volatile species outgassed in orbit from materials within the optical cavity. Relevant source materials can include: carbon fibre composite (in structures), paints used for stray light control, lubricants, and cements used to mount optics. Contamination dynamics have been investigated by Eesbeek and Zwaal 5 with particular reference to Hipparcos. They estimated contaminant layers in the order of 10-6 gm.cm -2 for semi-enclosed instrument volumes, after a period of one year. This contamination density would correspond to a thicknesses in the order of 10nm - up to 1/30 wavelength interferometric thickness at 450nm (assuming a refractive index of 1.5). In the case of Hipparcos, the relevant cavities were near iso-thermal, so that uniform thicknesses of contaminants were predicted for all surfaces. Where a detector window is cooled, it will be expected to collect a larger thickness of diffused contaminants. Within completely enclosed volumes, greater contamination density is predicted, since there is no loss to space by successive absorption-desorption processes. 2 Review of SPOT calibration at White Sands from launch to the present, D I Gellman, S F Bigger, M C Dinguirard, P J Henry, M S Moran, K J Thornea and P N Slater, Proc. SPIE Vol.1938, April The cleanliness aspects of the SOHO satellite, R Thomas, ESA Bulletin, November Calibration of the Thematic Mapper band 6 in the thermal infrared, James M Slater, Proc. SPIE Vol.1938, April Outgassing and contamination model based on residence time, M Van Eesbeek and A Zwaal, Proc. 3rd Symposium on Spacecraft Materials in Space Environment, October 1985 (ESA SP-232 Nov, 1985). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 27 of 245

28 Maudlin and Chu 6 have estimated the effects of contaminants on transmission and reflection of optics in the SAGE II instrument, which measures atmospheric constituents by absorption of solar power by the Earth limb, in the spectral region 385nm to 1020nm. They computed effects of contaminant films up to 30nm thick, on both pointing-mirror and transmitting surfaces. They assumed a contaminant refractive index of 1.5, which is generally realistic for volatile organics, and absorption coefficients either zero or 0.03 cm -1. For the pointing mirror, they estimated changes in reflectance at 385nm of around 2% for a non-absorbing film (or 6% for an absorbing film). More importantly, they calculated changes of reflectance with mirror angle of about 1% (2% for the absorbing film), with an angle variation from 54 to 58. Their mirror coating was designed to give very little change of reflectance over this angular range, without contamination. Optics exposed to the space environment - for example pointing mirrors - may be less affected by condensation of outgassed material from the instrument, since the materials can more readily diffuse into space. However, the exposed optics may receive materials produced from the launch vehicle and the platform, and any condensed materials may be polymerised by UV radiation to produce a permanent contamination film. Hall, Stewart and Hayes 7 have described possible processes that produce degradation in back-silvered silica mirrors that are used as space-radiators on sun-illuminated sides of satellites. The solar absorption of these mirrors (which can be measured by their thermal-control efficiency) typically increases at around 2% per year, during the first few years in orbit. Somewhat similar results can be inferred from LDEF data reported by Havey, Mustico and Vallimont. They reported (inter alia) loss of visible/near-ir transmission in fused silica samples outside the satellite, which could be eliminated by cleaning of the recovered samples (showing that the loss was due only to a surface layer). The loss of transmission was greatest at short wavelengths - about 20% at 450nm, reducing to about 2% at 1000nm. For PRISM and similar instruments, we are concerned with possible polymerised contamination of pointing mirrors and (to a lesser extent) telescope mirrors. These mirrors will probably not be exposed to direct sunlight (except perhaps very briefly for absolute and/or stray light characterisation in flight). However, they will be exposed to strong Rayleigh scatter of UV radiation from the Earth atmosphere Computed effects of contamination We have computed some transmission and polarisation effects, using a conventional thin-film analysis program, assuming contaminant film thicknesses of 10nm and 20nm. The contaminant films were assumed to have the refractive index of fused silica over the wavelength range 450nm to 1000nm:- around 1.47 with no absorption. We have taken two basic cases: (a) Mirror design:- silver substrate with a 81nm silica protective layer angles of incidence:- 30º, 45º and 65º contaminant thicknesses:- 10nm and 20nm, silica refractive index 6 Optical degradation due to contamination on the SAGE/SAGE 2 spacecraft instruments, L E Maudlin and W P Chu, Proc. SPIE Vol. 338, May Photo-enhanced spacecraft contamination deposition, D F Hall, T B Stewart and R R Hayes, Proc. 3rd Symposium on Spacecraft Materials in Space Environment, October 1985 (ESA SP-232 Nov, 1985). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 28 of 245

29 (b) Refracting surface design:- assumed perfectly anti-reflection coating angle:- 40º. contaminant thickness:- 10nm only Tables and show calculated changes in throughput (reflection or transmission as appropriate) and polarisation due to changes in contamination film thickness and mirror angle of incidence. surface wavelength throughput change - 10nm film throughput change - 20nm film polarisation change 10nm film polarisation change 10nm film mirror at nm 0.59% 1.07% 0.33% 0.57% mirror at nm -0.08% -0.17% -0.03% -0.08% refracting at nm 1.20% 0.44% refracting at nm 0.24% 0.09% Table Calculated effects of contamination films on mirror and refracting surfaces at fixed angles of incidence no contamination 10nm contamination 20nm contamination Wavelength 450nm 1000nm 450nm 1000nm 450nm 1000nm Reflectance change Polarisation change -1.00% 0.28% -0.78% 0.37% -0.67% 0.31% -1.55% 0.42% -0.56% 0.37% 0.29% 0.31% Table Calculated effects of contamination films on mirror surfaces as a function of change in angle of incidence These results are intended only to provide some guidance on the possible orders of magnitude of uncertainties in optics transmission. Real results will probably not be predictable by such simple analysis Transmission and polarisation uncertainties The PRISM optical system is likely to have at least about 15 optical surfaces for the VNIR and SWIR bands. Given transmission changes of order 0.5% per surface, a total change in transmission in the range 5% to 10% can reasonably be expected. Larger losses may occur in the visible region - losses will tend to decrease at longer wavelengths. It will be desirable to perform some analysis on the possible effects of contamination on polarisation produced by the PRISM instrument, due mainly to the pointing/calibration mirror 30 March 2001 COMMERCIAL IN CONFIDENCE Page 29 of 245

30 and the dispersing prisms. This will depend on coatings and of course on molecular contamination levels. At present, a change in the order of 1% may be considered a reasonable estimate for the solar bands Stray light effects Stray light is generated within instruments by a variety of processes, in general including: scatter from optical surfaces, diffraction, scatter from structures, and stray reflections between mirrors, lens and window surfaces, filters and detectors. However in an imaging spectrometer, with moderate care in design, it is generally possible to achieve very good control over stray light due to scatter from structures. The complexity of the design allows baffles and stops to be deployed such that the detector cannot see any of the internal structures of the telescope section (or the external baffle) that receive significant illumination from the external scene. The present preferred design form for PRISM is also well adapted to control of stray light due to specular reflections between optical surfaces. There are potential problems due to reflections between surfaces of the detectors, the entrance slit, the dichroic, and any filters or windows that may be required. However, these effects can again be controlled by sensible detailed design. Scatter from optical surfaces and diffraction are therefore expected to present the dominant stray light problems for the PRISM instrument Scatter and diffraction formulae Scatter The total integrated scatter (TIS) of fairly good optical surfaces either mirrors or refracting surfaces, including coatings is in the region 10-3 per surface (i.e. 0.1 of all incident light is scattered). The angular distribution of scatter (outside the region close to the geometrical focus) would typically be described by a simplified bi-directional reflection/transmission distribution function (BRDF or BTDF) of the form: L(b).Bo.b -A watts.m -2.steradian -1 This is the radiance of scatter produced by a surface, in a specified target direction, due to an incident radiance L(b) at an angle b radians from the target direction. (Note (a) that this is a pragmatic approximation for distributions that vary widely in practice, (b) the function is never valid for very small angles b.) The index A varies typically from 1.5 to 2 for different optical surface qualities, but may be approximated to 2 for good surfaces. With A =2, the BRDF or BTDF coefficient Bo is typically in the order 10-5 for a good surface (corresponding roughly to a TIR of 10-3 ). It is possible to produce optical surfaces with BRDF and BTDF coefficients smaller than 10-5 in the visible region. However, it may be unwise to assume that very low scatter will be achieved in practice. In the present preferred design for PRISM, the telescope system is common to both solar and thermal channels, which restricts to choice to mirror 30 March 2001 COMMERCIAL IN CONFIDENCE Page 30 of 245

31 materials, and the mirrors are aspheric, which would multiply the cost of a achieving very high polish quality. To compute the radiance error due to one surface, this expression should be integrated over the solid angle of the illuminating radiance: Ω L(b).Bo.b -A.dΩ where Ω is the solid angular field of illumination. Simplifying again, we may assume that L(b) is uniform (=L) between maximum and minimum angles b max and b min :. Setting A = 2, the integral then simplifies conveniently to give a total stray radiance from one surface: 2π.Bo.L.ln(b max /b min ) watts.m -2.steradian -1 The pointing/calibration mirror may see an Earth scene subtending a semi-angle b max of about 0.25 radians radians will generally be more typical for telescope mirrors. Values for b max in the order 0.01 radians will be appropriate for surfaces in the spectrometer. The scatter function is invalid for very small values of b min, where the distribution is better described by the central peak and inner rings of the diffraction distribution. However, the calculation is fairly insensitive to variations in the scene-subtense angle b max, and to the exact value assigned to b min, since the logarithm operator compresses the range of results Diffraction It is possible to describe the effects of diffraction by a function similar to the BTDF. The angular distribution of radiance in diffraction rings, due to diffraction at a circular aperture (excluding the central peak) is of the form: L(b).Do.b -3 watts.m -2.steradians -1 This is again the radiance for a target at an angle b radians from a small illuminating source of radiance L(b). The value for Do, associated with local averages of diffracted intensity (half the peak intensity of the local diffraction rings) is Do = /d, where is wavelength, d is the optics aperture diameter. The total effect of diffraction on any selected target area is computed by integrating over the angular field of the illuminating radiance L(b). If we again assume that it is reasonable to specify minimum and maximum angles b max and b min for a scene of uniform radiance L, the integrated stray radiance due only to diffraction reduces to 2 L.Do.(1/b min - 1/b max ) watts.m -2.steradian -1. Generally, b min will be substantially smaller than b max, so that it is reasonable to approximate this to: 2 L.Do/b min watts.m -2.steradian -1. It is necessary, to define what is considered stray light, as opposed to an acceptable PSF. If b min is set at radians for the telescope, corresponding to 10 x 50m pixels at an altitude of 767km, the stray light error thus defined is estimated at 8378.L.Do watts.m -2.steradian -1. At 600nm wavelength and, for an 85mm aperture, Do is , so that the error for the visible band is in the order 0.2% of the average scene radiance. For performance over non-uniform scenes (see section 2.1), the specified bright field is bounded by a straight line at 10 pixels (not by a circle of radius 10 pixels), so that the stray light error will be about 0.06% of the bright scene radiance. The error for a scene at the minimum radiance will then be in the order 1%. This estimate for diffraction is larger than a 30 March 2001 COMMERCIAL IN CONFIDENCE Page 31 of 245

32 fairly optimistic estimate for surface scatter (see section below), and is in principle significant Telescope stray light due to scatter The optics before the spectrometer entrance slit the telescope and the pointing/calibration mirror will produce only out-of-field stray light. Out of field stray light is radiation that derives from scene areas inappropriate for the detector elements on which it lands (mainly from outside the field of the instrument). In the present baseline, the telescope and pointing/calibration optics comprise four mirrors illuminated by various moderate cone-angles of scene light. We may take a value for b min, which is equivalent to 10 x 50m ground pixels at a range of 767km, and a typical value for b max of 0.05 radians for each mirror. This would give a typical value ln(b max /b min ) = 4, and an estimated total stray light error, due to the four mirrors, of order 100.Bo.L watts.m - 2.steradian -1. This assumes measurement of a dark scene 20 pixels in diameter, surrounded by a scene at radiance L. Taking a fairly optimistic value of 10-5 for the BRDF coefficient Bo, the out-of-field scene radiance error is estimated at 0.1% of the uniform scene radiance. This is a more stringent condition than that specified by ESA for performance over nonuniform scenes (see section 2.1), in which the specified bright scene is limited by a straight line at 10 pixels (not by a circle at radius 10 pixels). For this case, the equivalent estimate for stray light error generated by the telescope and pointing/calibration mirror will be in the order 0.03.L. In the present specification for performance over non-uniform scenes, the worst-case condition is that the bright scene radiance R is at the specified maximum, while the area to be measured is at the minimum. The ratio of maximum to minimum scene radiances is typically around 20, for short visible wavelengths, rising to around 40 at longer wavelengths. We may be equally concerned with long and short wavelengths, because BRDFs are typically worse at short wavelengths. Our estimated error for a minimum-radiance scene, as specified under performance over non-uniform scenes, is 0.6% Spectrometer stray light due to scatter The stray light produced within the spectrometer arrives on detector elements that are shifted, in both the spectral and spatial domains, with respect to the elements appropriate to their wavelength and field origin. Stray light in the spectrometer is therefore both out-of-field and out-of-band. Stray light is limited by the entrance slit, which allows very little light into the spectrometer camera. However, dispersion in the spectrometer spreads useful light over a relatively large field subtended at the optical components typically order of ±0.005 radian x ±0.05 radian at the prism surfaces and secondary mirror (and half these angles at the primary and tertiary mirrors). The spectrometer has a relatively large number of optical surfaces, and low-angle scatter at these surfaces is potentially significant. Spectrometer stray light is particularly difficult to estimate, since it will depend on surface scatter at low angles, for which there are no reliable BRDF data. We may guess a value ln(b max /b min ) in the region of 2. 9 surfaces (three mirrors, four prisms surfaces and two dichroic 30 March 2001 COMMERCIAL IN CONFIDENCE Page 32 of 245

33 surfaces) with typical BRDF/BTDF coefficients of 10-5, will then give a total stray light error in the order 0.1% of the average signal generated at the detector, for the visible band. Again there is a potentially serious impact on performance over non-uniform scenes. The specified bright scene will generate wavelength-averaged errors in the order 0.02% of the bright-scene radiance. However, this corresponds to an error of 0.4% in terms of the minimum radiance, as an average for short-wavelength visible radiation. The worst-case scene radiance errors will be larger, because the detector sensitivity is not spectrally flat:- larger errors will be generated on detector elements intended to receive wavelengths for which they have low sensitivity, due to stray radiation at wavelengths for which they have higher sensitivity. Errors in the order 1% may be produced for near-ir bands in the VNIR range Stray light error summary Table gives a summary of stray-light as a percentage of a uniform scene radiance, and also errors in terms of performance over non-uniform scenes as now specified. Contribution Fraction of average radiance Performance over nonuniform scenes Telescope scatter 0.1% (taking Bo = 10-5 ) 0.6% Spectrometer scatter 0.1% (taking Bo = 10-5 ) 0.4% + Diffraction 0.2% at 600nm 1% Table Summary of estimated stray light contributions Note that in the case of spectrometer (out-of-band stray light) errors, the scene radiance errors will be modified by non-uniform scene spectral radiances and non-uniform detector spectral sensitivities. Worst-case scene radiances errors will be larger than the percentages given above. Qualitative comparison of diffraction and scatter effects The above estimates appear to show that diffraction is more serious than scatter, on moderately optimistic assumptions about scatter. However, diffraction effects may be considered less serious than surface scatter effects of similar magnitude, since diffraction is highly predictable, unlikely to change in flight, and associated with small scene areas. The scene area, on which the error depends, will mostly be scanned by the instrument, so that correction of out-of-field errors due to diffraction errors is in principle feasible by deconvolution of data, using a fixed algorithm. Diffraction in the spectrometer may be treated as an effective extension of the spectral response curves to include long tails Detection system errors Uncertainties in response of the detection system will include some of the following: long term changes in gain, 30 March 2001 COMMERCIAL IN CONFIDENCE Page 33 of 245

34 long-term changes in response non-linearity, including changes in relative response of separate gain stages, long-term and short-term changes in dark signal levels, including spatial nonuniformity, long-term and short-term changes in electronics offsets, varying with gain settings, CCD detector smear (due to collection of signal during charge transfer), Long-term in this context means changes over periods longer than one orbit period, including particularly effects of: contamination, space radiation and through-life temperature changes. Short-term changes are significant over periods of less than one orbit we are particularly concerned with temperature changes due to operation of the detection system and due to orbital variations in radiant heat exchanges Linearity and differential linearity changes The present specification for absolute accuracy of PRISM is 2%. This may be taken to imply that linearity errors should be less than 1%. The present budget for random noise, including both spatial and temporal noise contributions, is typically 0.5% rms in the VNIR region. Pixel-to-pixel variations in linearity errors will contribute to this budget, and should therefore preferably be <0.25% rms. The radiometric resolution budget is more relaxed for the SWIR band, so that the rms variations in linearity error may be up to 0.5%. At present there is no indication that VNIR or SWIR detectors will show significant linearity changes. However, so far as we know, there have been no measurements of long-term linearity changes, in detection systems of the kinds likely to be used in PRISM, related to temperature, space radiation or other ageing effects. The PRISM development will preferable include either:! qualification of detection systems with respect to long-term linearity changes, or! an in-flight measurement to provide at least a check on linearity changes Electronics offsets Offset signals, introduced mainly in analogue electronics, may show significant variations due to changes in temperatures of components. In general, the changes will be different for different gain settings. Offset levels will preferably be monitored, at each gain setting in current use, by reading out detector elements that generate zero signal levels Dark signal Temperature-related changes in detector dark signal levels can in principle introduce significant errors. The PRISM mission requires control particularly on differential errors 30 March 2001 COMMERCIAL IN CONFIDENCE Page 34 of 245

35 between images in a set recorded over a period of order 400 seconds. Dark signal nonuniformity is also a potentially serious concern, introducing fixed pattern noise that has effects particularly on spatial radiometric accuracy. Non-uniformity will also change with temperature. Dark signal levels are modified, on a pixel level, by the effects of space radiation. Over one year in flight, this will typically be expected to change average dark signal levels by order of 1nA.cm -2 at 300K. Rms non-uniformity in dark signal level will be expected to change by a similar magnitude. This will produce changes in the order 1000 electrons per element-read, which are potentially significant in terms of absolute accuracy and spatial radiometric accuracy. The effects can be reduced by cooling the detectors, but this will not necessarily be considered desirable for the VNIR detector. Unless the detectors are cooled such that dark signal levels can be ignored, it is likely that dark levels will be regularly monitored in flight. The characterisation exercises will probably include: measurement of complete dark scenes (using an opaque area of filter wheel, in the present baseline) to characterise dark signal non-uniformity and absolute average levels, and recording of masked pixels with each image and calibration data set (including dark scenes) to characterise short and medium-term changes in average dark signal level. Complete dark scenes will be required critically to capture the effects of radiation damage, and for this purpose may be required at intervals in the order days to weeks. The effects of dark level, dark level drift and dark-level non-uniformity are very dependent on detailed design particularly on the selected detector temperatures. If very low temperatures are finally used, it may be possible to make some savings in complexity of the dark level characterisation process. However, dark level characterisation is generally fairly easy, compared with absolute response (gain) measurement, requiring no very expensive or heavy space hardware. The tendency may be to use frequent dark level measurements (with calibration on ground) to relax budgets for thermal control Smear Smear is a special problem in operation of frame-transfer CCDs. In these devices, signals generated in the image area are transferred down columns, at the end of each frame period, into the storage area, by transferring the charge between row-electrodes. Each element signal arriving in the storage zone is produced mainly by light falling on the associated image area, during most of the frame period. However, the image area of the CCD remains illuminated during the frame transfer period (since no fast shutter mechanism is included), so that each element signal also includes an error generated by light falling on the whole column length. The frame transfer period will typically be a few percent of the useful integration time, so that the error is typically a few percent of the average spectral radiance over the sensitive band of 30 March 2001 COMMERCIAL IN CONFIDENCE Page 35 of 245

36 the CCD. However, the error is weighted by the spectral sensitivity of the detector, and will be relatively severe for the IR spectral region, where the useful signal levels are low. It will be necessary to characterise the smear error, for every frame, by recording a smear band - one or more CCD rows that are in the image zone of the CCD, but outside the area that nominally receives scene radiation. The smear band may be a shielded area. However, if it is unshielded it may also be used to measure out-of-band stray light Thermal background signals In the case of the SWIR spectrometer channel, it may be found necessary, depending on detailed design of the instrument, to calibrate data for offset errors due to thermal background radiation. We are mainly concerned with thermal radiation generated by warm structures and optics inside the SWIR spectrometer (or the combined SWIR/VNIR spectrometer). At 300K, blackbody thermal radiation is W.m -2.sr -1.µm -1 at 2.5µm, rising to W.m -2.sr -1.µm -1 at 3.0µm. The detector bandwidth will preferably be cut above the nominal maximum wavelength (by material composition and/or a cold filter). However, the detector could receive background radiation at a spectrally-integrated radiance in excess of W.m -2.sr -1. This should be compared with a useful scene radiance level, at long SWIR wavelengths, of about 0.02 W.m -2.sr -1 integrated over a 10nm nominal waveband. The useful radiance will be confined to the nominal aperture of the optics. If the background radiation reaches the detector only within the solid angle defined by the optical aperture, the background signal will be in the region of 5% of the typical scene signal. But it is likely that the detector will also receive radiation from warm structure outside the optics aperture, since there is no obvious location for a cold stop in the present baseline design. Unless the entrance slit (or the whole spectrometer) is cooled, the background radiation may even exceed the useful signal levels at long wavelengths. In any case, it may be considered necessary to perform an in-flight characterisation of the offset due to background radiation, unless the spectrometer temperature is actively controlled. The measurements can probably be very infrequent, since temperature changes in the spectrometer will be small and slow Movements due to vibration and temperature-change Changes in optics and focal plane assemblies can in principle affect: positions of images on detectors focus of images on detectors These changes will respectively affect wavelength and waveband calibration: shift of the detector with respect to the image (produced either by optics or FPA changes) will shift the mid-wavelength on each element and 30 March 2001 COMMERCIAL IN CONFIDENCE Page 36 of 245

37 change of focus will spread (or sometimes compress) the entrance-slit image associated with each wavelength, increasing (or reducing) the spectral waveband on each detector pixel. Tolerances on movements of the dispersed image with respect to the detector are fairly severe. A relative lateral movement of only about 0.002mm will produce a wavelength shift of 1nm, at the lowest spectral resolution. Applying a simple geometrical model, a 0.01mm focus shift would produce a waveband change of 1nm. (Close to best-focus, the system will be less sensitive. However, it may be difficult to design and construct the system such that all wavelengths and field points will be near the best focus.) Realistic defocus and lateral shift errors are very difficult to predict, since they are dependent on detailed methods of optical and mechanical design and detailed methods of manufacture. Temperature-related changes of focus can probably be made very small by suitable choices of mirror and structure materials. However, the refractive index change of fused-quartz prisms with temperature will introduce a wavelength shift typically in the region of 1nm.K -1, unless this shift is compensated by a more complex structure design. The main concerns are associated with:! long-term stability of structures, at levels in the order and mm, and! movements due to launch vibration. It will probably be considered necessary to include an in-flight characterisation for wavelength. It may be considered necessary to include a simple control on the dispersed image position on the spectrometer, in the dispersion direction, to stabilise wavelength calibration through the instrument life. There may also be a case for in-flight characterisation of wavebands (or defocus in the spectrometer). However, waveband measurements are more difficult, and may be avoided by qualification of the spectrometer system for stability in the relevant respects. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 37 of 245

38 3 IN-FLIGHT CHARACTERISATION METHODS Calibration of data generated by the PRISM instrument will be needed to correct for errors introduced by the instrument. This part of data calibration must be based on knowledge of the instrument response functions, based on pre-flight and in-flight characterisation of the instrument. On-board hardware required for in-flight characterisation of the instrument is expected to add significantly to the complexity and size of the instrument, and it will therefore contribute a significant fraction of the mission costs, including development, construction, testing and launch. An important aim of the present study is to decide whether the costs of inflight characterisation, related particularly to the complexity and size of the on-board characterisation hardware, can reasonably be reduced. In this chapter, we discus methods that have been suggested for in-flight characterisation of the PRISM instrument, in the hyperspectral bands from 450nm to 2350nm, to meet the radiometric requirements discussed in Chapter DARK SIGNAL AND OTHER OFFSET MEASUREMENTS Full-frame at zero radiance In general, dark current levels will vary between detector elements. A dark level characterisation procedure will therefore include recording of scenes at zero radiance, to record the pattern of dark signals over the whole detector areas that are in use. Dark signal data (possibly with some adjustments discussed section below) will be subtracted from all digitised data collected from bright fields (including bright-field calibration data), in the first step of data calibration. Full-frame dark signal measurements will of course be included in pre-flight characterisation. However, dark currents are altered, at the element level, by the effects of space radiation, so that in-flight measurements are also likely to be necessary. The pattern of dark signals may alter significantly over periods of days, so that it may for example be found desirable to update the full-frame dark-signal measurements on a weekly basis (at least) during flight. The measurements must be made for every different configuration of the detection system (selection of spectral bands, integration times, gain settings etc.) that is used to image Earth. There are several ways of providing a zero-radiance scene for the solar bands, including: (a) (b) (c) (d) use of a filter wheel (as a shutter), viewing Earth on the dark side of the orbit, viewing dark space, viewing a black body (that is likely to required for absolute response measurement in the thermal bands). The present baseline design for PRISM includes a pointing mirror that can be used to view either a black body or space (or of course dark Earth), so that any of these views can be selected as a matter of convenience when operations are planned in detail. In fact, the 30 March 2001 COMMERCIAL IN CONFIDENCE Page 38 of 245

39 present baseline method is to use the pointing mirror to view the bright-field calibration source a full-aperture diffuser when the diffuser is covered by an opaque area of filter wheel (and therefore dark). Response characterisation for the thermal channels will require views of cold space and at least one black body. These views may also provide convenient opportunities to carry out fullframe dark level measurements for the solar bands. An option to view dark Earth may also be considered fairly easy, requiring no exceptional pointing or platform rotation, (though there may perhaps be a preference to minimise instrument power consumption on the dark sides of orbits). If a black-body source at 300K is used as a dark reference, this would produce a radiance of about W.sr -1.m -2 over a 10nm spectral waveband at 2.35µm wavelength. The shuttered diffuser will produce the same error, if it is surrounded by structures at 300K. This error (doubled for a source at 310K) is not quite negligible compared with the typical radiance given by ESA for the long-wave end of the SWIR band about 0.02 W.sr -1.m -2 over a 10nm waveband. There is a marginal case for preferring cold space as the dark-field source. Alternatively, the black body may be preferred, since its temperature will be monitored Dark signal and electronics offset drifts Dark signal levels will generally be expected to drift, due to changes in the temperatures of detectors and analogue electronics up to A-to-D converters. Changes in the orbital average will be very slow, but there may conceivably be significant changes within the orbit period. Relatively rapid temperature changes may be generated in detectors when they are switched on, so that continuous operation, or a warm-up period before data recording, may be considered. Analysis, preferably supported by experiments, should be performed to decide whether there will be significant drifts in dark signal levels, between full-frame dark signal measurements. If so, it may be reasonable simply to increase the frequency of full-field dark level measurements, for example by more frequent views of the covered diffuser or a black body. However, corrections can be made for dark signal drift without the possible inconvenience of making frequent reference to a dark source outside the main instrument. For example, CCDs normally include masked detector elements at the ends of each row in the image region. Signals from these masked pixels (with corrections for electronics offsets) will provide a measure of average detector dark signal, in the time frame of each full frame measurement. Area array detectors can also include lead-in pixels at the end of the output serial register, which contain essentially zero signal. Digitised signals from these elements can be used to provide a measure of the electronics offset, for each image frame and for each gain setting in use. Dark signal and offsets can therefore be corrected for example by: (a) (b) Recording and averaging the lead-in pixel signals for each gain setting, with each full frame of image and calibration data, to provide electronics offsets, Subtracting the electronics offsets from all data points in each full frame of data, including masked pixel data, 30 March 2001 COMMERCIAL IN CONFIDENCE Page 39 of 245

40 (c) (d) Recording and averaging the (offset corrected) masked-pixel signals, with each full frame of image and calibration data, to provide average detector dark signal data, For each (offset corrected) image frame: (i) (ii) (iii) taking the ratio of average dark signals between the image frame and the last full dark signal frame, multiplying the full frame of dark field data by this ratio and subtracting the corrected dark-field frame from the image frame. The same correction should be made for each frame of bright-field calibration data. However, note that the procedure may be much simpler if it can be shown that some error components will be very small in practice (for example because the detectors are cooled to make all variations negligible). Other tactics are feasible, and should of course be considered in detailed trade-offs. For example, detector temperatures may be measured as an indication of changes in (average) dark-signal levels, rather than direct measurements at masked pixels. The dark level calibration can in principle be performed on board, but may also be performed on ground, using calibration data (full dark fields, masked pixel signals etc.) transmitted with the Earth image data Background radiation, out-of-band stray light and smear Full-frame dark field measurements will normally include the effects of thermal background radiation reaching the SWIR detector from warm structure in the spectrometer. Infrequent measurements are likely to be adequate for this correction, since the spectrometer temperature is likely to be very stable. Smear error produced in CCDs will be measured for each frame of data by recording a smear band a set of CCD rows in the image zone of the CCD but not in the area actually occupied by the useful image. Smear signal will be subtracted from all other signals in every frame of data, after corrections for electronic offset and dark current, and allowing for different gain settings and numbers of CCD rows binned. If the smear band is unshielded, it will record signals due to out-of-band stray light (essentially stray light generated in the spectrometer), as well as smear. In this case, smear correction can be made to include a partial correction for out-of-band stray light error. Using a single smear band, it will be difficult to distinguish between the effects of smear and the effects of stray light. In detailed trades, it will be desirable to consider whether two smear bands should be used one close to the spectrum image and the other remote or actually shielded. The difference between signals generated in these two bands would provide a crude indication of the true stray light error. This would probably not allow an accurate correction for stray light errors, but could be useful as a measure of any changes in the instrument stray light function between pre-flight characterisation and flight. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 40 of 245

41 A similar technique may be applied to the SWIR channel. Although the SWIR detector will probably not generate smear, signals from one or two rows outside the actual image area can be used to indicate stray light Requirements for dark signal and offset corrections It will of course be essential to perform detailed analyses and to take appropriate measures to correct for significant effects. The measures may include adjustments in design of the main instrument for example detector cooling as well as appropriate in-flight characterisation sub-systems. However, in general, the necessary in-flight characterisations for dark signal and other offset errors are unlikely to be severe cost drivers for instrument development, construction and operation. 3.2 ABSOLUTE RESPONSE AND FLAT-FIELDING In-flight characterisation for absolute response (gain) is necessary mainly because of likely changes in optics transmission and possible changes in response of the detection system. Response is expected to change very slowly in flight, so that it may be reasonable, after an initial commissioning period, to repeat absolute characterisation at intervals of weeks or months. However, at least during an initial period in flight, it will be desirable to have a capability to measure response more frequently. The current ESA requirements for the PRISM instrument include stray light errors in the budget for absolute accuracy, so that the required accuracy for absolute response characterisation in flight is in effect less than the total budget of ±2%. Measurement of absolute response in flight requires essentially that the instrument shall be presented with two or more sources of known radiance, while calibration data are recorded. One of the sources will normally be a dark reference space, dark Earth, or an on-board black body or shuttered diffuser as outlined in section above. At least one other source must be at a higher known radiance we call this a bright-field source. The bright field source usually (but not always) fills the field of the instrument with a uniform radiance. It can therefore often be used to measure response non-uniformities across the field, in each recorded spectral band. This is called flat-fielding. In past developments of space-based radiometers, it has been found very difficult to provide a bright-field source for the solar spectral region, that has radiance known to adequate accuracy, at a high confidence level. In-flight measurement of absolute response is therefore expected to be a significant cost driver. A main objective of the present project is to examine the needs for absolute accuracy, and to re-examine the methods for measurement of absolute response in flight. Methods that have been proposed are described in the following sections, with comments on their status and likely performance, and on their relative impacts on the space mission. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 41 of 245

42 3.2.1 Sun-illuminated reflecting diffusers The current baseline proposal for PRISM is to use a sun-illuminated diffuser, that is protected by an opaque area of filter wheel when not in use, and viewed via the pointing/calibration mirror. The system is shown schematically in figure A second diffuser is provisionally proposed this will be used less frequently than the first to detect changes due to sunexposure. Both diffusers will have long baffles. The diffusers will be reflecting, and are likely to be made using Spectralon. main instrument diffuser filter filter wheel aperture sunlight scan/calibration mirror nadir view Figure In-flight radiometric characterisation using a sun-illuminated diffuser and a filter wheel schematic Large sun-illuminated diffusers are the most frequently-proposed bright-field sources for absolute response measurement in the solar bands. The basic advantages of the method are:! The diffuser fills the optical aperture of the instrument. This minimises errors due to nonuniform transmission of the optics across the optical aperture. Non-uniform transmission is not a trivial concern. In imaging spectrometers, diffraction at the entrance slit introduces significant non-uniformity, and unpredictable non-uniformity can in principle be produced by contamination of the optics. Very small light sources can produce Schleiren effects due to very small imperfections in surface polish.! The diffuser fills the field of the instrument. This allows the diffuser to be used for flatfielding. Wide-field illumination of the aperture may also generate stray light effects that are similar to those produced by the real world scene, providing some partial correction for stray light effects. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 42 of 245

43 ! Using sun-illumination, the sub-system requires no power, except for movements needed to place the diffuser in the field of the instrument! The method now has some useful heritage. Substantial work has been done particularly to improve the characteristics of Spectralon diffusers. Basic problems in use of large sun-illuminated diffusers are: The characterisation subsystem adds significantly to the overall system size and complexity: - The diffuser must be substantially larger than the optical aperture, if it is viewed at an oblique angle. - Size and complexity are increased by a second diffuser. - An added movement is generally required to allow both viewing and protection of the diffuser. - Errors in radiance of the reflecting diffuser can be produced by stray light received from any direction, potentially requiring long baffles on the diffuserillumination path. The reflectance of the diffusers may degrade after pre-flight calibration. This risk can be reduced by rigorous control of the diffuser manufacture, conditioning and integration and by protection pre-flight and through launch. The use of second diffuser is intended to monitor degradation due to in-flight exposure. However, the on-board system includes no means to check for unpredicted common-mode degradations of the two diffusers. Relatively minor concerns include: thermal control requirements associated with large apertures, and static charge build-up on the diffuser. Considering only the predictable errors, the method can offer absolute radiometric accuracy in the region of ±2% (even allowing a fraction of this budget for stray light). However, it would be desirable to provide an independent measurement on the diffuser reflectance or radiance in flight, to check for significant degradations due to unpredicted effects, and improve confidence in the ±2% accuracy level. The second diffuser provides a check of partial validity, but is clearly not ideal. One option is to use vicarious calibration. There are methods (some outlined below in sections and ) which would give higher confidence levels. These alternatives do not necessarily demand a substantial increase in complexity or system bulk, but they generally involve some new development. In further developments of hyperspectral radiometers, it will be desirable to investigate whether the cost/performance profile of the in-flight characterisation system can be improved Other diffuser options Other diffuser options, with brief summaries of advantages and disadvantages, are outlined below. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 43 of 245

44 Lamp illumination of a diffuser Tungsten filament lamps have been used to illuminate diffusers, as absolute radiance sources. This appears to be a fairly attractive option in some respects: lamps are routinely used on ground as secondary standards of radiant intensity (and with diffusers for radiance). Lamps can be used at any convenient points in the orbit, while the sun can generally be used only when the satellite is at an appropriate position. However, lamps have several disadvantages:! It is difficult to ensure an accurate prediction of lamp output in vacuum and zero gravity,! High lamp powers are required to provide adequate illumination levels on full-aperture diffusers,! Incandescent lamps give low spectral intensity at short wavelengths. Particularly for an instrument like PRISM that must satisfy extreme pointing requirements, use of the sun as a source is likely to be fairly easy, so that the possible convenience of a lamp is not needed. The sun will probably remain the preferred illumination source for diffusers Transmitting diffusers Reflecting diffusers have usually been preferred for space instruments for three reasons:! They give much more uniform polar distributions than do transmitting diffusers, which provides easier flat-fielding.! They can be used at a wide range of angles of incidence and reflectance. This flexibility has often been necessary to make use of sunlight at feasible platform attitudes. (For transmitting diffusers, it is very desirable for the transmitted beam to be in line with the incident beam, in a straight-through geometry.)! Reflecting diffusers are commonly preferred for radiometric work on ground, mainly because they provide more uniform polar distribution than transmitting diffusers. More work has therefore been done on reflecting diffusers, giving better heritage. There are some reasons for suggesting that transmitting diffusers should be considered more seriously for radiometers, like PRISM, that are intended mainly for land measurements at moderate spatial resolution:! The field angles of moderate- and high-resolution radiometers are small, so that a uniform polar distribution is needed only over a small angle, which can be provided by either reflecting or transmitting diffusers. Residual non-uniformity can in any case be corrected using pre-flight characterisation.! There is a trend, of which PRISM is a good example, towards use of platforms that are small, dedicated and agile. It will become easier to adjust the platform attitude, in calibration mode, to provide the straight-through geometry preferred for transmitting diffusers. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 44 of 245

45 ! Transmitting diffusers can occupy less space, because the straight-through geometry is more compact.! Transmitting diffusers can be simpler physical structures, that are less likely to degrade. (Reflecting diffusers are usually porous structures that have presented problems because they adsorb volatile materials.)! Transmitting diffusers can be less sensitive to stray light Diffuser monitors There will always be a concern over the stability of diffusers, and possibilities of contamination, during the long period between pre-flight calibration and use in orbit. Different potential problems may occur in periods of pre-launch storage, platform integration, phases of launch and life in orbit. Several types of methods, outlined below, have been suggested for monitoring the diffuser reflectance or radiance in flight Detector-based methods There are two basic types of detector-based monitor for on-board diffusers: simple filter radiometers, that point at the illuminated diffuser and record a signal, that can be compared with the signal measured in pre-flight calibration, and ratioing radiometers, that point alternately at the sun-illuminated diffuser and directly at the sun, and measure the ratio between incident irradiance and reflected radiance (effectively measuring the diffuser reflectance in situ). Both types of radiometer include a set of small detectors, filtered to measure radiance or reflectance in different parts of the solar spectrum. A simple monitoring system is indicated schematically in figure The radiometers can in principle be fairly compact, but one of the objections to their use has been that they add significantly to the system complexity. The simple filter radiometer is also open essentially to the same objection as the diffuser itself: it may degrade in flight due to unpredicted events for example some contamination of the filter or front window. The ratioing radiometers, as described for example by Slater and Palmer (SPIE Vol. 1493, p100, 1991), are more certain to provide a valid check on diffuser reflectance, because they are not dependent on avoiding all changes in the radiometer detection systems and optics. However, ratioing radiometers require an additional movement that allows the same optics and detectors to be pointed at the sun and the diffuser. Some variants on the ratioing radiometer idea have been suggested. Kriebel and Reynolds (ESA Journal 1984, Vol. 4) have suggested that a radiometer could be used to compare direct sunlight with Earth radiance, allowing the main instrument to be calibrated, using the same area of Earth, without a diffuser. Sira suggested adding a small telescope to the moving optics, to reduce the signal difference between diffuser (or Earth) and direct-sun views. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 45 of 245

46 main instrument diffuser sunlight filter radiometer scan/calibration mirror nadir view Figure Full-aperture diffuser with a detector-based monitor Calorific method Sira have suggested that the diffuser reflectance could be monitored indirectly by measuring the temperature of the diffuser during a period in which it receives sunlight. The power absorbed by the diffuser is a direct indication of any loss of reflectance. One problem in this approach is that the measurement is not sensitive to spectral variations in reflectance (or absorption), unless the incident light is filtered to provide a range of wavelengths. However, a very simple version of the method could be used to prove that there has been no change in absorption of the diffuser since pre-flight calibration Ratioing methods using two diffusers The sun-ratioing radiometer, outlined in section , gives the true reflectance of a diffuser, as the ratio of measurements on reflected sunlight and incident sunlight. The method offers greatly improved confidence in the absolute response characterisation provided by the diffuser. But the need for an added radiometer has generally been considered to introduce too much complexity, as noted above. The sun-ratioing concept may be more acceptable if the two measurements on the diffuser on incident and reflected (or transmitted) sunlight can be made using only the optics, detectors, electronics and data stream of the main instrument. The immediate problem is that the main instrument cannot measure direct sunlight, because the solar radiance is outside the instrument dynamic range, typically by 4 orders of magnitude. However, if diffused sunlight is used to illuminate the diffuser, the main instrument may be used to make both measurements the problem can be solved by adding a second diffuser to the on-board configuration. In general, the procedure is: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 46 of 245

47 (a) point the main instrument at diffuser A, with A sun-illuminated, and record signals, (b) point the main instrument at diffuser B, with B illuminated only by diffuse radiation from A, which is again sun-illuminated, and record signals, (c) take the ratio of the two sets of main-instrument signals, recorded in these two conditions, to give the diffuse reflectance (or transmission) of diffuser B, (d) calibrate the main instrument with diffuser B in direct sun-illumination (but with A not sunilluminated). This basic concept is investigated and discussed further in Appendix C On-board alternatives to diffusers A large number of different possible approaches have been considered to measurement of absolute response in flight. Most ideas make use of the sun, as a free source of known radiance or irradiance. (In fact the spectral irradiance of the sun is not at present known to sufficient accuracy to provide absolute calibration, in terms of radiance, to ±2%. The general assumption is that knowledge of solar irradiance will improve, so that errors due to this uncertainty can be ignored. Alternatively, the space instrument can be treated as a reflectometer measuring the reflectance of Earth rather than its radiance. In this case, it is unnecessary to know the solar irradiance.) Sieve plates and small lenses A sieve (or aperture) plate is normally an opaque plate with very small holes, through which the instrument images the sun directly onto the image plane. A sieve plate with few holes (or only one) may be considered to represent the ultimate in simplicity. One disadvantage is that the field of the radiometer will not usually be filled, since the sun subtense is too small a sieve plate can be used for absolute response measurements, but a diffuser will also be needed for flat fielding. Small lenses may also be set in a large opaque plate, through which the main instrument is pointed more or less directly at the sun. The effect of the small lenses is in some respects very similar to that of the aperture plate providing one or many small areas of illumination across the optical aperture of the main instrument. There may be a marginal preference for small lenses, because they fill the instrument field. In this respect they may be considered to act as a transmitting diffuser, but with some advantages and disadvantages compared with a conventional opal or ground quartz diffuser. These devices in effect sample only a very small part of the optical aperture. Because the solar radiance is about five orders of magnitude above the saturation level of the instrument, the total area of small holes in an aperture plate can be only around 1/100,000 of the area of the instrument aperture. For the PRISM instrument, a single hole will be around 0.5mm in diameter; if more holes are used, they must be smaller. In the case of small lenses, the total 30 March 2001 COMMERCIAL IN CONFIDENCE Page 47 of 245

48 area of sun-images formed by the lenses will be about 0.5mm diameter, giving a similar capability to sample the instrument response over the aperture. This under-sampling of the aperture reduces the credibility of the absolute calibration that is provided in flight. Non-uniform response across the aperture will introduce errors if it varies after pre-flight calibration, due to either particulate or non-uniform molecular contamination. There are possible problems of contamination of small apertures (discovered in use of small apertures in ground-based radiometry). Lenses are also of course susceptible to contamination. However, use of small apertures and lenses can be considered to have some significant advantages. The problem of under-sampling can be reduced by moving the apertures or lenses across the optics aperture. The movement adds complexity, but may be compared with the movement required to deploy or cover a full-aperture diffuser. The advantages are:! Without a movement, the systems can be extremely small and simple.! With a movement, the arrangements remain fairly small compared with full-aperture diffuser systems, may sample enough of the optical aperture, and can more readily be made self-checking for effects of contamination, without additional detectors Full-aperture attenuator alternatives to diffuser An image of the sun can be used as a radiance standard, provided that the brightness of the image is reduced by at least about 4 orders of magnitude, to bring it into the dynamic range of the PRISM instrument. Effective attenuation can be produced, as noted above, by using only a very small fraction of the instrument aperture. However, if we decide to sample the whole aperture, it is still possible to use a direct sun image, provided that it passes through a fullaperture filter or is reflected from a low-reflectance mirror. The filter or mirror is not an attractive strategy in some respects. It is not obvious that it could be more stable that a diffuser. Also the direct sun image is less satisfactory than diffused sunlight because it does not fill the instrument field (for flat-fielding). However, filters and mirrors offer some possibilities for sun-ratioing techniques, using only the optics and detectors of the main instrument. These ratioing methods are discussed in Appendix C Vicarious calibration Vicarious calibration has usually meant use of targets on Earth surface, whose radiance is measured by radiometers on board aircraft or at ground level. A ground site is selected that has good features for radiance prediction:! Uniform reflectance over a large area,! High altitude (to limit the effects of atmosphere),! Flat surface, to limit effects of shading,! Normally very clear skies. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 48 of 245

49 High desert areas have been preferred. Accessibility is desirable, but not necessarily achievable with the more important criteria. The site must usually be prepared. Possible sites selected for absolute and relative radiance calibration of PRISM include: White Sands, USA; La Crau, France; Dunhang, China. The older method, called the reflectance-based method, is based on measurements of the site and local atmosphere made from ground level. The reflectance of the ground is measured, in the time-frame of a satellite overpass, and sun photometers are used to measure the optical properties of the atmosphere. The radiance of the ground area, seen from space, is then computed using a radiation transfer model, and compared with the radiance measured from space. Alternatively, the radiance of the prepared site can be measured from a high-flying aircraft, in the radiance-based method. This offers better accuracy, since the measurement is basically simpler, and is much less dependent on estimation of atmosphere properties (since there is little atmosphere above the aircraft). Vicarious calibration can, at least in principle, provide absolute response characterisation for the PRISM solar bands (and conceivably for thermal bands also). The key advantage of vicarious calibration is that it reduces costs related to the space hardware, though not necessarily costs of the complete mission. Disadvantages of vicarious calibration include the costs of ground preparation and ground/atmosphere measurements or radiometer overflights. Vicarious calibration is a little unreliable, though normally performed in areas selected for good weather. Less frequent measurements may be required over measured sites, if a site of stable radiance can be used on a more frequent basis, to measure only changes. Earth sites that have been suggested are the North African and Saudi Arabian deserts. It has also been suggested that Rayleigh scatter over oceans may provide an absolute reference for the visible band. Other disadvantages of vicarious calibration are: It has limited accuracy at present estimated at ±2% for the radiance method, but worse for the reflectance based method. It does not provide flat-fielding, so that it will probably be desirable to retain at least a diffuser on board the satellite. It is in fact likely that some on-board hardware will be retained, even if vicarious calibration is included in the PRISM mission, to cover some of the deficiencies of the vicarious method. The on-board system will at least provide flat-fielding and relatively frequent measurements. Given that some on-board hardware will be very desirable, it is necessary to consider whether the on-board system should be improved to eliminate the need for vicarious calibration. At present, we would suggest that vicarious calibration carried out with care will always be of value at least as an independent check. Ideally, some elements of both on-board hardware and vicarious calibration should be retained. However, their precise roles are open to debate. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 49 of 245

50 3.2.5 Moon view It has been suggested that a view of the moon could be used in response calibration of the space instrument. The moon is likely to be accessible to PRISM, using the planned pointing capabilities and platform rotations. At present, the spectral radiance of the moon is not sufficiently well-characterised for it to be used as the only source for absolute measurements. However, views of the moon may perhaps be used to monitor changes in instrument response over long periods in flight. The radiance of the moon changes dramatically over the lunar-month period, but may be sufficiently repeatable at a selected phase (probably near full) to allow monthly changes to be monitored. 3.3 LINEARITY MEASUREMENTS Linearity measurements generally require that several different radiant signal levels should reach the detectors. For linearity measurements, it is not essential that the radiant signals should be known to good absolute accuracy it is necessary only that the ratios between the signal levels should be accurately known. There are many possible methods for providing radiant signals in known ratios. The present baseline design for PRISM includes an option to include a sieve plate, on the filter wheel movement, to reduce the sun-illumination of a diffuser. Sira have suggested using multiple small sources switched on separately and in combinations. Other possibilities, which we would now generally prefer, include: variation of integration time while viewing any stable source (for example the absolutecalibration diffuser), a fast-switchable source close to each detector inside the spectrometers, switched on for varying periods within the detector integration time, The internal sources, for both the VNIR and SWIR detectors, could be IREDs (infrared emitting diodes). They can have other uses, including basic function checks during integration, and a back-up in case of failure of the (external) absolute characterisation subsystem. 3.4 WAVELENGTH AND WAVEBAND MEASUREMENTS In-flight calibration for the spectral response functions (SRFs) defined by the sensor will require illumination of the sensor from a source having some distinctive spectral structure that can be detected in analysis of the images formed on the two detectors (VNIR and SWIR). Source options for in-flight characterisation, and related aspects of sensor design, are discussed in detail in Appendix D. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 50 of 245

51 4 SENSITIVITY ANALYSIS The study is concerned essentially with determination of the requirements that should be placed on hyperspectral space instruments like PRISM, including their in-flight characterisation sub-systems, in order to achieve certain accuracies in ground reflectance or ground-leaving radiance data, and hence in higher level data products. However, the spectral composition of solar radiation reaching the space instrument is strongly modified by scatter and absorption in the atmosphere. In order to assess requirements on the space instrument, it is therefore necessary to determine the sensitivity of at-sensor radiances, which are directly measured by the space instrument, to both ground reflectances and to representative atmosphere parameters. This chapter describes the sensitivity analysis. Calibration of data for the effects of atmosphere is essential, and errors in characterisation of the atmosphere limit the accuracy of this calibration. It will be unreasonable to specify instrument performance to achieve product accuracies that are precluded by typical errors in atmosphere characterisation. Thus it is also desirable to compare the errors that will be produced by imperfections in characterisation of the space instrument, with errors produced by uncertainties in some important atmosphere variables. The sensitivity analysis therefore includes the effects of variations in a set of important atmosphere variables. 4.1 STRUCTURE OF THE SENSITIVITY ANALYSIS Ranges of parameters for radiance computations The radiative-transfer model MODTRAN, version 3.7, was used for all computations of the atsensor radiance L for a given set of atmosphere parameters and ground reflectance ρ. Ground reflectance was varied between runs of the code, but for each run the ground reflectance was assumed to be spatially and spectrally uniform. MODTRAN assumes Lambertian reflectance. At-sensor radiance data are computed for the following conditions: (a) (b) (c) (d) (e) 3 nominal observation scenarios and atmosphere conditions, six nominal ground reflectances, nadir viewing (to provide a reference data set for each atmosphere/scenario), small differentials in ground reflectance, at each nominal value, (to provide partial derivatives of at-sensor radiance with respect to ground reflectance), moderate variations in atmosphere conditions: height, water vapour and visibility, at three selected ground reflectance values and for three atmospheres/scenarios, repeat of (a), (b) and (c) for a change of viewing direction to 40 off-nadir along-track, cloud radiance (used to estimate worst-case effects of stray light in the instrument). Results of MODTRAN runs and preliminary analyses of results are described in the following sections 4.2 to March 2001 COMMERCIAL IN CONFIDENCE Page 51 of 245

52 4.1.2 Conversion of radiance data to PRISM spectral bands MODTRAN always computes radiance for equispaced wavenumbers k ( k = 1 cm -1 ) over a user-specified spectral range. MODTRAN also provides a direct conversion of the results for the corresponding wavelengths λ k. Spectral convolution is supported by MODTRAN 3.7 for different sensor models, e.g. convolution by a Gaussian slit function of fixed full width at half maximum (FWHM) for a constant spectral sampling interval. For the main analysis tasks, reported in Chapter 5, the radiance data was spectrally convolved to provide average radiances in the spectral bands that are at present defined for PRISM. These bands are listed in Appendix B. For an investigation of the effects of errors in spectral calibration of the space instrument, the radiance data for the reference conditions (3 atmospheres, nadir viewing) was also convolved with these modified PRISM spectral bands: (i) (ii) each band shift +1nm and 1nm, each band changed in FWHM +1nm and 1nm Additional data available Full radiance data are also recorded at full spectral resolution, and spectrally convolved to a fixed bandwidth with full-width at half maximum (FWHM) of 12nm. Reflectance data, produced by dividing by the solar irradiance/π are also recorded. However, only the radiance data, in PRISM bands, are used in the analyses described in Chapter Fixed atmosphere/observation parameters MODTRAN runs are controlled by a large number of parameters to be specified by the user. Table presents those parameters kept constant for all MODTRAN runs. A detailed description of each parameter is given in the MODTRAN 3.7/4.0 users' manual. Note that MODTRAN internally resets the observer altitude to 100 km a.s.l. since no further atmospheric effects are modelled beyond this altitude. A multiple scattering model is used to account for path radiance contributions in the at-satellite radiance. MODTRAN parameter ITYPE= 3 IEMSCT = 2 IMULT = -1 M1-M6 = 0 MDEF = 1 DIS, NSTR = T8 LSUN, ISUN = T1 Description vertical or slant path to space or ground spectral thermal plus solar radiance mode multiple scattering default atmospheric profiles default heavy species profiles DISORT multiple scattering algorithm using 8 streams reads 1 cm -1 binned solar irradiance scanned with FWHM=1cm -1 Table Fixed MODTRAN parameters 30 March 2001 COMMERCIAL IN CONFIDENCE Page 52 of 245

53 CO2MX = LSUNFL = 4 SOLCON = 0 ISEASN = 0 RAINRT = 0 H1 = 800 IPH = 2 ISOURC = 0 TIME = CO 2 mixing ratio in ppmv Thullier plus corrected Kurucz database are used for solar irradiance default solar constant seasonal aerosol profile determined by MODEL no rain height of observer (sensor) in km a.s.l. MODTRAN integrated phase functions are used extraterrestrial source is the sun 11:20 GMT in decimal hours Table Fixed MODTRAN parameters cont d 4.2 REFERENCE DATA SET At-sensor radiance was computed for three nominal atmospheres and six nominal ground reflectance levels, for the sensor pointing to the nadir. A general description of the three nominal atmospheres is given in table Surface altitude was set to 0 m a.s.l. The resulting 3 6 data sets form a reference for the computation of the differentials with respect to ground reflectance, atmosphere variables and off-nadir pointing. Nominal conditions and ground reflectance values are detailed in Table Nominal atmosphere Day of year Latitude Ground reflectance (%) AT3: tropical atmosphere, rural aerosol extinction, visibility 23 km AM6: mid-latitude summer, rural aerosol extinction, visibility 23 km AA12: subarctic winter, tropospheric aerosol extinction, visibility 50 km 80 (spring equinox) 0 N 2, 6, 10, 20, 40, (summer solstice) 45 N 2, 6, 10, 20, 40, (winter solstice) 60 N 2, 6, 10, 20, 40, 100 Table Nominal atmospheres and ground reflectance levels AT3 and AA12 nominal atmospheres are considered as extremes for incoming solar radiation as well as for atmosphere parameters like air temperature or water vapour. The AT3 nominal atmosphere, however, is considered to be highly relevant for image acquisition due to the large extent of tropical (and subtropical) regions affected by similar radiation and atmosphere conditions. A mid-latitude summer nominal atmosphere was included in the study to investigate the relevance of atmosphere and ground-reflectance errors for the in-flight characterisation strategy of the PRISM instrument for intermediate conditions. Longitude was set to 0 in all cases. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 53 of 245

54 Figure At-satellite radiance at full MODTRAN spectral resolution (1cm-1 unconvolved) for 2%, 6%, 10%, 20%, 40% and 100% ground reflectance, plotted against wavelength - nominal atmosphere AT3, nadir pointing. Figure At-satellite radiance, convolved to nominal PRISM spectral resolution, for 2%, 6%, 10%, 20%, 40% and 100% ground reflectance, plotted against wavelength - nominal atmosphere AT3, nadir pointing. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 54 of 245

55 ` Figure At-satellite Earth reflectance, convolved to nominal PRISM spectral resolution, for 2%, 6%, 10%, 20%, 40% and 100% ground reflectance, plotted against wavelength - nominal atmosphere AT3, nadir pointing. Figures and show the effects on MODTRN radiance data of convolution over the instrument spectral bands. Figure shows radiance data a full spectral resolution (1cm -1 ), while figure shows the same data convolved over the nominal PRISM spectral bands. Figure shows Earth-reflectance for the convolved case. 4.3 DIFFERENTIALS WITH RESPECT TO GROUND REFLECTANCE VARIATIONS FOR NADIR POINTING ANGLE For each of the nominal atmospheres, AT3, AM6 and AA12, MODTRAN runs were performed using ground reflectance values adjusted by +1% and 1% with respect to the values listed in section 4.2. (i.e. at ground reflectance values of 1, 5, 9, 19, 39 and 99%, and 3, 7, 11, 21 and 41%.) This small-difference data is used, in the analysis described in Chapter 5, to infer partial differentials of at-sensor radiance with respect to ground reflectance. In general, we assume that at-sensor radiance varies linearly with ground reflectance, at each wavelength, over relatively small reflectance intervals. This assumption is justified by comparison of the radiance differentials produced by 1% changes in ground reflectance. Some results are presented in figures and for the nominal atmosphere AT3 and for each nominal reflectance level except 100%. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 55 of 245

56 Figure shows the change in apparent Earth reflectance (π.at-sensor radiance/solar irradiance) produced by a +1% change in ground reflectance, for a range of nominal ground reflectance values from 2% to 40%. The Earth reflectance differentials vary with atmosphere absorption and scatter. However, the changes in apparent Earth reflectance are almost independent of the nominal ground reflectance values, which indicates a linear relationship between at-sensor radiance and ground reflectance. There is a noticeable departure from linearity only in the visible range: at short wavelengths, the at-sensor radiance increases more rapidly with ground reflectance, as ground reflectance increases. This effect is due to multiple reflections between the ground and the atmosphere. Figure Differences in at-satellite reflectance due to 1% increase in ground reflectance at nominal ground reflectance levels 2%, 6%, 10%, 20% and 40%, plotted against wavelength (nominal atmosphere AT3, nadir pointing angle). Figure Ratio of absolute values of differentials for ground reflectance (-)scenarios and (+)scenarios for 2% (Τ), 6% ( ), 10% ( ), 20% ( ) and 40% (+) ground reflectance plotted against wavelength (nominal atmosphere AT3, nadir pointing angle). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 56 of 245

57 Figure shows the ratio of radiance changes produced by: (a) -1% change in ground reflectance, called the (-)scenario, and (b) +1% change in ground reflectance, called the (+)scenario. Departures from unity indicate non-linearities between at-sensor radiance and ground reflectance, over the ±1% ground-reflectance range, at each nominal reflectance level. Linearity over this range, as predicted by MODTRAN, appears to be very good. A 0.5% departure from linearity at short wavelengths may be associated with Rayleigh scatter, but the reason for it is unclear. 4.4 DIFFERENTIALS WITH RESPECT TO ATMOSPHERE PARAMETER VARIATIONS Table presents the three atmosphere parameters that were varied to compute the propagation of variations in atmosphere parameters to at-satellite radiance/reflectance: water vapour, visibility and altitude. These three atmosphere variables were selected since they significantly influence at-satellite radiance/reflectance in the studied spectral range. A detailed description of the parameters is given in the MODTRAN 3.7/4.0 users' manual. The parameter values used in this study cover typical ranges of realistic conditions for image acquisition by space-borne systems like PRISM. MODTRAN runs were performed for three nominal ground reflectance levels (2%, 10% and 40%) and for the three nominal atmospheres (AT3, AM6, AA12). Vertical water vapour column usually varies by ±20% or even more with respect to a representative value for the selected nominal atmosphere. This value is used as a representation characterisation error, in the analysis described below. However, typical real errors may be reduced to about ±10% by analysis of the instrument data in selected bands. Visibility varies over wide ranges, but a visibility error of ±3 km for tropical and mid-latitudinal rural regions is considered as a realistic case, at a nominal visibility of 23km, when measurements are employed. Visibility values of 5 and 45 km, as well as the AA12 nominal atmosphere in general, are used only as extreme cases to show the range of variations in the at-satellite values due to visibility variations, and hence, these runs are not of direct interest for the sensitivity study. Effects of errors in Earth-surface altitude above sea level have been computed for a wide range of altitude-error values, from 500m to 4km. Such large altitude errors may be accepted in sensing of mountainous regions. Since radiative-transfer models applied for atmospheric correction of satellite imagery are, in most cases, not spatially distributed models, an average value for surface altitude is often used for the whole study region. Much smaller errors will be associated with sensing of level terrain, which is more typical of land-mission targets. Effects of smaller errors are generally inferred by scaling. (Computation for relatively large errors, in altitude and other parameters, is of some value in reducing numerical errors.) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 57 of 245

58 Parameter Description Reference value Variations H2OSTR vertical water vapour column scaling factor 1 0.8, 1.2 VIS visibility, meteorological range (km) 23 (AT3, AM6), 5, 20, 26, (AA12) GNDALT surface altitude (km a.s.l.) 0 0.5, 1, 2, 4 Table Atmosphere parameter variations Figure Differences R in at-satellite reflectance produced by changes in atmosphere water vapour from 100% to 80% of nominal, and 100% to 120% of nominal. Top curves for 2% ground reflectance, middle curves for 10% ground reflectance, bottom curves for 40% ground reflectance. Nominal atmosphere AT3, nadir pointing angle. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 58 of 245

59 Figure shows differences in at-satellite reflectance values resulting from different vertical water vapour columns. Each plot shows the change due (a) to a decrease in water vapour from 100% to 80% of nominal ((-)scenario), and (b) to an increase in water vapour from 100% to 120% of nominal ((+)scenario). The three plots are from ground reflectance values of 2%, 10% and 40%. The symmetry of The 80% (H2OSTR 0.8) value for the vertical water vapour column forms the, while the 120% (H2OSTR 1.2) value is called the. There are significant variations in reflectance, measured from space, in both the VNIR and SWIR bands. The symmetry of the (-)scenario and (+) scenario plots shows fairly good linearity in reflectance and radiance variations with respect to water vapour column content, over the ranges tested. Figure shows the changes in at-satellite reflectance due to changes in visibility from 23km (nominal) respectively to 5, 20, 26 and 45 km, for three ground reflectance levels (2, 10 and 40%). Sensitivity of at-satellite radiance and reflectance to visibility variations decreases strongly with increasing wavelengths. There is of course low sensitivity around absorption bands. The effects are inverted between low ground-reflectance values and high groundreflectance values. At high ground reflectance, the dominant effect of reduced visibility is reduction in the ground-reflected radiation reaching the satellite. At low ground reflectance, the dominant effect of reduced visibility is an increase in radiance scattered from the atmosphere. The effects on at-satellite radiance and reflectance are of course non-linear with respect to visibility expressed in terms of range. The influence of different surface altitudes on at-satellite reflectance is shown in figure Since vertical atmosphere column is reduced with increasing surface altitude, all atmospheric absorption and scattering processes are affected by surface altitude variations. At low ground reflectance values, the most noticeable effect of increased surface altitude is a reduction in the Rayleigh scatter contribution of the atmosphere, which affects mainly short wavelengths. At high ground reflectances, increased altitude reduces the effects of atmosphere absorption and scatter across the whole VNIR/SWIR band. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 59 of 245

60 Figure Changes R in at-satellite reflectance due to visibility changes from 23km (nominal) to 5, 20, 26 and 45 km. Top curves for 2% ground reflectance, middle curves for 10% ground reflectance, bottom curves for 40% ground reflectance. Nominal atmosphere AT3, nadir pointing angle. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 60 of 245

61 Figure Changes R in at-satellite reflectance due to surface altitude changes from 0 km a.s.l. (nominal) respectively to 500, 1000, 2000 and 4000 m a.s.l. Top curves for 2% ground reflectance, middle curves for 10% ground reflectance, bottom curves for 40% ground reflectance. Nominal atmosphere AT3, nadir pointing angle. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 61 of 245

62 4.5 DIFFERENTIALS WITH RESPECT TO GROUND REFLECTANCE VARIATIONS - 40 OFF-NADIR MODTRAN parameter PHI (zenith angle at target towards sensor) is set to 40 to investigate changes in at-sensor radiance and reflectance due to changing the view direction from nadir to 40 off-nadir. This variation forces the MODTRAN parameter ANGLE (initial zenith angle as measured from the sensor) to a value of 140. The MODTRAN parameter PSIPO (true path azimuth from target to sensor) is set to 180, which means that the sensor is looking southward. These runs are calculated for all nominal atmospheres and nominal ground reflectance levels. Figures and illustrate the effect of different pointing angles on at-satellite reflectance, for atmospheres AT3 and AA12. (These differences are not considered as errors in the context of the present project, and the differences are not used in the analysis described in Chapter 5 the curves are included mainly as background information.) Radiances and reflectances are generally reduced for the tropical Spring scenario, due to increased atmosphere absorption and scatter in the increased slant path. However, there is a slight increase at short wavelengths, and for low ground reflectance values, due to Rayleigh scatter. For the very clear Arctic Winter scenario, the effects are small except for the enhanced Rayleigh scatter at short wavelengths. In the case of the nominal atmosphere AA12, the pointing azimuth (here: towards South) must be considered for a correct interpretation of the results, while northward and southward pointing is not relevant for nominal atmosphere AT3. As for the nadir-viewing case, partial derivatives of at-sensor radiance with respect to ground reflectance are derived by taking differences in at-sensor radiances produced by 1% changes in ground reflectances. (The partial derivatives are important for the analysis described in Chapter 5.) Figure shows differences in at-satellite reflectance values due to 1% increase in ground reflectance at nominal ground reflectance levels 2%, 6%, 10%, 20% and 40%, for the AT3 atmosphere. The curve is analogous to figure for the nadir viewing case. As for the nadir viewing case, the changes in at-sensor radiance and reflectance are almost equal for all ground reflectance values, which shows good linearity over the 1% ranges. There is again a departure from linearity at short wavelengths, due to multiple reflections between the atmosphere and ground. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 62 of 245

63 Figure Changes R in at-satellite reflectance between 40 off-nadir pointing angle (southward looking) and corresponding reference runs (pointing toward nadir) for 2%, 6%, 10%, 20%, 40% and 100% ground reflectance plotted against wavelength. Nominal atmosphere AT3. Figure Changes R in at-satellite reflectance between 40 off-nadir pointing angle (southward looking) and corresponding reference runs (pointing toward nadir) for 2%, 6%, 10%, 20%, 40% and 100% ground reflectance plotted against wavelength. Nominal atmosphere AA March 2001 COMMERCIAL IN CONFIDENCE Page 63 of 245

64 Figure Changes R in at-satellite reflectance produced by 1% increases in ground reflectance, at nominal ground reflectance levels 2%, 6%, 10%, 20% and 40%, plotted against wavelength (nominal atmosphere AT3, 40 off-nadir pointing angle). 4.6 DIFFERENTIALS WITH RESPECT TO ATMOSPHERE PARAMETER VARIATIONS - 40 OFF-NADIR All MODTRAN runs described in section 4.4 for the nadir-viewing case, were also performed for 40 off-nadir pointing angle. In general, the changes in at-satellite radiance and reflectance, produced by changes in water vapour concentration, visibility and altitude, appear very similar at 40 off-nadir pointing angle to the results described in section 4.4 for the nadir-viewing case. There are of course slight changes in the effects of absorption and scatter. 4.7 AT-SATELLITE RADIANCE OF CUMULUS CLOUD Cloud radiances are used in the analysis described in Chapter 5 for estimation of the worstcase effects of stray light in the space instrument. At-satellite radiance of cloud is calculated for the three nominal atmospheres AT3, AM6 and AA12 using the MODTRAN cumulus cloud model (ICLD = 1). Cloud base is set to 0.66 km above sea level, while the cloud top is located at 3.0 km above sea level. (Further information on cloud modelling can be obtained from the MODTRAN 3.7/4.0 users' manual). Ground 30 March 2001 COMMERCIAL IN CONFIDENCE Page 64 of 245

65 reflectance is set to 10%. The cloud radiances for the three nominal atmospheres are shown in figure Figure At-satellite radiance L of cumulus cloud for nominal atmospheres AT3, AM6 and AA12 for 10% ground reflectance (nadir pointing angle) 4.8 LINEARITY WITH RESPECT TO GROUND REFLECTANCE The variation of at-sensor radiance and reflectance is very close to linear with respect to ground reflectance, over small reflectance ranges (few percent), at all wavelengths. A linear assumption can be used (in Chapter 5) to derive ground-reflectance errors from errors in atsatellite radiances. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 65 of 245

66 5 EFFECTS OF CHARACTERISATION ERRORS This chapter describes a detailed analysis of the effects of uncertainties in: (a) space instrument characterisation and (b) atmosphere characterisation, in terms of errors in computed ground reflectance values. The analysis is based on detailed data generated as described in Chapter 4: at-sensor radiance values for ranges of ground reflectance and atmosphere characteristics, in three nominal observation scenarios described as: tropical Spring, mid-latitude Summer and Arctic Winter. The radiance values are averaged over the spectral bands that are at present specified for PRISM, in the range 450nm to 2350nm, and the analysis relates to ground-reflectance errors in these bands. The instrument errors included in the analysis are: absolute response (gain) error, dark level (offset) error, stray light, wavelength calibration error and error in assumed spectral wavebands. The atmosphere characterisation errors in the analysis are: ground height (depth of atmosphere), visibility, and water vapour content. The analysis also includes the effects of instrument and atmosphere characterisation errors on measurement of reflectance differences between viewing angles. Differences are computed for views at nadir and at 40 off nadir. The results are presented mainly as curves of ground-reflectance errors against wavelength, for each error type and for a set of true ground-reflectance values: 2%, 10% and 40%. Conclusions from the analysis are briefly summarised in Section 1.5 above, and discussed in greater detail in Chapter 7 below. 5.1 EFFECTS OF INSTRUMENT CHARACTERISATION ERRORS Modelling the effects of instrument errors Errors in ground reflectance, due to instrument errors, are computed in EXCEL files (t3analysis.xls, m6analysis.xls and a12analysis.xls). These three files contain MODTRAN radiance data respectively for the three observation scenarios: tropical Spring, mid-latitude Summer and Arctic Winter. All at-sensor radiance data have been prepared as described in Chapter 4. Computations of instrument errors are based on radiance data for each of the 30 March 2001 COMMERCIAL IN CONFIDENCE Page 66 of 245

67 three nominal scenarios (without perturbations that represent errors in atmosphere characterisation), and for sets of true ground reflectance values. In general, we calculate errors, L, in at-sensor radiance, due to various instrument-level errors. We then convert these errors into the equivalent errors in ground reflectance, ρ, using: ρ = L.(ρ 1 - ρ 2 )/(L 1 - L 2 ) where (L 1 - L 2 ) is the difference of two computed at-sensor radiances corresponding to reflectances ρ 1 and ρ 2. The computation is repeated for a set of ground reflectances ρ; the reflectances ρ 1 and ρ 2 are normally 1% above and 1% below the nominal reflectance ρ. Over this small reflectance range, the relation between at-sensor radiance and ground reflectance is very close to linear Gain errors Errors L in measured radiance, due to gain errors are modelled simply as: L = ge*radiance where radiance is true radiance. The value ge will typically vary through the spectrum, due to changes in relative spectral transmission of optics. However, we set a single value ge = gev for the VNIR band, and a single value ge = ges for the short wave IR band. Results are mainly presented for values of gev and ges equal to 0.02 (2% error in instrument response) Dark level errors Radiance errors due to uncertainties in dark signal level are calculated using the formula: L = de.rows/response Here, de is the estimated error in detector dark signal, expressed in terms of electrons generated in one detector element during the nominal integration period. Values for the VNIR and SWIR detectors are de = dev and de = des respectively. For both channels, we generally work with nominal values, for both dev and des, of 100 electrons. Spectral bands at the short-wave end of the VNIR channel will be produced by summing signals from more than one row of detector elements. The dark signal error for these bands will be larger by the factor rows, which is the number of CCD detector rows assigned to each spectral band. The assumption here is that the dark signal error will be equal for all detector elements; this is a reasonable approximation if the error is due to a temperature drift since the last dark-field measurement. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 67 of 245

68 Response is the estimated spectral response of the PRISM instrument, in terms of signal per unit at-sensor radiance. Signal is expressed in electrons of primary signal generated in each band, over the nominal integration period, for one spatially-resolved area. For most of the spectral bands, this means the signal generated in one detector element. However, for the short VNIR wavelengths, the bands are produced by more than one detector row. The response values are calculated assuming: optics aperture diameter: 85mm ground pixel size (and gsd): 50m platform altitude: 767km frame period: 7.49ms SWIR detector quantum efficiency: 0.6 VNIR detector sensitivity: back-illuminated CCD values The frame period is calculated as the time of flight over a 50m gsd, assuming that the platform points always to nadir, and the integration time is assumed equal to the frame time. (In practice, the integration time can be increased by controlling platform pitch rate during imaging, so that this parameter may change. The integration time will be slightly smaller than the frame time, at least for the VNIR detector, due to the time required to transfer charge, but we ignore this correction.) Detector sensitivity for the VNIR band was taken from measured values for the CCDs used in the Sira CHRIS instrument (CCDs derived from the MERIS programme). Optics transmission is assumed to be 50% for all bands, except for bands 57 and 58 at 25% and bands 56 and 59 at 45%. These lower transmissions allow for use of a dichroic splitter in the spectrometer. Apart from actual dark level errors, transmission figures and detector sensitivities, these assumptions are derived from Reference 3. The element signal levels, at the maximum radiances specified by ESA for PRISM, are 1.22 million electrons for the VNIR band, and 0.79 million electrons for the SWIR band. The VNIR maximum appears high compared with typical CCD saturation levels, so that the aperture or transmission assumed for the VNIR channel may be high Stray light errors The radiance error due to stray light is calculated simply as small fraction stray of cloud radiance. L = stray*cloud radiance Again, separate values for stray, strayv and strays, can be input for the VNIR and SWIR bands. The error is added to the true ground radiance Non-linearity errors Radiance errors due to uncalibrated non-linearities in instrument response are modelled using: L = lin*max*sin(π*response*radiance/max)/response 30 March 2001 COMMERCIAL IN CONFIDENCE Page 68 of 245

69 The assumption here is that there is a sinusoidal variation in system response with the primary signal level, due for example to non-linear gain in analogue electronics chains. The primary signal level is calculated as response*radiance, for each true radiance level, where response is defined as in section above. The value max is a nominal maximum primary signal level, in electrons, calculated as the highest single-band signal produced by the maximum radiance values defined by ESA in Reference 4. The value max takes different values, maxv and maxs, for the VNIR and SWIR bands. The amplitude of the sinusoidal response-curve error is lin, which can also be given separate values linv and lins for the VNIR and SWIR bands Wavelength and waveband errors Radiance errors due to imperfect wavelength and waveband calibration of the PRISM instrument are computed directly from MODTRAN radiance data. Radiance L λ, λ is computed as an average for the centre wavelength λ and the full-width-at-half-maximum (FWHM) bandwidth λ. The radiance error due to a shift δλ in instrument-defined wavelength is calculated as: L = L λ+δλ, λ - L λ, λ The radiance error due to a change dλ in the FWHM of the waveband defined by the instrument is calculated as: L = L λ, λ+dλ - L λ, λ. The results are calculated for values of both errors, δλ and dλ, equal to + and 1nm Effects of gain errors We have generally assumed a gain error of 2% for all wavelengths. This means that, with offset errors (dark level etc.) corrected, the instrument reads at-sensor radiances with an error equal to 2% of true radiance, at all wavelengths and for all true radiance values. This is comparable with the current PRISM specification (which however includes stray light effects in a 2% error budget). Results for the three observation conditions, with nadir viewing, are shown in figures , and No other instrument errors are included and it is assumed that perfect atmosphere correction is applied. Each plot gives errors for three true ground reflectance levels: 2%, 10% and 40%. Where atmosphere scatter is a small proportion of total at-sensor radiance, typically at long wavelengths, the ground reflectance error approximates 2% of the true ground reflectance. The graphs therefore show ground reflectance errors as % of true ground reflectance values not absolute reflectance errors. However, at short wavelengths, atmosphere scatter increases the radiance errors and hence the ground reflectance errors. Reflectance errors also increase in and near the atmosphere absorption bands (since absorption increases the significance of atmosphere scatter with 30 March 2001 COMMERCIAL IN CONFIDENCE Page 69 of 245

70 respect to ground-reflected radiance). The atmosphere effects are most significant in the extreme Arctic Winter scenario, where ground radiance is drastically reduced by obliquity of solar illumination. (The increase in absolute errors at short wavelengths is slightly larger for low true-reflectance values, due to slight non-linearity of the radiance/reflectance curve.) Reflectance errors can clearly be very large as percentages of true reflectances. At 450nm, a 2% gain error produces a reflectance error of about 16% of true reflectance for the nominal tropical and mid-latitude cases. The error is 60% of the true value at 450nm for the Arctic scenario. The errors, as calculated, will scale exactly with the assumed gain error. The ground reflectance errors generally increase with the viewing angle. Figures , and show the differences in computed ground reflectance values, between views at 40 off nadir (along-track) and at nadir (still due to a 2% gain error). Figure (a) shows errors for one case on an enhanced scale. The calculated changes are small for the tropical and mid-latitude scenarios, but quite large for the Arctic Winter case (increasing total absolute-reflectance errors to >10%). The changes are remarkably uniform with true ground reflectance values, and are shown as absolute differences not % of true reflectance in this case. Reflectance errors, % of true reflectance, produced by gain error reflectance error, % of true % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true ground reflectance, produced by 2% gain error tropical Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 70 of 245

71 Reflectance errors, % of true reflectance, produced by gain error reflectance error % of true % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true ground reflectance, produced by 2% gain error mid-latitude Summer 50 Reflectance errors, % of true reflectance, produced by gain error reflectance error, % of true % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true ground reflectance, produced by 2% gain error Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 71 of 245

72 Reflectance errors due to gain error, nadir to off-nadir difference difference in absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by 2% gain error tropical Spring Reflectance errors due to gain error, nadir to off-nadir difference difference in absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by 2% gain error mid-latitude Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 72 of 245

73 0.010 Reflectance errors due to gain error, nadir to off-nadir difference difference in absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure (a) Difference of reflectance errors between views at nadir and 40 off nadir, produced by 2% gain error mid-latitude Spring 0.8 Reflectance errors due to gain error, nadir to off-nadir difference 0.7 difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by 2% gain error Arctic Winter Several messages may perhaps be derived from this analysis: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 73 of 245

74 (a) (b) (c) (d) it will be desirable to avoid using short wavelengths where possible, and of course to avoid atmosphere absorption bands except for atmosphere characterisation, in derivation of higher-level products, it may be desirable to use reflectance differences rather than reflectance ratios, particularly at short wavelengths, larger gain errors may be tolerated for relative BRDF measurements (since the errordifferences with along-track pointing angles appear small, except for the extreme Arctic scenario), the sensitivity of the system to atmosphere radiance at short wavelengths may indicate that Rayleigh scatter should be used as one element of in-flight characterisation (as suggested in Reference 3). In general, it must be accepted that there appears to be a case for very good in-flight absolute response characterisation of PRISM. However, the requirement cannot be positively quantified without considering effects on the final products of the PRISM mission Effects of dark level errors Dark level errors can vary very widely, depending on detailed instrument design and in-flight calibration strategy. In the analysis described here, we have generally worked with a primary error-signal level of 100 electrons, for both optical channels. Uncalibrated dark-signal levels can certainly exceed 100 electrons. For example, if a CCD detector is operated at 300K, it will generate a dark signal of a few hundred electrons (per element and integration period) at beginning of life. This would rise possibly to >1000 electrons at end of life, due to the effects of space radiation. The dark signal level will vary from pixel to pixel However, dark signal levels from all detector elements can be characterised at least once per orbit, for both channels, by recording the image of a dark area (black body, dark sky or dark area of Earth). The effects of temperature drift between full-field dark-level calibration and Earth-imaging, can be inferred from dark signals on masked pixels, in the time-frame of each imaging period. It should therefore be possible to measure dark signals to a fraction of the random noise level, the fraction depending on how many frames of dark signal are averaged in the characterisation procedures. A typical rms noise level is order of 100 electrons, so that we would generally expect to characterise dark signal, on a pixel basis, to much better than 100 electrons possibly to 10 electrons. The 100 electrons level is therefore probably a pessimistic assumption for PRISM. (The values assumed for response may be slightly optimistic.) Figures , and show results for dark signal errors in the three nominal observation conditions, with nadir viewing. These curves show errors in computed ground reflectances, due to 100 electrons of dark signal error. Again, it is assumed that perfect atmosphere correction is applied, and each plot gives errors for three true ground reflectance levels: 2%, 10% and 40%. Figure (a) shows the same results on an enhanced scale for one case. The absolute ground-reflectance errors are almost independent of the true ground reflectance level (increasing slightly at low reflectance levels due to non-linearity of the 30 March 2001 COMMERCIAL IN CONFIDENCE Page 74 of 245

75 radiance/reflectance curves). The reflectance errors are generally small, compared for example with the effects of gain errors. However, the errors increase where the useful signals from ground are low particularly at long SWIR wavelengths, short visible wavelengths and in-and-near the atmosphere absorption bands. The errors are clearly larger in the very low solar-illumination conditions of the Arctic Winter scenario. (The absorption feature at 2060nm appears to have a much stronger effect in this scenario.) In this case, and for the extreme wavelengths, the reflectance errors due to 100 electrons dark signal, exceed 1% absolute; this may be considered significant, at least for targets of low reflectance. Figures , , (a) and show the differences in ground reflectance errors due to a fixed 100 electrons dark signal error, between views at 40 off nadir (alongtrack) and at nadir. The ground reflectance errors due dark level error increase with the viewing angle, due to reduction in useful signal levels with increased atmosphere absorption. However the differences are very small Reflectance errors produced by dark level error absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by 100 e - dark signal error tropical Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 75 of 245

76 0.35 Reflectance errors produced by dark level error absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by 100 e - dark signal error mid-latitude Summer 0.05 Reflectance errors produced by dark level error 0.04 absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure (a) Reflectance errors produced by 100 e - dark signal error mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 76 of 245

77 2 Reflectance errors produced by dark level error absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by 100 e - dark signal error Arctic Winter 0.12 Reflectance errors due to dark level, nadir to off-nadir difference difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by 100 e - dark signal error tropical Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 77 of 245

78 0.08 Reflectance errors due to dark level, nadir to off-nadir difference difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by 100 e - dark signal error mid-latitude Summer Reflectance errors due to dark level, nadir to off-nadir difference difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure (a) Difference of reflectance errors between views at nadir and 40 off nadir, produced by 100 e - dark signal error mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 78 of 245

79 difference in %-reflectance error Reflectance errors due to dark level, nadir to off-nadir difference 2% nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by 100 e - dark signal error Arctic Winter It is difficult to assess realistic requirements for in-flight characterisation of dark levels, because the scale of the problem will be critically dependent on instrument design details. With sufficient detector cooling, it is conceivable that dark signals will be very low in all conditions, so that no in-flight calibration is in principle required. If dark signals are significant, in-flight characterisation to an accuracy below the random noise level will be desirable, but will probably be found fairly easy. The main concern for relative accuracy in BRDF measurements will be in possible dark signal drift between recording of views at different angles a 100-electron drift will give difference errors close to the values plotted in figure , and It is likely to be desirable to monitor average dark signal in the time-frame of each Earth imaging period, and also with each full dark-field recording and each bright-field calibration, for example by monitoring signals from masked detector elements Effects of electronics offset errors Offsets in analogue electronics, between the detectors and the A to D converters, will be expected to produce effects generally similar to the effects of dark signal errors, as discussed above in section Differences include: (a) offset errors will be relatively low at short visible wavelengths, because they are not a function of the number of CCD rows summed on the chip, 30 March 2001 COMMERCIAL IN CONFIDENCE Page 79 of 245

80 (b) offset errors will vary between gain settings (assuming that a variety of gains is used to maximise use of the A to D dynamic range) and hence potentially with reflectanceradiance levels and spectral band. Offset errors will vary, like dark signal levels, with temperature of relevant components, and there may also be variations through life due to effects of space radiation. The magnitudes of electronics offset errors may be comparable with those of dark signal errors. It will probably be desirable to measure offsets to an accuracy below the random noise level, in the timeframe of each Each-imaging period, dark field calibration period and bright field calibration period. This will generally be possible by injecting true-zero reads into the analogue electronics chains Effects of stray light errors In a remote sensing instrument, pointed at Earth (except possibly for some calibration measurements), the source of stray light is the Earth disc. It is therefore reasonable to estimate the radiance error produced by stray light as a fraction of the Earth scene radiance. Stray light errors can vary substantially between instruments. The error also generally varies with the wavelength of the radiation and (considerably) with the spatial distribution of scene radiance with respect to the instrument field. In this technical note, we have chosen to assume: (a) that the radiance error due to stray light is a fixed fraction of a nominal scene radiance, (b) that the scene is dominated by cloud (so that we take a fraction of cloud radiance as the error), and (c) that the stray light effect in each instrument spectral band is produced only by scene radiance in the same spectral band. This last assumption means that we consider only the out-of-field stray light, which is stray light produced mainly by scatter in the instrument telescope; we ignore out-of-band stray light, which is produced only by scatter inside the spectrometer. We have assumed that the stray radiance is 1% (of cloud radiance) in the VNIR band, and 0.5% in the SWIR band. Cloud radiance also falls at long wavelengths. In terms of relative spectral distribution, these assumptions are broadly justified, since instrument stray light (particularly due to surface scatter) tends to fall with wavelength. The absolute levels selected may be considered pessimistic: (a) it should be possible to achieve stray light down to 0.1% of scene radiance and (b) a mainly cloud-filled scene presents a worst case, at least in the VNIR band. Figures , and show the effects of stray light errors in the three observation conditions, with nadir viewing. These curves show errors in computed ground reflectances, due to a stray radiance equal to 1% of cloud radiance in the VNIR band, and 0.5% of cloud radiance in the SWIR band. As before, it is assumed that perfect atmosphere correction is applied, and each plot gives errors for three true ground reflectance levels: 2%, 10% and 40%. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 80 of 245

81 Reflectance errors produced by out-of-field stray light absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by stray light errors tropical Spring 1.4 Reflectance errors produced by out-of-field stray light absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by stray light errors mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 81 of 245

82 2 Reflectance errors produced by out-of-field stray light absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by stray light errors Arctic Winter The assumed cloud source gives approximately 100% reflectance at shorter wavelengths. Unsurprisingly, 1% stray light gives ground reflectance errors of approximately 1% through most of the VNIR band, and 0.5% stray light gives about 0.5% ground reflectance errors at the short-wave end of the SWIR band. Errors increase in the atmosphere absorption bands. They also increase at short wavelengths, particularly in the Arctic scenario, due to the effects of Rayleigh scatter on the radiance/reflectance conversion factors. The errors fall at longer wavelengths through the SWIR band (with cloud radiance). Figures , and show the differences in ground reflectance errors due to the same instrument stray light defects, between views at 40 off nadir (along-track) and at nadir. The ground reflectance errors increase with the viewing angle, but the differences are quite small. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 82 of 245

83 0.45 Reflectance errors due to stray light, nadir to off-nadir difference difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by stray light errors tropical Spring 0.27 Reflectance errors due to stray light, nadir to off-nadir difference 0.24 difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by stray light errors mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 83 of 245

84 0.1 Reflectance errors due to stray light, nadir to off-nadir difference difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between views at nadir and 40 off nadir, produced by stray light errors Arctic Winter The above analysis indicates, as would be expected, that the effects of stray light are smoothly distributed as a function of wavelength, except in a few absorption bands. No very large errors are generated, even on the pessimistic assumptions of 1% stray light and a cloudfilled scene. In practice, the spectral distribution of stray light effects will be less uniform for these reasons: (a) in real instruments, the contribution of optical surface scatter will be expected to increase at short wavelengths, (b) out-of band stray light (generated in the spectrometer, and not included in the above analysis) will produce larger ground-reflectance errors in spectral regions where useful signal levels are low, including both ends of the VNIR band and the long-wave end of the SWIR band, and (c) the spectral distribution of out-of-field stray light will of course vary with the spectral content of the scene (although a cloud-filled scene probably represents a worst case for absolute error levels) Effects of non-linearity errors No mechanisms for significant change of linearity have been positively identified; it may be considered likely that there will be no significant changes after pre-flight characterisation. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 84 of 245

85 However, manufacturers have not measured non-linearities in detector arrays and electronics, to levels that may be significant for PRISM. The possibility of significant in-flight changes cannot therefore be ruled out. Ideally, changes in linearity (associated with ageing, space radiation and temperature changes) will be measured during the PRISM system development. Meanwhile, the forms and amplitudes of linearity errors cannot be predicted with any confidence. We have included an analysis of the effects of one type of linearity error (specified in section ) as an example of the kind of analysis that will be useful when the possibly linearity errors (if significant) are better understood. The result of the linearity error analysis may be considered very provisional. Figures , and show the effects of the assumed linearity errors in the three observation conditions, with nadir viewing. The curves show errors in computed ground reflectances, due to linearity errors having amplitude up to 1% of the nominal peak signal level (i.e. linv = lins = 0.01, as defined in section ). Each plot gives errors for three true ground reflectance levels: 2%, 10% and 40%. 0.0 Reflectance errors produced by linearity error absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by 1% linearity error tropical Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 85 of 245

86 0.0 Reflectance errors produced by linearity error absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by 1% linearity error mid-latitude Summer 0.0 Reflectance errors produced by linearity error -0.5 absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by 1% linearity error Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 86 of 245

87 For low signal levels particularly for the lower ground-reflectance values and all the results for the Arctic Winter scenario the assumed non-linearity gives effects very similar to those of a simple gain error. In fact, for small signal levels, the sinusoidal perturbation that we have selected is almost linear, approximating to a simple π% change in gain. The effects are more interesting at the higher signal levels produced by 40% ground reflectance in the tropical and mid-latitude scenarios. Here, the higher signal levels give errors significantly less than π% of true radiance. The effect of signal oscillations due (a) to changes in numbers of CCD rows assigned to VNIR bands, and (b) to atmosphere absorption, have more noticeable effects on the distribution of ground-reflectance errors. If a different non-linearity function were assumed, for example a sine-squared function, these effects would appear at different scene radiance levels. Because of uncertainties in the non-linearities that can actually be expected, few useful conclusions can be drawn from the non-linearity analysis in its present form. It is clear that small non-linearities can in principle: (a) introduce quite large local variations in the gradient of the response curve, which may for example produce large errors in small ground-reflectance values, as fractions of true reflectances, and (b) add spurious spectral structure associated with switches in numbers of CCD rows summed to produce spectral bands Effects of wavelength and waveband errors In general, we have analysed the effects of wavelength errors that are either +1nm or 1nm for all specified PRISM bands. The effects on radiance errors (and ground reflectance errors) are almost equal and opposite for these two cases, so we show only the effects of a +1nm shift in the figures below. Waveband errors (FWHM of the waveband) are also assumed to be either +1nm or 1nm. Again we choose to plot results only for the +1nm case, since the effects for 1nm waveband change are almost equal and opposite. Real errors in centre wavelengths are likely to be <1nm, if some in-flight wavelength calibration is performed, but could be several nanometres if there is no in-flight calibration, since a 1nm error corresponds typically to a shift of only 0.002mm in a detector (except at the shorter VNIR wavelengths). A 1nm waveband error would be produced by a focus shift in the order of 0.01mm (except again at the shorter VNIR wavelengths). This shift could be generated, for example, by a 0.005mm shift in position of any of the spectrometer mirrors. It may be unreasonable to expect stability of this order, against launch vibration, unless a very stringent qualification is performed. However, in-flight characterisation of wavebands will be relatively difficult. Waveband errors therefore present a significant potential problem. The dispersion of the quartz prisms in the PRISM spectrometer increases rapidly at short wavelengths. Movements in the spectrometer will tend to produce equal movements of the image with respect to the detector, for all wavelengths. This means that wavelength and 30 March 2001 COMMERCIAL IN CONFIDENCE Page 87 of 245

88 waveband errors will typically be smaller at visible wavelengths than at near-ir and SWIR wavelengths. We are therefore most concerned with the effects of wavelength and waveband errors in near-ir and SWIR bands. Figures , , (a) and show the ground-reflectance errors produced by a 1nm centre wavelength shift, in each of the three observation scenarios. Figures , , (a) and show the ground reflectance errors produced by a 1nm change in wavebands. For a large part of the wavelength range, the reflectance errors tend to be proportional to the ground reflectance. Figures through therefore present the ground reflectance errors as percentages of the true ground reflectance values: 2%, 10% and 40%. Ground reflectance errors due to 1nm wavelength shift are small in most of the wavebands defined for PRISM. However, there are significant error spikes for a large minority of the specified bands, due to the effects of fine structure in the atmosphere absorption spectrum. For the high ground reflectance (40%), the errors exceed 2% of this ground reflectance in about 30 of the PRISM bands (out of a total of 136). The errors, as % of true reflectance, are generally larger for the low ground reflectance values, and the difference becomes substantial at short wavelengths. (However, wavelength errors will in practice be smaller at short wavelengths, due to the larger dispersion of the spectrometer optics.) The errors are much larger for the extreme Arctic Winter scenario, particularly at short wavelengths where a large part of the at-sensor radiance is due to Rayleigh scatter. This region also shows a larger enhancement of the errors for low ground reflectance values. Reflectance errors due to 1nm FWHM waveband change are smaller than the errors due to a 1nm wavelength shift, by a factor typically about 4, but otherwise show a somewhat similar pattern. Errors for most wavebands are small, but there are significant error spikes due to fine structure in the atmosphere absorption spectrum. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 88 of 245

89 10 Reflectance errors, % of true reflectance, for 1nm wavelength shift 8 6 reflectance error, % of true % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true ground reflectance, produced by a 1nm centre-wavelength error tropical Spring Reflectance errors, % of true reflectance, for 1nm wavelength shift 2% nominal reflectance 10% nominal reflectance 40% nominal reflectance reflectance error, % of true wavelength, nm Figure Reflectance errors produced by a 1nm centre-wavelength error midlatitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 89 of 245

90 Reflectance errors, % of true reflectance, for 1nm wavelength shift 2% nominal reflectance 10% nominal reflectance 40% nominal reflectance reflectance error, % of true wavelength, nm Figure (a) Reflectance errors produced by a 1nm centre-wavelength error midlatitude Summer reflectance error, % of true Reflectance errors due to +1nm wavelength shift, % of true reflectance 2% nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by a 1nm centre-wavelength error Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 90 of 245

91 5 Reflectance errors due to +1nm waveband change, % of true reflectance 4 3 reflectance error, % of true % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by a 1nm FWHM bandwidth error tropical Spring 5 Reflectance errors, % of true reflectance, due to +1nm waveband change 4 3 reflectance error, % of true % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by a 1nm FWHM bandwidth error midlatitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 91 of 245

92 Reflectance errors, % of true reflectance, due to +1nm waveband change 2% nominal reflectance 10% nominal reflectance 40% nominal reflectance reflectance error, % of true wavelength, nm Figure (a) Reflectance errors produced by a 1nm FWHM bandwidth error midlatitude Summer 10 Reflectance errors due to +1nm waveband change, % of true reflectance 8 6 reflectance error, % of true % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by a 1nm FWHM bandwidth error Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 92 of 245

93 5.2 EFFECTS OF ATMOSPHERE CHARACTERISATION ERRORS Modelling of atmosphere error effects Errors in ground reflectance, due to atmosphere characterisation, are computed in the EXCEL files at3analysis.xls, am6analysis.xls and aa12analysis.xls. These three files contain MODTRAN radiance data respectively for the three observation scenarios: tropical Spring, mid-latitude Summer and Arctic Winter. The data include at-sensor radiances for nominal observation conditions, and also for three types of perturbations: changed ground height above sea level changed visibility changed water vapour content. We calculate errors in ground reflectance, ρ h, due to an error in ground height, using: ρ h = (L h1 - L h2 ).(ρ 1 - ρ 2 )/(L 1 - L 2 ) As for computation of instrument-generated errors, (L 1 - L 2 ) is the difference of two computed at-sensor radiances, in the nominal atmosphere condition, corresponding to reflectances ρ 1 and ρ 2. L h1 is the computed radiance for a ground height h1, and L h2 is the computed radiance for a ground height h2. The difference h2 - h1 is of course the representative error in the assumed ground height. Similarly, errors in ground reflectance, ρ v, due to an error in characterisation of visibility (v1 v2), are computed using: ρ v = (L v1 L v2 ).(ρ 1 - ρ 2 )/(L 1 - L 2 ) where L v1 is the computed radiance for a visibility v1, and L v2 is the computed radiance for a visibility v2. And errors in ground reflectance, ρ w, due to an error in characterisation of water vapour (w1 w2), are computed using: ρ w = (L w1 L w2 ).(ρ 1 - ρ 2 )/(L 1 - L 2 ) where L w1 and L w2 are the computed radiances for water vapour contents w1 and w Effects of height errors The effects of errors in estimation of ground height are illustrated in figures , , (a) and , for the three scenarios: tropical Spring, mid-latitude Summer and Arctic Winter. The plots show the computed errors in ground reflectance produced by an error in ground height estimation of 0.5km. The errors tend to be proportional to ground reflectance errors, except at low reflectance, and are shown as percentages of true reflectance. The ground reflectance errors appear to vary almost linearly with height errors. The diagrams show reflectance errors estimated for 100m height error, actually scaled by a factor 1/5 from the computed errors at 500m. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 93 of 245

94 12 Errors % of true reflectance produced by a 100m height error - nadir reflectance error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true reflectance, produced by a 100m height error tropical Spring 2.5 Nadir to off-nadir differences in reflectance errors, % of true reflectance, due to a 100m height error 2.0 difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true reflectance, produced by a 100m height error mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 94 of 245

95 1.0 Errors % of true reflectance produced by a 100m height error - nadir reflectance error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure (a) Reflectance errors, % of true reflectance, produced by a 100m height error mid-latitude Summer 6 Errors % of true reflectance produced by a 100m height error - nadir reflectance error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true reflectance, produced by a 100m height error Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 95 of 245

96 2.5 Nadir to off-nadir differences in reflectance errors, % of true reflectance, due to a 100m height error difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors, % of true reflectance, between nadir and 40 off nadir views, produced by a 100m height error tropical Spring 2.5 Nadir to off-nadir differences in reflectance errors, % of true reflectance, due to a 100m height error 2.0 difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors, % of true reflectance, between nadir and 40 off nadir views, produced by a 100m height error mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 96 of 245

97 0.6 Nadir to off-nadir differences in reflectance errors, % of true reflectance, due to a 100m height error difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure (a) Difference of reflectance errors, % of true reflectance, between nadir and 40 off nadir views, produced by a 100m height error mid-latitude Summer 0.2 Nadir to off-nadir differences in reflectance errors due to a 0.5km height error 0.1 difference in %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors, % of true reflectance, between nadir and 40 off nadir views, produced by a 100m height error Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 97 of 245

98 The reflectance errors are generally small, for all ground-reflectance values, but are significant, at this large height error, in a few atmosphere absorption bands. In these bands, the errors tend to be proportional to ground reflectance values. (However, there is always a tendency for larger errors to be produced at short wavelengths and for the low ground reflectance values, due to the enhanced significance of Rayleigh scatter.) Differences in the ground-reflectance errors, between views at nadir and 40 off nadir, are shown in figures , , (a) and The errors are again shown as % of true reflectance values, except in the case of the Arctic Winter scenario. The nadir-to-off-nadir differences are very small, except again for the atmosphere absorption bands. In general, height errors seems likely to be the least significant problem for correction of atmosphere effects, if we can assume that a 100m error is generally a reasonable limit Effects of visibility errors The effects of errors in characterisation of visibility are illustrated in figures , and , for the three observation scenarios. Figures and , for the tropical Spring, and mid-latitude Summer cases, show the ground reflectance errors due to a 3km error in estimation of visibility the difference between 23km visibility in the nominal case and an actual 20km visibility. Figure , for the Arctic Winter case, shows ground reflectance errors for a 5km visibility error the difference between 45km visibility in the nominal case and an actual 50km. The errors tend to be proportional to ground reflectance values for most wavelengths. The errors are therefore shown as percentages of true ground reflectance values. The ground reflectance errors tend to be very small at long wavelengths. At short wavelengths, the effects of Rayleigh scatter enhance the reflectance errors. The errors are generally low typically <0.5% for the visibility errors that have been plotted. But for low ground reflectance values, the errors at short wavelengths may be considered significant as percentages of true reflectance values. For high reflectance values (40%), there is some compensation between loss of ground radiance and increased atmosphere scatter, which reduces the magnitudes of absolute reflectance errors. The curves for higher ground reflectance show oscillations due to atmosphere absorption bands. Figures , and show differences in the ground reflectance errors, produced by the same visibility errors in the three scenarios, between views at nadir and 40 off nadir. The differences appear very small. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 98 of 245

99 0.5 Absolute reflectance errors due to 20km visibility (cf 23km true) absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by a -3km visibility error (cf 23km nominal) tropical Spring 0.4 Absolute reflectance errors due to 20km visibility (cf 23km true) absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by a -3km visibility error (cf 23km nominal) mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 99 of 245

100 0.6 Absolute reflectance errors due to 45km visibility (cf 50km true) absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors produced by a -5km visibility error (cf 50km nominal) Arctic Winter 0.15 Nadir to off-nadir difference in reflectance errors due to 20km visibility (cf 23km true) absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between nadir and 40 off nadir views, produced by a -3km visibility error (cf 23km nominal) tropical Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 100 of 245

101 0.20 Nadir to off-nadir difference in reflectance errors due to 20km visibility (cf 23km true) absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between nadir and 40 off nadir views, produced by a -3km visibility error (cf 23km nominal) mid-latitude Summer 0.18 Nadir to off-nadir difference in reflectance errors due to 45km visibility (cf 50km true) absolute %-reflectance error % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors between nadir and 40 off nadir views, produced by a -5km visibility error (cf 50km nominal) Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 101 of 245

102 5.2.4 Effects of water vapour errors The effects of errors in estimation of atmosphere water vapour are illustrated in figures , , (a) and , for the three scenarios: tropical Spring, mid-latitude Summer and Arctic Winter. The plots show the computed errors in ground reflectance produced by a 10% error in water vapour estimation. (The MODTRAN computations are for water vapour errors of 20% and +20%. The effects of 10% error were computed by taking ¼ of the radiance differences between the ±20% cases.) The errors tend to be proportional to ground reflectance values; the curves therefore show errors as percentages of true ground reflectance values. The effects of water vapour errors are of course substantial in the water vapour absorption bands, and small outside these bands. In principle, the errors due to water vapour could be more significant than errors due to visibility. However, for some users, it may be possible either to avoid water vapour bands, or else to use the characteristic signature of water vapour to provide an improved characterisation of water vapour. Differences in the ground-reflectance errors, between views at nadir and 40 off nadir, are shown in figures , , (a) and The nadir-to-off-nadir differences are very small, except again for the atmosphere absorption bands. Errors % of true reflectance due to 10% water vapour error 0-5 error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true reflectance, produced by a 10% water vapour error tropical Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 102 of 245

103 Errors % of true reflectance due to 10% water vapour error 0 error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true reflectance, produced by a 10% water vapour error mid-latitude Summer Errors % of true reflectance due to 10% water vapour error 2% nominal reflectance 10% nominal reflectance 40% nominal reflectance error % of true reflectance wavelength, nm Figure (a) Reflectance errors, % of true reflectance, produced by a 10% water vapour error mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 103 of 245

104 Errors % of true reflectance due to 10% water vapour error 0 error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Reflectance errors, % of true reflectance, produced by a 10% water vapour error Arctic Winter Nadir to off-nadir error difference, % of true reflectance, due to 10% water vapour error 0 difference in error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance, % of true reflectance, errors between nadir and 40 off nadir views, produced by a 10% water vapour error tropical Spring 30 March 2001 COMMERCIAL IN CONFIDENCE Page 104 of 245

105 Nadir to off-nadir error difference, % of true reflectance, due to 10% water vapour error difference in error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors, % of true reflectance, between nadir and 40 off nadir views, produced by a 10% water vapour error mid-latitude Summer 0.1 Nadir to off-nadir error difference, % of true reflectance, due to 10% water vapour error difference in error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure (a) Difference of reflectance errors, % of true reflectance, between nadir and 40 off nadir views, produced by a 10% water vapour error mid-latitude Summer 30 March 2001 COMMERCIAL IN CONFIDENCE Page 105 of 245

106 Nadir to off-nadir error difference, % of true reflectance, due to 10% water vapour error difference in error % of true reflectance % nominal reflectance 10% nominal reflectance 40% nominal reflectance wavelength, nm Figure Difference of reflectance errors, % of true reflectance, between nadir and 40 off nadir views, produced by a 10% water vapour error Arctic Winter 30 March 2001 COMMERCIAL IN CONFIDENCE Page 106 of 245

107 6 CASE STUDY PLANT WATER In Chapter 5, the effects of uncertainties in characterisation of the PRISM space instrument, and in characterisation of the atmosphere, are analysed in terms of effects on the computed ground-reflectance data. This analysis may be expected to provide a reasonable basis for comparison of the importance of different uncertainties, since the data products of the PRISM mission will often be derived from ground reflectance data. However, different data products are derived using widely different sets of spectral bands, and different relationships between these spectral bands, so that conclusions based on a superficial examination of groundreflectance errors may be misleading. It is therefore desirable to check the general validity of conclusions based on ground reflectance errors, by at least one case study, in which we investigate the effects of instrument and atmosphere errors on a higher-level data product. In this Chapter, results from a case study are presented and discussed. Plant water content was selected from a short list of higher-level data products identified in an early task, as described in Appendix A. The sensitivity in the retrieval of plant water content, with respect to different instrument and atmospheric characterization errors, was analyzed to show the relative importance of several errors types. Reasons for selection of plant water content, for the case study, include: (a) (b) (c) it is a likely product from the Land Mission, it is an essentially hyperspectral application, requiring use of a large number of spectral bands and high spectral resolution, the need to distinguish liquid water absorption from atmospheric water vapour absorption provides a critical test for hyperspectral sensing. The investigations are based on the results of sensitivity analyses described in Chapter 4, with some further MODTRAN runs that were needed to provide complete data sets. Ground spectra for three different types of vegetation were taken from spectral libraries forming part of the ENVI image processing software. Three different atmosphere characterization errors and five different calibration errors were studied in detail. Nominal atmosphere AM6 (midlatitude Summer) was used in all cases. 6.1 CASE STUDY DESIGN Retrieval of plant water content from vegetation spectra A description of the general approach for retrieving plant water content from vegetation spectra, derived from Roberts et al (Roberts, Brown, Green, Ustin and Hinckley: "Investigating the Relationship Between Liquid Water and Leaf Area in Clonal Populus", Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1998 Workshop Proceedings, JPL, Pasadena, Ca., 1998) is given in Appendix A. Here, we focus on specific aspects of the implementation of the method for this sensitivity study. We start from the modified Beer-Lambert law: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 107 of 245

108 I = α d ( f ) I e 1, 0 where I 0 is the initial radiance, I the radiance after passing through a medium with an absorption coefficient α, d is the optical path length, and f is the partial blocking factor (i.e. the fraction of total surface area over which radiation is prevented from passing through the medium). Substituting reflectance R for I/I o we get: ln( R) = α d + ln(1 f ). Over a certain spectral range λ i, where α i is known and varies significantly, and R i is obtained from an atmospherically corrected vegetation spectrum, we can set-up a linear regression model of the form: where y = c0 + c1 x x i = 1 α i, yi = ln( Ri ), c0 = ln(1 f ), c = d. Linear regression not only provides an estimate for the path length d, which gives the plant water content as equivalent path in cm, but also an error estimate σ for d and the percentage r 2 of the variance in y explained by the linear regression model. After several tests and literature studies, PRISM bands 40 to 69, giving the spectral range from 800 to 1200 nm, were chosen for the sensitivity study. On the one hand, the total number of PRISM bands in this spectral range is large enough to guarantee statistical significance of the regression results; on the other one, the influence of further spectral features not related to plant water content is reduced as far as possible. The absorption coefficients for liquid water over this spectral band are plotted in figure These coefficients were taken from Kou et al. (Kou, L., Labrie, D. and Chylek, P. (1993): "Refractive indices of water and ice in the µm spectral range", Appl. Opt., 32, ). The main problems in extraction of plant water content are due to atmosphere water vapour absorption in the same spectral range. See also Absorption coefficients were spectrally convolved to the PRISM band definitions. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 108 of 245

109 1.5 absorption coefficient (cm-1) wavelength Figure Absorption coefficients for liquid water (taken from Kou et al., 1993) to be used for the retrieval of plant water content after spectral convolution to the PRISM bands Vegetation spectra Three different vegetation spectra were used in this study. A lawn grass spectrum was measured at the USGS Denver Spectroscopy Lab. Wavelength accuracy is in the order of 0.5 nm in the near infrared. Full details of the USGS vegetation spectral library and the descriptions of the samples are available at: Live oak and red willow spectra were provided by Chris Elvidge, DRI, and are unpublished data from the Jasper Ridge spectral library for green vegetation, dry vegetation and rocks (for further details cf. ENVI 3.1). All vegetation spectra were spectrally convolved to the PRISM bands. The resulting spectra are shown in figure Sensitivity analyses with respect to wavelength and waveband errors were not carried out for the lawn grass spectrum due to the insufficient spectral resolution of this vegetation spectrum. The live oak and red willow spectra were also spectrally convolved using a spectral sampling rate of 1 nm and a Gaussian slit function of a FWHM of 1 nm for the sensitivity analyses of wavelength and waveband errors. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 109 of 245

110 Figure Ground reflectance spectra for three different vegetation types spectrally convolved using the PRISM band definitions Sensitivity analysis Two slightly different methodologies were used in the case study. Figure shows the scheme employed for analyzing the effects of atmosphere characterization errors on the retrieved plant water contents, while figure presents the scheme for space-instrument characterisation errors. At-satellite spectrum Nominal atmosphere Modified atmosphere True ground spectrum Nominal ground spectrum Modified ground spectrum Nominal plant water content Modified plant water content Figure Scheme for sensitivity analysis with respect to atmosphere characterization errors 30 March 2001 COMMERCIAL IN CONFIDENCE Page 110 of 245

111 At-satellite spectrum Characterisation error Modified at-satellite spectrum Nominal atmosphere Nominal atmosphere True ground spectrum Nominal ground spectrum Modified ground spectrum Nominal plant water content Modified plant water content Figure Scheme for sensitivity analysis with respect to space-instrument characterisation errors The starting point of all analyses is the 'true' ground spectrum. Except for the wavelength and waveband error analyses, ground spectra were convolved to the PRISM band definitions. Using the MODTRAN runs for nominal atmosphere AM6 and ground reflectance values of 2, 6, 10, 20, and 100%, transfer functions for each PRISM band were computed, as shown in figure , to obtain the at-satellite spectrum from the corresponding true ground spectrum. (Tests revealed that additional MODTRAN runs for 60 and 80% ground reflectance are necessary to obtain accurate data for the transfer functions. Hence, MODTRAN runs for both these ground reflectance levels and all atmospheric variations of AM6 were carried out.) Figure Transfer functions for nominal atmosphere AM6 used for converting ground reflectance to at-satellite reflectance. Transfer functions are shown for a set of selected PRISM bands 30 March 2001 COMMERCIAL IN CONFIDENCE Page 111 of 245

112 For investigation of wavelength and waveband errors, true ground spectra for live oak and red willow were convolved using a spectral sampling rate of 1 nm and a Gaussian slit function of 1 nm FWHM. Then, transfer functions for each 1 nm band were computed from the same MODTRAN runs mentioned before. Hence, the resulting at-satellite spectra also have a spectral resolution of 1 nm. Nominal at-satellite spectra were computed by spectral convolution of the high-resolution at-satellite spectra using the PRISM band definitions. The second step in the sensitivity analysis is the computation of the nominal ground reflectance spectrum from the corresponding at-satellite spectrum. The transfer functions of each PRISM band were inverted and then applied. Obviously, the nominal ground reflectance spectra are nearly identical to the true ground spectra. Nevertheless, the nominal ground spectra were used for computing the differentials to include the same numerical effects in the computations, so that any deviation results only from an error in atmosphere or spaceinstrument characterization. Figure presents the at-satellite and nominal ground reflectance spectra for the three different vegetation types in the spectral range used in this study. Figure Ground (+) and at-satellite (*) vegetation spectra from 800 to 1200 nm (PRISM-bands 40-69). Three different atmosphere characterization errors, as discussed in Chapters 4 and 5, were addressed in the case study: columnar water vapour content, visibility and surface height. The corresponding MODTRAN runs for AM6 were inverted to obtain the transfer functions for the modified atmospheres used to compute the modified ground spectra (see figure ). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 112 of 245

113 Five different space-instrument characterisation errors, as discussed in Chapter 5, were analyzed: simple gain error (uniform over the whole spectrum), relative spectral response, stray light, centre wavelength and waveband shift. The simple gain error is estimated by L'=L d, where d equals to 0.9, which corresponds to a 10% underestimation of the reflectance by the sensor. The spectral response error is estimated by L'=L (1-d λ -4 ), where L is the at-satellite spectrum, L' the modified at-satellite spectrum, λ the wavelength (in µm), and d equals to µm 4 in the VNIR and 0 µm 4 in the SWIR, respectively. Modified at-satellite spectra due to stray light errors are computed by L'=L+d L cloud, where L cloud is the reflectance spectrum computed in WP 202 for a cumulus cloud scenario, and d equals to 1% in the VNIR and 0.5% in the SWIR, respectively. Centre wavelength and waveband errors were studied by applying different spectral convolutions to the high-resolution (1 nm spectral sampling) at-satellite spectra. The PRISM band definitions were used in the nominal cases, while additional shifts of ±1 nm for the centre wavelengths respectively the FWHM of each PRISM band where assumed during spectral convolution resulting in the modified at-satellite spectra (figure ). The modified ground spectra are computed from the modified at-satellite spectra by means of the inverted transfer functions for the nominal atmosphere AM6. The final step in the analysis was the application of the retrieval method both on the nominal and the modified ground spectra to obtain the corresponding plant water contents, which can then be compared. 6.2 RESULTS - ATMOSPHERE CHARACTERIZATION ERRORS Water vapour Figures to show the at-satellite spectra and the different ground spectra for 80, 100 and 120% columnar water vapour for the three different vegetation types. Compared to the original ground spectrum, which corresponds to the nominal value of 100% for atmosphere AM6, the resulting ground spectra for the 80% runs reveal a significant underestimation of ground reflectance near or in the water vapour absorption bands, while the 120% runs show the inverse effect. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 113 of 245

114 Retrieved plant water contents presented in Figures to reflect the respective underestimation and overestimation of ground reflectance near or in the water vapour absorption bands by values that are too high in the case of the 80% runs and too low for the 120% runs. The small spectral separation between the water vapour and liquid water absorption bands is the reason for this effect. Figure Live oak ground spectra resulting from atmospheric water vapour column variations. The nominal water vapour column is 100%. Figure Live oak ground spectra resulting from atmospheric water vapour column variations. The nominal water vapour column is 100%. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 114 of 245

115 Figure Lawn ground spectra resulting from atmospheric water vapour column variations. The nominal water vapour column is 100%. Figure Retrieval of plant water contents from live oak ground spectra, with perturbations due to atmospheric water vapour column variations. The nominal water vapour column is 100%. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 115 of 245

116 Figure Retrieval of plant water contents from red willow ground spectra, with perturbations due to atmospheric water vapour column variations. The nominal water vapour column is 100%. Figure Retrieval of plant water contents from lawn ground spectra, with perturbations due to atmospheric water vapour column variations. The nominal water vapour column is 100% 30 March 2001 COMMERCIAL IN CONFIDENCE Page 116 of 245

117 6.2.2 Visibility Figures to show the at-satellite spectra and the different ground spectra for 20, 23 and 26 km visibility for the three different vegetation types. Compared to the original ground spectrum, which corresponds to the nominal value of 23 km, the resulting ground spectra for the 26 km runs reveal a small underestimation of ground reflectance over the whole spectral region, while the 20 km runs show the inverse effect. Figure Live oak ground spectra resulting from visibility variations. The nominal visibility is 23 km. Figures to show that moderate errors in characterization of visibility result in only minor errors of retrieved plant water contents. The reason is that visibility variations do not strongly change the shapes of the resulting ground spectra on which the retrieval method is mainly sensitive. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 117 of 245

118 Figure Red willow ground spectra resulting from visibility variations. The nominal visibility is 23 km. Figure Lawn ground spectra resulting from visibility variations. The nominal visibility is 23 km. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 118 of 245

119 Figure Retrieval of plant water contents from live oak ground spectra, with perturbations due to visibility variations. The nominal visibility is 23 km. Figure Retrieval of plant water contents from red willow ground spectra, with perturbations due to visibility variations. The nominal visibility is 23 km. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 119 of 245

120 Figure Retrieval of plant water contents from lawn ground spectra, with perturbations due to visibility variations. The nominal visibility is 23 km Altitude Errors in surface altitude characterization used in this study show strong effects on the resulting ground spectra as seen in figures to This is mainly because a large fraction of the atmospheric water vapour is located in the lowest parts of the troposphere, so that errors in assumed surface altitude introduce relatively large changes in column water vapour content. The effects of the modeled surface altitude (height) errors on retrieved plant water contents are presented in figures to Water vapour absorption not correctly considered during atmospheric correction is wrongly attributed to higher liquid water absorption, and therefore leads to higher plant water contents. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 120 of 245

121 Figure Live oak ground spectra resulting from surface height variations. The nominal height is 0 km a.s.l.. Figure Red willow ground spectra resulting from surface height variations. The nominal height is 0 km a.s.l.. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 121 of 245

122 Figure Lawn ground spectra resulting from surface height variations. The nominal height is 0 km a.s.l.. Figure Retrieval of plant water contents from live oak ground spectra with perturbations due to resulting from surface height errors. The nominal height is 0 km a.s.l. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 122 of 245

123 Figure Retrieval of plant water contents from red willow ground spectra with perturbations due to resulting from surface height errors. The nominal height is 0 km a.s.l. Figure Retrieval of plant water contents from lawn ground spectra with perturbations due to resulting from surface height errors. The nominal height is 0 km a.s.l. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 123 of 245

124 6.3 RESULTS - SPACE-INSTRUMENT CHARACTERISATION ERRORS Simple gain error Figures to show the effects of a simple gain error of -10% both on the atsatellite and the corresponding ground spectra of the three vegetation types. As expected, the modified ground spectra show a nearly linear reduction in reflectance of 10%, hence the shapes of the spectra are not strongly affected. Figure Live oak ground (+) and at-satellite (*) spectra showing the effect of a simple gain error of -10%. Retrieved plant water contents, figure to 6.4-6, show only minor variations due to the simple gain error. Most of the observed changes are attributed to differences in partial blocking, i.e. the offset terms in the regressions are changed, while the slopes of the regression lines, i.e. the plant water contents, remain stable. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 124 of 245

125 Figure Red willow ground (+) and at-satellite (*) spectra showing the effect of a simple gain error of -10% Figure Lawn ground (+) and at-satellite (*) spectra showing the effect of a simple gain error of -10% 30 March 2001 COMMERCIAL IN CONFIDENCE Page 125 of 245

126 Figure Retrieval of plant water contents from live oak ground spectra showing the effect of a -10% simple gain error Figure Retrieval of plant water contents from red willow ground spectra showing the effect of a -10% simple gain error 30 March 2001 COMMERCIAL IN CONFIDENCE Page 126 of 245

127 Figure Retrieval of plant water contents from lawn ground spectra showing the effect of a -10% simple gain error Relative spectral response Figures to present the results for the relative spectral response error. The relatively small at-satellite reflectance error of -0.5% at 1000 nm, which is increasing to -1.2% at 800 nm, results in ground reflectance errors with nearly the same spectral characteristics. Although the calibration error does not strongly affect the ground reflectance curves, the effects on the retrieved plant water contents, shown in figure to , are significantly stronger than in the case of the simple gain error. This is due to the systematic spectral effect (the spectra are tilted) caused by this kind of calibration error. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 127 of 245

128 Figure Live oak ground (+) and at-satellite (*) spectra showing the effect of a relative spectral response error (see text) Figure Red willow ground (+) and at-satellite (*) spectra showing the effect of a relative spectral response error (see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 128 of 245

129 Figure Lawn ground (+) and at-satellite (*) spectra showing the effect of a relative spectral response error (see text) Figure Retrieval of plant water contents from live oak ground spectra showing the effect of a relative spectral response error (see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 129 of 245

130 Figure Retrieval of plant water contents from red willow ground spectra showing the effect of a relative spectral response error (see text) Figure Retrieval of plant water contents from lawn ground spectra showing the effect of a relative spectral response error (see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 130 of 245

131 6.3.3 Stray light The effects of a stray light error on the at-satellite and ground spectra are presented in Figures to In general, ground reflectance errors are larger than in the case of the spectral response error, but do not reveal a clear spectral tendency besides a more pronounced increase of ground reflectance in the VNIR. The effects on the retrieval of plant water contents, shown in figures to , are stronger than in the case of the simple gain error, though less than in the case of the relative spectral response error. An interesting result is that the accuracy of the plant water content as inferred from the σ and r 2 values (summarised in tables to 6.4-3) is not negatively affected by stray light, in the lawn and willow cases. Figure Live oak ground (+) and at-satellite (*) spectra showing the effect of a stray light error (see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 131 of 245

132 Figure Red willow ground (+) and at-satellite (*) spectra showing the effect of a stray light error (see text) Figure Lawn ground (+) and at-satellite (*) spectra showing the effect of a stray light error (see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 132 of 245

133 Figure Retrieval of plant water contents from live oak ground spectra showing the effect of a stray light error (see text) Figure Retrieval of plant water contents from red willow ground spectra showing the effect of a stray light error (see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 133 of 245

134 Figure Retrieval of plant water contents from lawn ground spectra showing the effect of a stray light error (see text) Wavelength and waveband errors Figures and present the spectra for live oak and red willow after introducing a shift of ±1 nm for the centre wavelengths of each PRISM band. The spectra without these errors are shown at high spectral resolution (spectral sampling 1 nm). Figures and show the same spectra for changes of ±1 nm in the FWHM of each PRISM band. The wavelength and waveband errors have effects mainly around the water vapour absorption bands. The effects of wavelength errors on the resulting ground spectra are much stronger than those induced by waveband errors, although the general spectral characteristics are comparable. The effects on retrieved plant water contents are very strong in the case of centre wavelength shifts, shown in figures and , since the shapes of the spectra are significantly changed in parts of the spectrum where liquid water absorption takes place. Waveband errors do not have a strong influence on the retrieved plant water contents, as shown in figure and , but the predicted accuracy of the retrieved values is reduced. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 134 of 245

135 Figure Live oak ground and at-satellite spectra with wavelength changes (high resolution spectra for distributions without waveband changes, see text) Figure Red willow ground and at-satellite spectra with wavelength changes (high resolution spectra for distributions without waveband changes, see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 135 of 245

136 Figure Retrieval of plant water contents from live oak ground spectra, with wavelength errors Figure Retrieval of plant water contents from red willow ground spectra, with wavelength errors 30 March 2001 COMMERCIAL IN CONFIDENCE Page 136 of 245

137 Figure Live oak ground and at-satellite spectra with waveband changes (high resolution spectra for distributions without waveband changes, see text) Figure Red willow ground and at-satellite spectra with waveband changes (high resolution spectra for distributions without waveband changes, see text) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 137 of 245

138 Figure Retrieval of plant water contents from live oak ground spectra, with waveband errors Figure Retrieval of plant water contents from red willow ground spectra, with waveband errors 30 March 2001 COMMERCIAL IN CONFIDENCE Page 138 of 245

139 6.4 OVERVIEW OF THE CASE STUDY RESULTS An overview of the results of the sensitivity analyses for the three different vegetation types is presented in Tables to The tables include: the retrieved plant water content d (in cm), the relative error of d with respect to the nominal value, the percentage r 2 of the variance in ln(r) given by the regression model, and the predicted rms error σ (in cm) for the retrieved d. The tables give these values for each kind of atmosphere/instrument characterisation error. Nominal values are retrieved with no added atmosphere or instrument errors. The three different vegetation types have different plant water contents, and the retrieval method has different accuracy in the three cases. However, the analysis of sensitivity to errors in atmosphere and instrument characterisation shows similar effects in the three cases. A comparison of the results should consider not only the actual errors in the retrieved plant water content, but also the predicted accuracy and confidence levels derived from σ and r 2 values. A good example for this requirement is given by the results for stray light error in the live oak case. The calculated error from nominal is only 4.7% (see table 6.4-2), but the predicted rms error is much larger, indicating that low confidence is justified. Lawn error source d (in cm) rel. error r 2 σ (in cm) Nominal value H 2 O 80% % default 100% 120% % Visibility 5 km % (default 23 km) 20 km % km % km % Height a.s.l. 500 m % (default 0 m) 1000 m % m % m % Simple gain error L'=L d, d= % Relative spectral response error Stray light L'=L (1-d λ -4 ) d=0.005 µm 4 in VNIR d=0 µm 4 in SWIR L'=L+d L cloud d=0.010 in VNIR d=0.005 in SWIR % % Table Overview of the results for the lawn spectrum 30 March 2001 COMMERCIAL IN CONFIDENCE Page 139 of 245

140 Live oak error source d (in cm) rel. error r 2 σ (in cm) Nominal value H 2 O 80% % (default 100%) 120% % Visibility 5 km % (default 23 km) 20 km % km % km % Height a.s.l. 500 m % (default 0 m) 1000 m % m % m % Simple gain error L'=L d, d= % Relative spectral response error L'=L (1-d λ -4 ) d=0.005 µm 4 in VNIR d=0 µm 4 in SWIR % Stray light L'=L+d L cloud % d=0.010 in VNIR d=0.005 in SWIR Wavelength error 1 nm % nm % Waveband error 1 nm % nm % Table Overview of the results for the live oak spectrum Red willow error source d (in cm) rel. error r 2 σ (in cm) Nominal value H 2 O 80% % (default 100%) 120% % Visibility 5 km % (default 23 km) 20 km % km % km % Height a.s.l. 500 m % (default 0 m) 1000 m % m % m % Simple gain error L'=L d, d= % Relative spectral response error L'=L (1-d λ -4 ) d=0.005 µm 4 in VNIR d=0 µm 4 in SWIR % Table Overview of the results for the red willow spectrum 30 March 2001 COMMERCIAL IN CONFIDENCE Page 140 of 245

141 Stray light L'=L+d L cloud % d=0.010 in VNIR d=0.005 in SWIR Wavelength error 1 nm % nm % Waveband error 1 nm % nm % Table Overview of the results for the red willow spectrum cont d 6.5 CONCLUSIONS FROM THE CASE STUDY Looking on atmosphere characterization errors, the model results must be interpreted with respect to realistic values during image acquisition by PRISM. A realistic estimate for the relative error in columnar water vapour may be 10%; however this will generally require PRISM data analysis with special focus on water vapour absorption. An error of 3 km for the visibility, i.e. the value used in the sensitivity study, is regarded to be realistic. Using a highquality digital elevation model and an accurate co-registration of the PRISM image, it should be possible to reduce the surface altitude error to 50 m or even less. Based on these realistic error assumptions, a ranking of the relative importance of the atmosphere characterization errors for retrieving plant water contents from atmospherically corrected PRISM spectra is possible: columnar water vapour, surface altitude, visibility. If height errors are reduced to smaller, but realistic values, and other assumed errors are considered to be realistic, the ranking of importance for instrument and atmosphere characterisation errors is: 1. centre wavelength, 2. atmospheric water vapour content, 3. relative spectral response, 4. surface altitude, 5. stray light errors, 6. visibility, 7. wavebands, 8. simple gain error. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 141 of 245

142 7 CONCLUSIONS 7.1 COMPARISON OF CONTRIBUTIONS TO GROUND-REFLECTANCE ERRORS It is difficult to make a simple comparison of the effects of the different instrument and atmosphere characterisation errors, because the effects have different spectral profiles and different relationships to true ground reflectance values. For example it is difficult to compare the effects of wavelength calibration errors with the effects of stray light. Wavelength error effects are small in most spectral bands but large in a substantial minority of bands; errors due to stray light or simple gain errors tend to be larger, but are much more smoothly distributed through the spectrum. Again, some characterisation errors give ground reflectance errors that are approximately proportional to true ground reflectance values (e.g. gain error effects), while others, like dark signal, give effects that are approximately independent of true ground reflectance. One obvious conclusion is that the relative importance of the different characterisation errors will be dependent on individual data products, and on the algorithms used to retrieve them. However, it appears reasonable to make some rough comparisons, on the basis only of errors in ground reflectance values. Table lists average ground reflectance errors for the midlatitude Summer case, with ground reflectance fixed at 10%. In this table, the averages are given as both: average of absolute values (signs removed), and root mean square. These results include all the nominal PRISM spectral bands except for bands 80, 81 and 82, where atmosphere absorption makes most results unusable. In table 7.1-2, we assign typical errors in order to provide a basis for comparison of the effects of different characterisation error. The errors are mainly derived from the averages listed in table for 10% ground reflectance, in the mid-latitude Summer scenario. The value assigned to visibility is increased, since at 10% ground reflectance, the error component due to atmosphere transmission tends to balance the component due to atmosphere radiance. Table includes a rating for the relative difficulty of achieving ground-reflectance accuracy, with respect to each aspect of instrument and atmosphere characterisation. The rating is given from 1 to 10, with 10 representing the greatest difficulty. In some cases, there is a realistic option to avoid in-flight characterisation by taking measures in design, construction and qualification that are needed to ensure that there are no relevant changes after pre-flight characterisation. For example, we may prefer to avoid in-flight characterisation for wavebands by ensuring the spectrometer will not defocus significantly after pre-flight characterisation - trading a stringent qualification program against an in-flight measurement. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 142 of 245

143 Aspect of characterisation Characterisation error Average absolute reflectance error Rms reflectance error Instrument gain 2% 0.24% 0.25% dark signal 100 electrons 0.05% 0.08% stray light 1% (cloud) 0.58% 0.72% linearity 1% 0.38% 0.39% wavelength 1nm 0.17% 0.34% waveband 1nm 0.05% 0.13% Atmosphere height 100m 0.09% 0.20% visibility -3km at % 0.09% water vapour 10% 0.15% 0.34% Table Average ground reflectance errors at 10% ground reflectance, mid-latitude Summer Aspect of characterisation Nominal characterisation error Typical reflectance error produced Difficulty rating (out of 10) for characterisation or qualification Instrument gain 2% 0.25% 10 dark signal 100e % 2 stray light 1% (cloud) 0.7% 4 linearity 1% 0.4% 4 wavelength 1nm 0.25% 4 waveband 1nm 0.08% 6 Atmosphere height 100m 0.17% 3 visibility -3km at % 4 water vapour 10% 0.25% 5 Table Relative importance/difficulty of characterisation functions Instrument characterisation and qualification The most significant characterisation problem for the space instrument appears to be in-flight characterisation of instrument gain usually called absolute calibration. It has been found difficult to provide 2% accuracy with high confidence. Comparable dark level characterisation, and also characterisation of electronics offsets, are likely to be easy (but must be addressed). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 143 of 245

144 Stray light, linearity and wavelength calibration present intermediate problems: In-flight characterisation for the instrument stray light function is not obviously needed, but a simple check for changes after pre-flight characterisation is desirable. For an instrument on an agile platform, a simple check may be fairly easy, using the sun as an out-of-field source. Good pre-flight characterisation for linearity is essential. There are relatively easy methods to check for linearity changes in flight, which may be preferred to fairly extensive programs of work to prove that no significant changes will occur. In-flight calibration for wavelength is likely to be considered necessary. There are several possible methods. will not be extremely difficult. If requirements on waveband calibration are relaxed to around ±2nm, it may be considered reasonable to avoid in-flight characterisation by a qualification programme to prove spectrometer stability. However, in-flight characterisation should be considered as an alternative to a stringent qualification requirement Atmosphere characterisation comparison In general, the ground reflectance errors generated by typical uncertainties in atmosphere characterisation are comparable with the ground reflectance errors that will be produced by uncertainties in response of the space instrument if the current radiometric requirements on the space instrument are retained. The review of atmosphere-generated errors does not present a clear case for either relaxation or enhancement of the required instrument performance. 7.2 INSIGHTS FROM THE CASE STUDY The ranking of importance of characterisation errors, given in section 6.5 for one particular case study, is somewhat different to the ranking that would be derived from a simple study of ground reflectance errors. Table gives a comparison, with the case-study results scaled to the characterisation errors assumed for the ground-reflectance errors calculations. (Note that the effects of linearity error were not calculated for the case study, and the effects of a relative spectral response error were not calculated for ground reflectances. Atmosphere characteristics are shown in italics to distinguish them from instrument characteristics.) Striking differences include the low ranking of simple gain error and stray light for the case study, while these are among the top three error-generators for ground reflectance errors (at the levels of characterisation errors assumed). This shows, as we should perhaps expect, that characterisation errors with a bland spectral distribution have relatively little effect on the higher-level product. Plant water content (probably in common with many other data products) is derived from the shape of the spectral distribution, rather than from its absolute level. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 144 of 245

145 Ranking For effects on ground reflectance For effects on plant water content 1 Stray light (1%,.5%) Wavelength (1nm) 2 Linearity (1%) Water (10%) 3 Gain (2%) Height (100m) 4 Wavelength (1nm) Relative spectral response (1.5% in 800 to 1200nm range) 5 Water vapour (10%) Stray light (1%,.5%) 6 Height (100m) Waveband (1nm) 7 Visibility (-3km) Visibility (-3km) 8 Waveband (1nm) Gain (2%) Table Comparison of ranking of error importance case study and ground reflectance In contrast, wavelength, height and water vapour errors are more highly ranked for importance in the case study. The wavelength and water vapour errors both generate strong spectral structure resolved by PRISM, that would be expected to corrupt the algorithm for derivation of plant water content. (The main effect of height error is to introduce errors in the water vapour column content.) It is also notable that the relative spectral response error, calculated only for the case study, was significantly more important than the absolute response (gain) error. It is of some interest that waveband errors introduce very low errors in plant water content (compared particularly with wavelength errors). However, waveband errors significantly reduce confidence in the results of the retrieval, as indicated by the r 2 values. It is essential to note that only one case study has been performed, and that no very rigid conclusions can be drawn from it. The case study used wavebands only in the range 800nm to 1200nm, which avoids most effects due to Rayleigh scatter. In the visible region, simple errors in gain characterisation will introduce significant relative spectral variations in groundreflectance errors. We would therefore expect simple gain errors to assume greater importance when short wavebands are used. 7.3 IN-FLIGHT CHARACTERISATION REQUIREMENTS AND METHODS In-flight calibration requirements that appear to be essential, given the present specification on PRISM performance, are summarised in the following sections, with notes on methods Dark level and offset errors drift and non-uniformity Dark levels and other offset levels will be very dependent on detection system design. However, it is likely that dark level characterisation measurements will be considered necessary or very desirable. Measurements will probably include:! Recording of full dark-field images at intervals typically of days, and! Recording of masked pixel signals with all other image and characterisation data. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 145 of 245

146 In-flight dark field characterisation will generally be quite easy for the solar spectral bands, providing no clear motive to seek a significant relaxation of requirements Absolute spectral response (gain) and relative spectral response It will be necessary to monitor absolute spectral response of the instrument in flight, mainly to take account of changes in optics transmission through life in orbit. The measurements may be performed at relatively infrequent intervals at least a few days and possibly months following an initial commissioning period. Accuracy required It is not clear from the study results that the current requirement on absolute accuracy (±2%) is justified in terms of effects on higher level products, since only one has been studied, and this one shows small effects. There is an indication that spectral variations in response may be more significant. More detailed work on data products may indicate that a tighter specification is required on relative spectral response over limited spectral ranges, perhaps with a more relaxed absolute requirement. However, at present it is not possible to make a clear case for modification of the requirements on absolute response, which in effect include requirements on relative spectral response. The requirement on the instrument remains difficult. PRISM baseline method The most recent proposal for PRISM is to use a sun-illuminated diffuser, that is protected by a filter wheel when not in use, and viewed via the pointing/calibration mirror rotated in-plane. A second diffuser is provisionally proposed this will be used less frequently than the first to detect changes due to sun-exposure. Both diffusers will have long baffles. Problems presented by on-board hardware include:! The diffusers must fill the aperture of the optical system, which dictates a fairly large scale for the calibration system, including diffusers, filter wheel movement and baffles.! The method requires two movements coarse movement of the pointing/calibration mirror, and a filter wheel.! There is no method of monitoring common-mode changes in degradation of the two diffusers. It is doubtful that the method offers 2% accuracy at useful confidence levels.! The method does not cover changes in reflectance of the pointing mirror with acrosstrack pointing angle. Vicarious calibration is also suggested (at example sites: White Sands, USA; La Crau, France; Dunhang, China). It is also suggested that long-term changes in response may be monitored over sites expected to be stable (North African and Saudi Arabian deserts). Use of Rayleigh scatter over oceans is suggested as a possible source for the visible band. Comments 30 March 2001 COMMERCIAL IN CONFIDENCE Page 146 of 245

147 Based on an analysis of predictable errors, the present baseline method using two full aperture diffusers can probably meet the current PRISM requirements. However it does not offer a high confidence level, because there is no independent check, except vicarious calibration, on common-mode degradations of the diffusers. Similar complexity would apparently allow a ratioing method to be used for example as described in Appendix C. Such methods would provide a check for degradation in flight, and should be considered. Vicarious calibration has some potential to reduce the complexity of the in-flight hardware, if it is finally included in the mission plan. The best accuracy predicted for vicarious calibration is not quite adequate to meet existing requirements. However, with some relaxation of the absolute response requirement possibly with a new specification on relative spectral response across limited spectral regions it may be found possible to adopt a simpler onboard system, relying on vicarious calibration for occasional re-validation Linearity Linearity measurements should certainly be made pre-flight. It will be desirable to include some in-flight measurements. However, the method should be kept simple, since it is likely that no changes will be detected. To be useful, linearity measurements should be made at radiance levels over the specified range, to accuracies better than ±0.5% of each level. There are several possible methods for in-flight measurement on linearity. A strong candidate is use of internal sources for example IR-emitting diodes close to each focal plane. Such internal sources can be switched on for controlled periods to check for linearity changes after pre-flight calibration. The same sources can be used for simple functional tests during and after platform integration Response non-uniformity Response non-uniformity must be characterised in flight and calibrated in order to meet requirements on spatial radiometric accuracy. It is desirable to measure response non-uniformity to <<0.5% rms. In practice, response non-uniformity will probably be measured using the absolute calibration source a diffuser will be expected to provide radiance levels that are very uniform over the small instrument field. In-flight characterisation for response non-uniformity does not apparently add substantially to the cost of absolute response characterisation. (However, it could inhibit some possible simplifications of the absolute measurement hardware.) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 147 of 245

148 7.3.5 Stray light Pre-flight characterisation is essential. Instrument stray light coefficients will probably not change significantly after pre-flight characterisation, though an in-flight check is desirable in principle to improve confidence. Performance required The stray light performance demanded by the PRISM specification on performance over nonuniform scenes remains very difficult. A significant part of the budget appears to be needed to account for simple diffraction. It will be necessary to control production and testing of every optical surface and every coating to ensure that most surfaces have TIS (total integrated scatter) <0.1%. Care in design will also be required to avoid significant double-reflections (particularly including the detector, filters and the entrance slit) and scatter from structures. Comment Stray light appears to have relatively small effects on errors in ground-reflectance values. A relaxation of the requirement should considered. A large part of the stray light budget is required to account for simple diffraction. A useful relaxation of requirements might therefore take the form of an increase in separation of the target area from the bright areas, for example from 10 pixels to say 20 pixels. There is a marginal case for checking instrument stray light characteristics in flight. This would probably be done using a large rotation of the platform to point near (but not at) the sun Spectral response calibration - wavelengths Wavelength calibration of the instrument (location of spectral response function centrewavelengths) is likely to shift on launch, so that in-flight characterisation will probably be considered necessary. In principle, measurements may be made at only one wavelength for each of the two solar detectors (VNIR and SWIR). Accuracy required Wavelength calibration to ±1nm is at present required. The study shows significant sensitivity to errors in wavelength calibration. Errors in the region of 1nm are severe for the case study on plant water content, indicating that the requirement should not be further relaxed, and should probably be made more stringent for example to ±0.5nm. Comment Correction of smile (field-variation of wavelength calibration) in the spectrometer is probably feasible to around 0.1nm. Calibration to either 1nm or 0.5nm probably requires an in-flight check for at least one wavelength in the VNIR channel and one wavelength in the SWIR channel. It is therefore not clear that a more stringent specification on wavelength calibration will have a substantial impact on cost of development. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 148 of 245

149 There are several reasonable approaches to in-flight spectral calibration, discussed in detail in Appendix D Spectral response calibration - wavebands (spectral widths) Wavebands defined by detector rows may be changed by defocus in the spectrometer. The PRISM system would work at about f/5, so that, on a simple geometrical model, 0.01mm of defocus will produce about 1/10 pixels of defocus, changing the waveband by about 1nm in near IR and SWIR bands. Accuracy required Spectral widths are at present required to be known to 1nm. The study indicates that ground reflectance errors, due to waveband errors of 1nm, are a factor 3 to 4 smaller than the errors due to a 1nm wavelength shift. It may be considered reasonable to relax the requirement on knowledge of wavebands to ±2nm (to be consistent with a ±0.5nm requirement on wavelengths). Comment Unless the instrument is calibrated in flight for wavebands, there will be a fairly stringent requirement on stability of the spectrometer optics and detectors, after pre-flight calibration. Manufacturers will probably opt for stability, proved by a qualification programme, rather than for in-flight characterisation. However, an in-flight check on wavebands is in principle desirable. Some relatively simple methods are reviewed in Appendix D. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 149 of 245

150 APPENDIX A - SELECTION OF DATA PRODUCTS FOR ANALYSIS OF EFFECTS OF INSTRUMENT AND ATMOSPHERE CHARACTERISATION ERRORS A.1 INTRODUCTION This appendix describes the initial selection of five data products to be used in analysis of the effects of instrument and atmosphere characterisation errors on the derivation of geophysical variables from the hyperspectral images expected from the PRISM sensor. The following selection criteria for suitable data products and the corresponding retrieval algorithms were applied: Data products should be of relevance for the Land Surface Processes and Interactions Mission within the ESA Earth Explorer Programme. Data products should be geophysical variables, i.e. they are physical quantities that can be measured in nature, and show a continuum of values over a certain range. Algorithms for retrieving data products from hyperspectral images must already be available and clearly described in literature. Data products and algorithms should cover a significant part of the spectrum of geoscientific utilisation of hyperspectral image data. The data products selected are: Atmospheric water vapour Snow grain size Soil fraction Leaf area index Plant water content These data products are discussed below, with their retrieval algorithms, in Chapters A.2 through A.6. A.2 ATMOSPHERIC WATER VAPOUR General remarks Accurate measurement and prediction of the amount of atmospheric water vapour is an important task for remote sensing applications, because water vapour is one of the main driving forces in the global atmospheric circulation, and is mainly involved in mesoscale air transport processes. The sensors of the currently available imaging spectrometers (e.g. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 150 of 245

151 AVIRIS) provide hyperspectral data in up to hundreds of bands in the visible and near infrared part of the electromagnetic spectrum (usually between 400 and 2450 nm) in higher spectral and spatial resolutions compared to the current operational systems for water vapour detection (AVHRR, GOES, ATSR, Meteosat, DMSP). Beside its influence on atmospheric processes, water vapour data are relevant for atmospheric correction of multi- and hyperspectral images. Standard atmosphere profiles used in numerical models like MODTRAN are in many cases not sufficient for an accurate correction of water vapour influences on satellite measurements of surface variables to be studied e.g. in the Land Surface Processes and Interactions Mission by using PRISM data. Algorithmic approach Optical measurement of atmospheric trace gases is performed using selected sensor channels in bands or lines of the absorption spectrum. To quantify water vapour (like other trace gases) by determining the total amount of water vapour in an atmospheric column (in kg m 2 ), differential absorption techniques (Schläpfer 1998) are applied. The ratio between channels influenced by water vapour, i.e. within the absorption band (measurement channels), and non-influenced channels on the sides of the band (reference channels) is related to the apparent transmittance, which depends on water vapour column. Reference channels are used for a simplified continuum removal. There are various methods which differ from one another in number of selected channels and calculation techniques. Evaluation factors, each representing an important channel property and considering the whole spectral range of one or more absorption feature, are defined for all channel criteria. The single factors, scaled between 0 and 1, are then multiplied which defines common qualification equations for both channels. Table A.2-1 shows an example for channel selection results from AVIRIS data (Schläpfer 1998). Reference channels: located close to absorption features with relatively high transmittance. not influenced by any atmospheric species, signal to noise ratio as large as possible. Evaluation factors: transmittance, radiance uncertainty. Measurement channels: lie within absorption bands, must be sensitive to variations of water vapour amount, difference between the signal of the absorbing gas and the noise should be clearly discernible, other atmospheric species must not disturb the signal. Evaluation factors: sensitivity, significance, cross-sensitivity. AVIRIS 1991 AVIRIS 1995 Measurement channels 910 nm, nm nm reference channels nm, nm nm, nm Table A.2-1 Channel selection results from AVIRIS data (Schläpfer et al. 1998). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 151 of 245

152 In general, a ratioing between the radiance at channels within the absorption feature (measurement channels) and an interpolated radiance of channels in its vicinity (reference channels) is performed. The two major techniques for hyperspectral imaging spectroscopy are: The Narrow/Wide technique (N/W, Frouin et al. 1990) and the Continuum Interpolated Band Ratio (CIBR, Green et al. 1989). All differential absorption techniques are based on a direct relationship between apparent atmospheric transmittance and the ratio numbers R; R = L L s s, PW =0 τ wv where L s is the total radiance at sensor, PW the precipitable water column, and τ wv the total apparent path transmittance of water vapour. An enhanced differential absorption technique, based directly on the radiative transfer equations, was developed by Schläpfer (1998), the Atmospheric Precorrected Differential Absorption technique (APDA). The main feature of APDA is an atmospheric precorrection term which accounts for the reflectance of the observed pixel, the effect of the terrain slope ( cosine effect ) and the path scattered radiance reflected by the adjacent area: τ wv R APDA = LIR [ Lm Latm, m ] i [ λ ],[ L L ] ( r ) j r atm, r [ ]i j λ m The expression LIR([λ r ],[L r]) denotes the linear regression line defined by the reference points (λ r, L r ) which is evaluated at the central wavelength λ m (cf. figure A.2-1). Parameters in brackets are the centre wavelengths and atmospheric pre-corrected radiances of i measurement channels and j reference channels, respectively. Index m denotes a measurement channel, index atm the atmospheric path. See Schläpfer (1998) for a detailed description of the APDA technique. Usually, an exponential approach is used to relate the differential absorption ratio number R to the corresponding water vapour column. Schläpfer (1998) proposed an extended equation with three empirical regression parameters k, b, and c: ( c+ k ( PW ) ) τ wv RAPDA = e. b 30 March 2001 COMMERCIAL IN CONFIDENCE Page 152 of 245

153 Solved for water vapour column PW, the above equation gives ln( RAPDA ) + c PW ( RAPDA) =. k 1 b Figure A.2-1 Schematic view of the APDA technique in an absorption band (adapted from Schläpfer 1998). Literature Frouin, R., Deschamps, P.-Y., and Lecomte, P., 1990: Determination from Space of Atmospheric Total Water Vapour Amounts by Differential Absorption Near 940 nm: Theory and Airborne Verification, J. of Appl. Meteorology, 29, Green, R. O., Carrère, V., and Conel, J. E., 1989: Measurement of Atmospheric Water Vapour Using the Airborne Visible/Infrared Imaging Spectrometer, Workshop Image Processing, ASPRS, Sparks (NV), pp. 6. Schläpfer, D., 1998: Differential Absorption Methodology for Imaging Spectroscopy of Atmospheric Water Vapour, PhD thesis, University of Zurich, Zurich. Schläpfer, D., Borel, C. C., and Keller, J., 1998: Atmospheric Precorrected Differential Absorption Technique to Retrieve Columnar Water Vapour, Remote Sensing of Environment, 65, (3), March 2001 COMMERCIAL IN CONFIDENCE Page 153 of 245

154 A.3 SNOW GRAIN SIZE General remarks Snow has the highest albedo of any natural and spatially extensive surface and plays an important role in the Earth s radiation balance. Additionally, the area extent of snow cover is likely to be a sensitive indicator of climate change. Spatial distributions of snow-covered area (SCA) are crucial inputs to models of various subjects such as hydrology, alpine climates, snowmelt, etc. Therefore it is necessary to monitor SCA and other snow properties at different temporal and spatial scales. Particularly snow grain size is of interest, since it is one of the most sensitive variables with respect to processes within the snow cover, and moreover, it controls radiative fluxes at the snow-atmosphere interface. Algorithmic approach The spectral signature of pure snow is primarily sensitive to grain size at the snow surface. An increase in particle size lets visible reflectance unchanged while near infrared and short-wave infrared reflectance decreases (cf figure A.3-1). Snow covered mountainous regions often exhibit large surface grain size gradients driven by changes in air temperature and incident solar radiation. The sensitivity of the spectral signature to particle size translates these grain size gradients into spectral gradients. It was shown by Painter et al. (1998a) (figure A.3-2) that a suite of snow endmembers varying with grain size is required to map SCA and grain size with spectral mixture analysis. Figure A.3-1 Directional hemispherical reflectance of snow for illumination angle of 0 and grain radii r = µm (adapted from Painter et al. 1998a) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 154 of 245

155 Spectral mixture analysis is based on the set of equations defined by: R c = N i= 1 F R i + E i, c c, where R c is the apparent surface reflectance in AVIRIS band c, F i is the fraction of endmember i, T i,c is the reflectance of endmember i, R i,c is the reflectance of endmember i in AVIRIS band c, N is the number of spectral endmembers, and E c is the residual error in AVIRIS band c for the fit of the N endmembers. The residual error E c is a rearrangement of the linear mixture model: E c = R c N i= 1 F R i i, c Analysis of residuals reveals the spectral locations of errors in modelling the measured spectrum. The quality of the spectrum-wide fit by the mixture model is the average root mean squared (RMS) error: = M RMS M E c, c= 1 where M is the number of AVIRIS bands in the spectral mixture analysis. The shadenormalised snow fraction f s then provides the estimate of subpixel snow-covered area (SCA): f s = F s F s + F v + F r Fs = 1 F shade where F s is the spectral snow fraction, F v is the spectral vegetation fraction F r is the spectral rock fraction and F shade is the spectral shade fraction. A mixture simulation of grain size and snow fraction with a pure quartz spectrum (Painter et al. 1998a) showed that the proper grain size-snow endmember is necessary to spectrally characterise and accurately estimate the subpixel snow-covered area for a pixel containing snow. The Multiple EndMember Snow Covered Area and Grain size (MEMSCAG) automated algorithm presented by Painter et al. (1998b) is based on the Multiple Endmember Spectral Mixture Analysis (MESMA) (Roberts et al. 1998). N endmember models are run, in which the first N-1 endmembers are physical constituents (snow, vegetation, rock etc.) and the N th endmember is photometric shade. A pixel must fulfil the following constraints to be accepted for the model: RMS error < 2.5%, no 7 consecutive residuals can exceed 2.5%, and spectral fractions must be between 0.01 and It is possible for each N that multiple models meet the constraints for some pixels (overlapping 30 March 2001 COMMERCIAL IN CONFIDENCE Page 155 of 245

156 models). To select the optimal model, minimum RMS error is used. To select from overlapping models across varying N, initially established priority selections are used. Snow grain size determination is based on absorption feature at 1.03 µm (Nolin 1993). The depth of the absorption feature directly corresponds to the diameter of ice particles in the surface layer of snow. Since single band estimates are suspect due to instrument errors, Nolin computes the area of the absorption feature instead of its depth by calculating a continuumscaled band depth (as per Clark and Roush 1984) for each AVIRIS channel in the absorption feature. Calibrated Radiance App. Surface Reflectance (MODTRAN) Spectral library 2 endmembers 3 endmembers 4 endmembers constraints constraints constraints RMS < 2.5% 7 resid < 2.5% -0.01<f<1.01 sca/grain size sca/grain size sca/grain size Priority sorting SCA grain size veg rock/soil other Figure A.3-2 Flowchart of the MEMSCAG algorithm (adapted from Painter et al. 1998b) Literature Clark, R. N. and Roush, T.L., 1984: Reflectance Spectroscopy: Quantitative Analysis Techniques for Remote Sensing Applications, Journal of Geophysical Research, 89, Nolin, A., 1993: Radiative Heating in Alpine Snow, PhD thesis, University of California, Santa Barbara. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 156 of 245

157 Painter, T. H., Roberts, D. A., Green, R. O., and Dozier, J., 1998a: The Effect of Grain Size on Spectral Mixture Analysis of Snow-Covered Area from AVIRIS Data, Remote Sensing of Environment, 65, (3), Painter, T. H., Roberts, D. A., Green, R. O., and Dozier, J., 1998: Automated subpixel snow parameter mapping with AVIRIS data, in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1998 Workshop Proceedings, Jet Propulsion Laboratory, Pasadena, California. Roberts, D. A., Gardner, M., Church, R., Ustin, S., Scheer, G., and Green, R. O., 1998: Mapping Chaparral in the Santa Monica Mountains Using Multiple Endmember Spectral Mixture Models, Remote Sensing of Environment, 65, (3), A.4 SOIL FRACTION General remarks As the interface between the atmosphere and solid earth, soils mark a dynamic region for the formation, evolution, and exchange of gases, organic compounds, and mineral constituents. Therefore, a comprehensive inventory of soil types and their spatial distribution is an important contribution to understand the implications of soil processes at global and regional scales. Compared to imaging systems like TM, hyperspectral sensors like AVIRIS are capable to monitor and detect continuous broad spectral changes, characteristic for soil spectral evolution, as well as the sharp absorption features of clay mineralogy, which are important in characterising soils. Algorithmic approach Spectral Mixture Analysis (SMA) provides a tool of analysing images to extract compositional information based on field measured reference spectra or/and spectral libraries. It is a means of determining the relative abundances of materials depicted in hyperspectral imagery based on the materials' spectral characteristics. The reflectance of each pixel is assumed to be a combination of the reflectance of each material (or endmember) present within the pixel. A composition of different (soil) endmembers each representing spectrally distinct surface materials will be investigated according to their behaviour in changes of fractional portion, atmospheric correction (MODTRAN), and sensor calibration (SIRA) (cf also chapter 3). Literature Mustard, J. F., 1991: Distributions of Soil, Rock and Grass in the Western Foothills of the Sierra Nevada, in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1991 Workshop Proceedings, Jet Propulsion Laboratory, Pasadena, pp Fischer, A. F. III, 1991: Mapping and Correlating Desert Soils and Surfaces with Imaging Spectroscopy, in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1991 Workshop Proceedings, Jet Propulsion Laboratory, Pasadena, pp Gillespie, A. R., Smith, M. O.. Adams, J.B. Willis, S.C., Fischer III, A. F. and Sabol, D.E., 1990: Interpretation of residual images: Spectral mixture analysis of AVIRIS images, Owens 30 March 2001 COMMERCIAL IN CONFIDENCE Page 157 of 245

158 Valley, California, in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1990 Workshop Proceedings, Jet Propulsion Laboratory, Pasadena, pp A.5 LEAF AREA INDEX General remarks Leaf Area Index (LAI) is one of the most commonly employed biophysical parameters used to characterise vegetation canopies. It is a critical parameter in regional scale estimates of evapotranspiration, photosynthesis, primary productivity and carbon cycling. Therefore, detailed knowledge about vegetation structure (e.g. LAI and vegetation cover) is important in order to evaluate processes such as evapotranspiration or erosion dynamics. The increased spectral and spatial resolution of hyperspectral sensors like AVIRIS provides a greater level of information than the most widely used sensors like TM and AVHRR. LAI describes the three-dimensional space filling, whereas vegetation cover defines the twodimensional ground coverage. In this study, we will concentrate on LAI. Algorithmic approach LAI is usually estimated using ratio-based techniques, such as the Normalized Difference Vegetation Index (NDVI). It is based on the high spectral contrast between scattered nearinfrared (NIR) and absorbed red radiation in canopies. An increasing number of leaves present in a canopy over a unit area causes an increasing NIR reflectance while red reflectance decreases resulting in an increase in the ratio. Usually NDVI is calculated by the following general equation: NDVI ( R = ( R NIR NIR R + R red red ) ) where R is the reflectance, NIR is a near-infrared band and red is a red band. Gamon et al. (1993) and Wesman et al. (1998) use the reflectance at 677 nm as red band and at 833 nm as NIR band (corresponding to AVIRIS bands 22 and 49, respectively) to calculate NDVI. ENVI (Environment for Visualizing Images, Research Systems Inc.) provides a tool for NDVI transformation on widely used sensor data (including AVHRR, TM and AVIRIS), or bands can be entered for other sensors. Many studies have shown that NDVI is strongly related to LAI, green biomass, fapar (fractional absorbed photosynthetically active radiation), fipar (fractional intercepted photosynthetically active radiation) and other measures of canopy structure and biochemistry. Some relationships between fapar and NDVI have been shown to be near linear, in contrast to non-linear and saturation problems experienced, when the NDVI is used to derive LAI (Huete et al. 1996). Many of the NDVI to biophysical parameter relationships involve site specific regression plots which are subject to variability associated with canopy background, atmosphere, instrument calibration, sun angle, and view angle. Gamon et al. (1993) obtained good correlation between NDVI and LAI and fipar, respectively, applying a log-linear regression (cf. figure A.5-1). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 158 of 245

159 Figure A.5-1 Correlations between ground-based NDVI and LAI (left) and NDVI and fipar (right) (adapted from Gamon et al. 1993) Strub et al. (1998) found the linear spectral unmixing algorithm implemented in ENVI to be a reliable tool to determine vegetation cover and LAI. Endmember selection in their study was derived using a vegetation spectrum with a 100% coverage and a bare soil spectrum. Wessman et al. (1998) applied spectral mixture analysis (SMA) to produce five endmembers (grass, shrub, soil, shade and litter) characteristic for their site. Median values of LAI and fipar (fractional intercepted photosynthetically active radiation) for the herbaceous zone (M herb ) and the grove/drainage class (M grove ) were determined from landscape unit fipar/lai data. Assuming fipar values for litter, shade and soil endmembers to be zero, SMA weighted values of fipar (fipar SMA ) and LAI (LAI SMA ) were calculated from grass fraction f grass and shrub fraction f shrub after: fipar LAI SMA SMA = = f f grass grass M M herb, fipar herb, LAI + f + shrub f shrub M M grove, LAI grove, fipar They concluded that the SMA model approximates the true field values well, but field data must be incorporated into any model (i.e. the regression of field data and remotely sensed values) to predict absolute field values adequately. Literature Gamon, J. A., Field, C. B., Roberts, D. A., Ustin, S. L., and Valentini, R., 1993: Functional Patterns in an Annual Grassland during an AVIRIS overflight, Remote Sensing of Environment, 44, Huete, A., Justice, C., and van Leeuwen, W., 1996: MODIS VEGETATION INDEX, Algorithm theoretical basis document. Strub, G., Keller, P., Kneubühler, M., Schläpfer, D., Schaepman, M., Itten, K. I., Joshi, J., Diemer, M., B., S., and Spehn, M., 1998: Extraction and validation of biophysical variables of 30 March 2001 COMMERCIAL IN CONFIDENCE Page 159 of 245

160 grassland communities using field spectroradimetric measurements, in 1st EARSeL Workshop on Imaging Spectroscopy, edited by Schaepman, M., Schläpfer, D., and Itten, K., Remote Sensing Laboratories, Zurich, pp Wessman, C. A., Nel, E. M., Bateson, C. A., and Asner, G. P., 1998: A method to access absolute FIPAR of vegetation in spatially complex ecosystems, in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1998 Workshop Proceedings, Jet Propulsion Laboratory, Pasadena, California. A.6 PLANT WATER CONTENT General remarks Plant water content has strong influence on spectral reflectance of vegetation, and is highly correlated with standing biomass (Zhang et al. 1997). Therefore it can be related to productivity. Moreover, spatial and temporal estimates of canopy water content are one vital input to fire hazard models. Recent studies by Roberts et al. (1998), Ustin et al. (1998) and Sanderson et al. (1998) have shown that liquid water maps are one of the most innovative products available from AVIRIS. Algorithmic approach In order to separate water vapour in the atmosphere from liquid water at or near ground, Green et al. (1993) incorporated a simple model for the expression of liquid water in a reflectance spectrum. In this model the assumption is made that depth of the liquid water band across the 865 to 1035 nm region can be approximated using Beer-Lambert s law for exponential extinction in an absorbing or scattering medium. This means that depth of the water band will vary as a function of the strength of the absorber (described by the absorption coefficient for liquid water) and path length of light within an absorbing/scattering element. Figure A.6-1 gives a schematic view of the approach. Two formulations of the Beer-Lambert law are presented in the upper two frames. In the example shown to the left, light attenuated as it passes through an absorbing medium is modelled, whereas on the right side part of the light is partially blocked. The natural log of transmittance (or reflectance) can be modelled as a linear function that passes through the origin and has a slope equal to the path length. An intercept is added to the equation considering a blocking factor. Two leaf reflectance spectra are shown in the middle of figure A.6-1 on the left side, on the right side the absorption coefficient of liquid water is plotted. At the bottom of figure A.6-1 the natural logarithm of reflectance ln(r) is plotted against the absorption coefficient for two wavelength regions. Liquid water thickness is then derived from the slope of the line. Literature Green, R. O., Conel, J. E., and Roberts, D. A., 1993: Estimation of aerosol optical depth and additional atmospheric parameters for the Calculation of Apparent Reflectance from Radiance Measured by the Airborne Visible/Infrared Imaging Spectrometer, Summaries of the 4 th Annual JPL Airborne Geoscience Workshop, JPL Publication 93-26, Oct, Washington, D.C., pp March 2001 COMMERCIAL IN CONFIDENCE Page 160 of 245

161 Roberts, D. A., Green, R. O., and Adams, J. B., 1997: Temporal and Spatial Patterns in Vegetation and Atmospheric Properties from AVIRIS, Remote Sensing of Environment, 62, Roberts, D. A., Brown, K., Green, R. O., Ustin, S. and Hinckley, T., 1998: Investigating the Relationship Between Liquid Water and Leaf Area in Clonal Populus, in Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) 1998 Workshop Proceedings, Jet Propulsion Laboratory, Pasadena, California Sanderson, E. W., Zhang, M., Ustin, S. L., and Rejmankova, E., 1998: Geostatistical Scaling of Canopy Water Content in a California Salt Marsh, Landscape Ecology, 13, Ustin, S., Roberts, D. A., Pinzón, J., Jaquemoud, S., Gardner, M., Scheer, G., Castañeda, C. M., and Palacios-Orueta, A., 1998: Estimating Canopy Water Content of Chaparral Shrubs Using Optical Methods, Remote Sensing of Environment, 65, (3), Zhang, M., Ustin, S. L., Rejmankova, E., and Sanderson, E. W., 1997: Monitoring Pacific Coast Salt Marshes using Remote Sensing, Ecological Applications, 7, (3), March 2001 COMMERCIAL IN CONFIDENCE Page 161 of 245

162 Figure A.6-1 Schematic view of the retrieval method for the absorption coefficient of liquid water (adapted from Roberts et al. 1998). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 162 of 245

163 APPENDIX B - PRISM INSTRUMENT SPECTRAL BANDS Tables B-1 and B-2 below list the nominal centre-wavelengths and spectral sampling intervals at present specified for the PRISM instrument, in the VNIR and SWIR spectral bands. In these tables, pixel number refers to the number assigned to a single row of the area array detector, and associated centre wavelength and sampling interval are given for each row. For short wavelengths in the VNIR channel, row signals are binned on the detector chip, in fixed groups, to compose spectral bands. At longer VNIR wavelengths and all SWIR wavelengths, single detector rows define spectral bands. The required spectral bands are also numbered in the two tables, and centre wavelengths and spectral sampling intervals for the bands are listed. Some detector rows in the SWIR focal plane fall in atmosphere absorption bands, that are not required for the PRISM mission as defined at present. Only the required bands are listed. Figures B-1 and B-2 show the spectral sampling intervals for the VNIR and SWIR channels respectively. Band No. Pixel No. Centre wavelength (nm) Spectral sampling (nm) With binning (nm) March 2001 COMMERCIAL IN CONFIDENCE Page 163 of 245

164 March 2001 COMMERCIAL IN CONFIDENCE Page 164 of 245

165 Table B-1 PRISM specifications for VNIR focal plane Band No. Pixel No. Centre wavelength (nm) Spectral sampling (nm) March 2001 COMMERCIAL IN CONFIDENCE Page 165 of 245

166 Table B-2 PRISM specifications for SWIR focal plane 30 March 2001 COMMERCIAL IN CONFIDENCE Page 166 of 245

167 16 PRISM VNIR specification spectral sampling interval (nm) wavelength (nm) Figure B-1 Spectral sampling interval VNIR channel PRISM SWIR specification 15 spectral sampling interval (nm) wavelength (nm) Figure B-2 Spectral sampling interval SWIR channel 30 March 2001 COMMERCIAL IN CONFIDENCE Page 167 of 245

168 APPENDIX C - RATIOING METHODS FOR IN-FLIGHT CHARACTERISATION OF ABSOLUTE RESPONSE IN THE VNIR AND SWIR SPECTRAL BANDS C.1 INTRODUCTION This appendix describes an investigation on a group of methods that can be applied to in-flight characterisation of space-based radiometers for response to scene radiance. We are concerned mainly with characterisation of hyperspectral imaging radiometers with the following performance profiles: spectral range limited to the solar region, in which Earth radiances are dominated by reflected solar radiation particularly the visible/near-ir and short-wave IR (VNIR and SWIR) bands, spectral resolution in the order 10nm and spatial resolution of a few tens of metres from low Earth orbit. Instruments with these characteristics are used principally for imaging land surfaces. They typically have aperture sizes in the region 50 to 250mm, and field angles of a few degrees. C.1.1 THE KEY PROBLEM ABSOLUTE RESPONSE Measurements on instrument response provide data for calibration of the instrument output. It is generally necessary to characterise instrument response in flight, since changes in response are likely after pre-flight characterisation and during life in orbit. Accuracies in the region ±2% are typically required. In-flight response measurement in general requires at least two targets, of known radiance, that can be presented to the space instrument, for recording of raw calibration data. Usually, one of the sources will have nominal zero radiance, and provision of this dark level usually presents no serious difficulties. Given a dark level and one known upper radiance level, there are several fairly easy methods by which departures from linearity can be measured or checked, allowing a confident extension of the calibration to all radiance levels in the instrument dynamic range. The main problem in absolute response measurement, in the solar spectral region, is to provide one target, with an upper-level radiance that is known with high confidence: Even in laboratory conditions on ground, it is fairly difficult to provide a radiance known to accuracy better than a few percent. The characteristics of an on-board source for example a sun-illuminated diffuser can be measured pre-flight, but any subsequent changes in the standard cannot be measured without some significant added complexity in the on-board hardware. Various efforts can be made to reduce known sources of error by careful preparation of diffusers or other standards. However, confidence in the results will always be limited by the possibility of unpredicted changes, during the long and eventful period between pre-flight measurements and end of life in orbit. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 168 of 245

169 C.1.2 SCOPE OF THIS INVESTIGATION RATIOING METHODS This appendix concentrates on a particular set of solutions to the problem outlined above provision of a target for in-flight characterisation of absolute response. The investigation relates to methods using on-board targets. Vicarious calibration of space instruments which involves using ground scenes of measured/calculated radiance can in principle provide an update on the radiance of an on-board standard. However, it is desirable in principle to improve the on-board hardware method such that vicarious calibration becomes unnecessary, except as an infrequent and independent check. We are particularly interested in ratioing methods, in which: Sun-illumination is used with an on-board attenuator to provide a reference radiance, and the main instrument detectors are used to monitor the attenuation factor of the attenuator, by taking a ratio of readings in different configurations. C.1.3 SUMMARY OF CONCLUSIONS Several types of ratioing method have been investigated. All have advantages in: providing high confidence in absolute response characterisation moderate added complexity no added detectors/electronics or on-board radiation sources There is a preference for methods using transmitting diffusers. These tend to offer: compactness minimum movements. C.2 BASIC CONCEPT OF RATIOING METHODS C.2.1 USE OF THE SUN AND AN ATTENUATOR Ratioing methods will usually apply to in-flight radiometric characterisation methods in which the sun is the primary source of radiation for the characterisation measurements. Solar radiance is normally outside the dynamic range of remote-sensing radiometers, so that measurements using the sun require an on-board attenuator. Possible attenuators include: reflecting diffusers (the most commonly-used attenuators), transmitting diffusers (including small lenses), low specular reflections, for example at polished fused quartz surfaces, sieve plates (i.e. opaque plate with small holes), dense optical filters. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 169 of 245

170 C.2.2 ATTENUATORS AND THEIR RELEVANT PROPERTIES If a diffuser is used, the radiance of the diffuser is given by: R d = I s.ρ.cos(θ) Watts.m -2.steradian -1.nm -1 where I s Watts.m -2.nm -1 is the solar spectral irradiance arriving at the diffuser, θ is the angle of incidence of sunlight on the diffuser, and ρ is the diffuse reflectance or transmittance factor of the diffuser, for the relevant angles of incidence and reflectance. In practice, ρ will vary as a function of θ, and also of the view angles, although the variation is small for diffusers with approximately Lambertian characteristics. If the attenuator works by providing low specular reflections (e.g. glass plates) or by low unscattered transmission (e.g. sieve plate or filter) the main instrument will form an image of the sun, and the radiance it sees will be given simply by: R f = R s.t Watts.m -2.steradian -1.nm -1 Where R s Watts.m -2.steradian -1.nm -1 is the spectral radiance of the sun, and T is the effective transmission factor of the attenuator, for unscattered radiation. An assumption is generally made that the solar spectral irradiance or the solar spectral radiance is known to sufficient accuracy. This assumption is not in fact justified at present. But when, at some time in the future, solar radiance becomes known to high accuracy, the results of space-instrument radiance measurements can be upgraded to improve their absolute validity. Meanwhile, when sunlight is used, space instruments can be considered to be calibrated as reflectometers: regardless of the actual solar irradiance, they can measure the ratio of signals received from the Earth and the attenuator. This ratio gives the diffuse reflectance of Earth, if the reflectance of the attenuator (or a parameter equivalent reflectance, if it is not a reflecting diffuser) is known. The critical problem is to provide knowledge of the diffuse reflectance value ρ for a reflecting diffuser, or the equivalent to this reflectance for other attenuators. The equivalent for a transmitting diffuser is of course the diffuse transmittance factor, which we also call ρ. The equivalent for a filter, a sieve plate or a low-specular reflectance device is T.R s /I s. The ratio of solar radiance to solar irradiance, R s /I s, can be known very accurately, given measurements on the relative radiance distribution across the solar disc. These measurements (which may be necessary to allow for sun spots etc.) can be made from ground. For a filter or specular-reflection attenuator, the problem is of course to ensure knowledge of the specular transmission factor T. C.2.3 IN-FLIGHT MEASUREMENT OF ATTENUATOR PROPERTIES In general, the attenuator properties ρ or T, with relevant angular distributions will be calibrated pre-flight to accuracy at least as good as the required accuracy of absolute response measurements in space. However, the value ρ or T may change after the last preflight characterisation measurements, due for example to molecular contamination. Efforts can be made to minimise the known risks of changes, but in-flight measurements will always 30 March 2001 COMMERCIAL IN CONFIDENCE Page 170 of 245

171 be desirable to check for unpredicted effects, and to provide a basis for correction to calibration coefficients. The attenuator properties are optical characteristics that must be measured using radiation sources and detectors. However, ρ and T are both measured by taking the ratio of two sets of signals, associated respectively with input and output beams. Provided that the same source and the same detector are used to generate both sets of signals, it is not necessary for the absolute source output or the absolute detector sensitivity to be known. For this fundamental reason, a ratio measurement in flight has the potential to provide absolute response measurement, using only on-board hardware, at a very high confidence level. In making a ratio measurement, using a common source and detector, it is necessary for the source and detector to be stable over the period required to take two sets of readings, but this is not generally a significant concern. It is necessary for the input and output beam geometries to be known in some specific respects: for measurement of a simple transmission factor T, the beam shape should typically be unchanged between input and output, for a diffuse reflectance or transmittance measurement, ρ has the dimension: steradians -1, which implies knowledge of a solid angular subtense within the measuring system. However, with sensible design, the geometrical properties of a measurement systems can be very stable. C.2.4 USE OF MAIN INSTRUMENT FOR RATIO MEASUREMENTS Whether a ratioing system should in practice be used for a space-based radiometer depends of course on a trade-off against the competing possibilities, including considerations of performance, overall mission costs, mass, volume etc. The sun-ratioing radiometer concept, using a common small radiometer to point alternately at a diffuser and the sun, has not been widely adopted, because it is seen as adding too much complexity to the space hardware. The added radiometer must be moderately complex, operating in several spectral bands over the range of the space instrument, in order to measure changes in spectral reflectance of the diffuser. It must also include a movement to provide the required pointing directions. In the following discussion, we are therefore mainly interested in concepts in which the main instrument is used as the ratioing radiometer, avoiding the need for any additional detectors or detection electronics. In general, we also prefer to consider use of the sun as a common source for the ratio measurements. Use of lamps for ratio measurements (but probably not for subsequent maininstrument characterisation measurements) is also of potential interest, recalling that the source output need not be known. However, the sun has an obvious advantages in that it provides high radiant levels for the whole spectral band, without a high demand on platform power. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 171 of 245

172 C.3 RATIOING WITH DIFFUSERS When the sunlight attenuator (that is used to provide a source for characterisation of the main instrument) is a diffuser, we need to measure the diffuse reflectance or transmittance factor of the diffuser by recording signals from incident and diffused beams. The immediate problem is in measurement of an incident beam: solar radiance is typically 5 orders of magnitude above the dynamic range of the instrument, so that we cannot use the main instrument to measure direct sunlight. However, if we use an irradiance much lower than that of sunlight (e.g. filtered sunlight or lamp light) this will not provide a measurable diffused radiance. One solution is to introduce a second diffuser. Diffused sunlight can then be used as the source for ratio measurements. A lamp can also be considered as the source for ratio measurements. In some circumstances (depending on mission details and the design of the main instrument) a lamp may have important advantages in flexibility of design and operation; it may be relatively difficult to receive sunlight in the required relative directions, at convenient point in the orbit. However, solutions using lamps tend to require high lamp power, so that we consider mainly options in which the sun is the only source. One arrangement using two diffusers is described in section C.3.1 below. The theory for this design form is discussed in section C.3.2. Other two-diffuser options are described in section C.3.3, with variants on the theory of operation. C.3.1 TWO FULL-APERTURE TRANSMITTING DIFFUSERS fixed Db moving D diffuser diffuser sunlight senso pointing mirror nadir Figure C Ratioing method using two transmitting diffusers Figure C shows a two-diffuser arrangement in which: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 172 of 245

173 the main instrument is pointed alternately through two sun-illuminated apertures, A and B, slightly larger than the optics aperture, two flat transmitting diffusers, D a and D b (also slightly larger than the optics aperture), are used, diffuser D b is fixed in aperture B, diffuser D a can be moved between three positions: stowed, in aperture A, and in aperture B (between diffuser D b and the main instrument). Measurements are then made as follows:! the instrument is first pointed at diffuser D b, and readings S b are recorded (with D a either stowed or over aperture A); for these measurements, diffuser D b is sunilluminated in the viewing direction, possibly via a refracting wedge to avoid a need for platform roll,! the diffuser D a is then moved so that it lies under diffuser D b, and readings S ab are recorded,! the diffuser D a is then moved back to aperture A, and the instrument is pointed directly at the sun through the diffuser readings S a are recorded.! Diffuser D a is then stowed, and the same movement may cover both aperture A and aperture B. C.3.2 THEORY OF TWO-DIFFUSER SYSTEMS It is convenient to discuss the theory of two-diffuser ratioing systems, initially, with reference to the system described in section C.3.1. We assume that the polar radiance distributions provided by sun irradiance, I s, on the two diffusers D a and D b and the combination D ab can be expressed as: I s.t a.f a (β), I s.t b.f b (β) and I s.t a.t b.f ab (β), where T a, T b and T ab are angle-independent transmission factors, and the functions F a, F b and F ab are the relative angular distributions of diffused radiance, with respect to the off-normal angle β of the diffused beam. The bi-directional distribution functions F a, F b and F ab are simplified by the assumptions: that the incident beam is always normal to the diffuser surface, so that there is no need to include the incident angle coefficients, and that we use only diffusers with random structure, so that the transmitted beams are always symmetrical, eliminating the need to include any azimuth coefficient. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 173 of 245

174 The signal levels recorded, after correction for dark signal level, are: S a = I s.t a.f a (β).g, S b = I s.t b.f b (β).g and S ab = I s.t a.t b.f ab (β).g, where g is the linear response coefficient of the instrument, converting incident radiance to digital counts. We take the ratios of signals: S ab/a = S ab /S a and S ab/b = S ab /S b. Assuming that the instrument response g and the solar irradiance do not change during the period required to make all of the measurements, the ratios give: S ab/a = T b.f ab (β)/f a (β) and S ab/b = T a.f ab (β)/f b (β). We make similar ratio measurements pre-flight, using a sun simulator. In general, we have to expect that the diffuser characteristics will change between pre-flight and in-flight measurements, so we represent the pre-flight bi-directional distribution functions of the diffusers as: P a.g a (β), P b.g b (β) and P a.p b.g ab (β), The ratio measurements on ground provide: Sg ab/a = P b.g ab (β)/g a (β) and Sg ab/b = P a.g ab (β)/g b (β). We again assume that instrument gain and the sun simulator irradiance do not change in the period required to make the measurements, but it is not necessary for the sun simulator to mimic the spectral distribution of sunlight. For characterisation in flight, we compare the ratios measured in flight with the ratios measured on ground, to give: S ab/a /Sg ab/a = (T b /P b ).(F ab (β)/f a (β))/(g ab (β)/g a (β)) and S ab/b /Sg ab/b = (T a /P b ).(F ab (β)/f b (β))/(g ab (β)/g b (β)) The most important assumption is that the relative polar distributions of diffuse transmission do not change between pre-flight and in-flight measurements: i.e. F a (β) = G a (β), F b (β) = G b (β) and F ab (β) = G ab (β). On this assumption, the in-flight to pre-flight comparison yields: S ab/a /Sg ab/a = (T b /P b ) and S ab/b /Sg ab/b = (T a /P a ). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 174 of 245

175 The in-flight radiances of diffusers D a and D b, used alone in sunlight, are: I s.p a.g a (β).s ab/b /Sg ab/b and I s.p b.g b (β).s ab/a /Sg ab/a. We assume values for the solar irradiance Is, and the values P a.g a (β) and P b.g b (β) are measured on ground, so that the ratio measurements complete a theoretically precise knowledge of diffuser radiance in flight. Either of the two diffusers can then be used alone for in-flight characterisation of absolute response. C Effects of changes in relative polar distributions of scatter The simple ratioing method, as outlined above, is well adapted to measurement of the nondirectional effects of contamination etc. on the on-board characterisation standard, represented by the angle-independent transmission factors T a, and T b. These factors will be expected to change (from the pre-flight values P a, and P b ), due to the most obvious effects of molecular and particulate contamination, and any bulk transmission effects of ageing, ionising space radiation, solar UV or other radiation. The changes can in principle be measured very precisely, provided that the shape functions, F a, F b and F ab in flight, remain unchanged compared with pre-flight values G a, G b and G ab. The most serious concern, in reliance on the ratioing method as outlined above, is that these shape functions may change. Shapes of the functions can be changed in principle by changes in the fine structure of diffusers, in principle including: propagation of micro-cracking in ground surfaces etching of ground surfaces by oxygen ions and filling of surface profiles by molecular contamination. For reflecting diffusers, changes may be due to compression of porous structure, or adsorption of volatile materials that may alter bulk diffusion effects. Given these concerns, there is a preference for diffusers that are unlikely to suffer changes in shapes of diffusing fine structure. For example, we may prefer to avoid using exposed porous structures (reflecting or transmitting) because of the potential for change of density by any accidental contact. Lenslet arrays or opal diffusers are probably least susceptible to significant shape changes, but both present practical problems of different kinds. Ground surfaces are likely to be preferred in other respects, but will preferably not be located on outer surfaces (or touching any other surfaces), and should be investigated for stability of microcracking. Regardless of measures taken to limit shape changes, there will always be some doubts that adequate measures have been taken. If there are significant measured changes in the angleindependent coefficients T a and T b, it will be desirable to allow for an in-flight check on changes in shapes of the functions, F a, F b and F ab (or at least in two of these three). This will generally be possible by varying the angle of the incident beam, probably by varying the platform angle with respect to the sun, to measured the relative distributions F a (α), F b (α) and F ab (α), for varying incidence angle α and a fixed viewing angle. The functions F a (β), F b (β) and F ab (β) are not identical to the functions F a (α), F b (α) and F ab (α), though they are very similar 30 March 2001 COMMERCIAL IN CONFIDENCE Page 175 of 245

176 at low angles. However, it is extremely unlikely that significant changes in F a (β) etc., would occur with similar changes also in F a (α) etc. (The potential problem of changes in relative polar distributions also affect other ratioing methods. For example, the sun-ratioing radiometer depends on a measurement of diffuser radiance at an angle different from that used to calibrate the sensor, so that the method is valid only if the diffuser BRDF shape does not change.) C Problems of multiple reflections The theory given in section C assumes that the angle-independent transmission factor of the two-diffuser combination can be represented as the product of the angle-independent coefficients of the two component diffusers T a.t b in flight and P a.p b on ground. In effect, this treats the two diffusers as purely sequential modifiers, ignoring the possible effects of reflections between them, which could produce some error terms in higher powers of T a and T b. The validity of this approximation will depend in practice on the selection of diffuser types. Bulk diffusers, such as opal and Spectralon (used in transmission) tend to give relatively strong diffuse reflectance, compared with their diffuse transmittance. If there is a change in absorption at a surface between two such diffusers, the double-reflected component of transmission will be reduced more than the component that is not reflected. This may not be a serious problem in practice, partly because a change of absorption is less likely at an enclosed interface. However, there is a bias in favour of surface-shape diffusers e.g. ground quartz or lenslet arrays that produce reflection mainly by Fresnel reflection. Fresnel reflections at air/vacuum-to-substrate interfaces are much weaker than the transmitted components, and also spread over much larger angles, tending to have very little effect on the near-axis diffuse transmission. (Internal reflections at ground surfaces are much stronger, due to significant total-internal reflection there is a bias in favour of ground surfaces only on the nominal incident-beam sides.) If the in-flight and pre-flight measurements show small changes, this is an indication that there is no large absorption at either diffuser. In this case, higher order terms in the transmission coefficients cannot have a significant effect. In general, provided that strongly-reflecting diffusers are avoided (in transmitting configurations) the problem of reflections is unlikely to prove significant, but checks should be made in pre-flight experiments. Such checks could include placing an ND filter between diffusers to check linearity of the absorption effect. C Problems of stray light The theory in section C ignores possible stray light effects, due to scatter from components other than the two diffusers. It will generally be possible to ensure that there is no significant uncertainty in the initial illumination of the diffusers (for example using platform attitude and baffles to avoid significant Earth-light illumination). However, the diffusers will scatter light in all directions, and some of this light will be returned to the diffusers by reflections from other components, and then scattered onto the main instrument axis. The main concern is that the reflectances of these other components will change, producing effects in flight that are not taken into account in pre-flight calibration of the system. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 176 of 245

177 Note that stray light errors are not peculiar to the ratioing methods they are likely to affect any in-flight characterisation system using diffusers. The importance of the stray light effects will depend on the characteristics of the diffusers, and of course on the design of other components. It will be an advantage to use transmitting diffusers with relatively low diffuse reflectance. In this case: the diffusers will back-scatter a minimum of light onto external baffles (which could then reflect back to the diffusers), and transmitted scatter from the diffusers, which is reflected back to the diffusers by internal structures, will be mainly transmitted back towards space. Again, there tends to be a bias in favour of transmitting diffusers that work by fine surface structure e.g. ground quartz or lenslet arrays that give low reflected scatter. Reflections from baffles and internal mounting structures can be controlled by suitable coatings it is difficult to analyse the problem for a sufficiently general case, but in general structure-scatter usually proves to be insignificant. {Taking the case of a Lambertian reflecting diffuser:- with P Watts.m -2 initially incident on the diffuser, it will have a primary radiance of P/π Watts.m -2.sterad -1. If the diffuser subtends an effective solid angle of one steradian at scattering structure, the structure will receive P/π Watts.m -2. With 5% reflectance, the structure will have a radiance of P/(20.π 2 ) Watts.m -2.sterad -1. If the scattering structure subtends one steradian at the diffuser, the diffuser will receive a stray irradiance of P/(20.π 2 ) Watts.m -2. The error is about 0.5%, but most of this error can be corrected in pre-flight calibration. Errors for transmitting diffusers should be lower.} More serious stray light problems can in principle be associated with the main instrument optics. For example, if a Cassegrain form of design is used for the telescope, the diffuser may be close to the centre of curvature of the telescope primary mirror, returning a large fraction of scattered radiance to the diffuser. However, we would expect only minor changes in the primary mirror reflectance, so that the pre-flight calibration can compensate the stray light errors. C.3.3 OTHER TRANSMITTING DIFFUSER CONFIGURATIONS MINIMISING MOVEMENTS In general, we prefer to minimise the number of movements required in space instruments, and so far as possible to avoid movements that present risks of catastrophic failure. It is difficult to avoid a need for movements in providing in-flight radiometric characterisation (except by vicarious methods), but it is important to minimise the complexity, bulk and risks that the characterisation system adds. This involves trade-offs against performance of in-flight characterisation systems particularly in terms of the confidence levels that they provide. It is also important to address possibilities for multiple-use of each movement. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 177 of 245

178 C Full aperture systems For optimum confidence level, an on-board diffuser should fill the aperture of the sensor. Unless this is done, there is a possibility that errors will be produced by changes in optics transmission that are non-uniform across the aperture. This automatically introduces a requirement for a critical movement either: the view direction of the instrument must be rotated, probably by a pointing mirror as indicated in figure C.3.1-1, to point at the diffuser, or if the instrument has no pointing mirror, the diffuser itself must be deployed across the instrument aperture, as indicated in figure C In either case, if the movement fails with the diffuser in the aperture, the instrument becomes useless. Earth view in imaging mode Da in ratioing or characterisation mode Sunlight in ratioing or characterisation mode Da stowed Db in ratioing mode sensor Db stowed Figure C Two deployed full-aperture diffusers no pointing mechanism In a 2-diffuser ratioing system, again for optimum confidence level, both of the diffusers will ideally fill the optics aperture. If we use one small diffuser and one full-aperture diffuser, the ratio measurements will be valid only for a small part of the full-aperture diffuser area. In this case, there is a possibility of errors due to changes in diffuse transmission (or reflection) of the full-aperture diffuser that are non-uniform over the diffuser area. The arrangements in figures C and C therefore both show two large diffusers. In both cases, an additional movement is required, capable of moving one of the diffusers through more than the aperture diameter. Comparing these two configurations, there are substantial reasons for preferring the system shown in figure C Two movements are provided for in-flight characterisation, but both have other functions also, so that the added complexity required for the ratioing method is more acceptable: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 178 of 245

179 The pointing mirror can also provide: pointing for Earth-view on one axis (probably across-track), viewing other in-flight characterisation sources e.g. a black-body source for thermal IR channels. The second movement, applied to one of the diffusers, may also protect both diffusers when they are not in use. The pointing movement is a single-point catastrophic failure risk, but a pointing mechanism will in any case present a failure risk. The arrangement shown in figure C is much less attractive in these respects. The movements are used only for in-flight characterisation, though this might include thermal IR and/or wavelength characterisation, and both of the two movements are single-point catastrophic failure risks. One possible conclusion is that a pointing mirror should be considered seriously, even where platform roll could in principle be used to provide across-track pointing in Earth imaging mode. This conclusion is probably most appropriate for the most capable hyperspectral instruments, like PRISM, where it is desirable to combine: full aperture radiometric characterisation SWIR and thermal channels demanding stable thermal control (easier if there is no requirement for platform roll, in a sun-synchronous orbit). However, if a pointing mirror is included, it will preferably rotate in the telescope axis, as indicated in figure C In this case, the angle of incidence on the mirror is the same for all Earth-view directions and characterisation modes, avoiding errors due to change of reflectance with angle of incidence. C Full-aperture diffuser + part-aperture diffuser The size and complexity of a ratioing system can be reduced by using only part of the main instrument aperture for the ratio measurements. In general, a small diffuser will be fixed in position over part of the instrument aperture; this part of the aperture will be used only for ratio measurements and other characterisation tasks, and will not be usable for Earth imaging. This makes the radiometric characterisation system smaller, and eliminates one movement. An example configuration is shown in figure C We assume in this case that there is no pointing mirror the mission probably requires across-track pointing, and may also require along-track pointing, but pointing on both axes is produced only by platform rotation. This arrangement includes only one full-aperture diffuser, the transmitting diffuser D a, which can be moved between two extreme positions: covering the aperture of the main instrument and stowed away from the aperture. A small transmitting diffuser D b occupies a fixed position over part of the optical aperture of main instrument. Diffuser D a moves in its own plane, and this plane is between diffuser D b and the instrument aperture. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 179 of 245

180 Da in ratioing or characterisation mode Earth view in imaging mode Sunlight in characterisation mode sunlight in ratioing mode Da stowed sensor Db fixed Figure C Full aperture diffuser and part-aperture diffuser For the ratio measurements, the small diffuser D b is sun-illuminated, via a reflecting prism and a condensing lens system. It will be illuminated only at a selected instrument/platform attitude with respect to the sun, typically when the platform is over the Arctic or Antarctic region, on the dark side of the terminator. For the ratio measurements, the instrument will receive diffused sunlight from the part of its aperture occupied by diffuser D b, but it will receive nearzero solar-region radiation through other parts of its aperture. For the first set of ratio measurements, the instrument will receive diffused radiation only from the small diffuser D b. For the second set of ratio measurements, diffuser D a will be moved to various positions within its movement range. In each position, the instrument will receive radiation that is transmitted through both diffusers, and signals will be recorded. As described in detail in section C.3.2, the average signal S ab produced by the combination of the two diffusers will be compared with the average signal S b received from the small diffuser alone. The ratio S ab /S b will be compared with the same ratio measured in pre-flight characterisation. The change in ratio, between in-flight and pre-flight measurements will provide a measurement of the change in transmission of diffuser D a since pre-flight calibration, valid for every waveband recorded by the main instrument. For main-instrument characterisation measurements, diffuser D a is fully deployed across the instrument aperture, and the instrument is pointed directly at the sun. In this attitude, diffuser D b is dark, since the condenser lens axis is pointed towards dark space. Diffuser B b is also dark when the instrument is in use for recording Earth images. The ratio measurements give changes in transmission of diffuser D a, only for selected areas of the diffuser. It would be fairly difficult for the method to sample to whole area of D a. There are therefore potential errors due to non-uniform contamination of the full-aperture diffuser. However, the set of measurements on different areas of the diffuser would be expected to detect any significant non-uniformity. In other respects, the potential errors of the system are similar to those of a system using two full-aperture diffusers, as outlined in sections 3.2.1, and above. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 180 of 245

181 The method involves some loss of optical aperture available for Earth imaging, with some impacts on useful signal levels and diffraction. However, provided that the small diffuser occupies less than, say, 10% of the aperture area, the effects on performance are likely to be considered acceptable. Signal levels can generally be retrieved by a small increase in aperture diameter, and the spatial resolution of most hyperspectral instruments is not diffraction limited. The basic method indicated in figure C , using a full-aperture diffuser with a partaperture diffuser, is suggested as particularly appropriate for an instrument without a pointing mirror, on a platform that rotates to provide across-track pointing (and any required alongtrack pointing, including motion compensation). The space-hardware strategy including both (a) elimination of a pointing sub-system and (b) restricting in-flight characterisation to one movement will reduce instrument development costs and compact instrument size, with potential savings on platform size and launch costs. Design and performance aspects Suggested solarband characterisation Suggested optics Pointing mirror ratioing with two fullaperture diffusers Pointing Platform roll ratioing with full-aperture and part-aperture diffusers layout common telescope and pointing mirror separate optics for solar and thermal bands Thermal control easier varying radiant input to cold face impacts on cooling of SWIR/thermal detectors Radiometric errors Modularity (for systems with solar and thermal channels) Redundancy (for systems with solar and thermal channels) errors due to pointing mirror, in some configurations requires common optics for all channels failure of pointing mirror can eliminate value in all channels marginally lower confidence in ratioing method separation of solar and thermal band optics. separation of risks for solar and thermal channels Size and complexity larger, more complex better Other marginal impact on optical aperture requirement Table C Comparison of approaches using a pointing mirror and platform roll for across-track pointing. This approach is not necessarily suggested for a new Land Mission instrument. For instruments like PRISM, that are required to operate in many wavebands, the trade-offs are complex. Table C summarises the arguments for and against elimination of the 30 March 2001 COMMERCIAL IN CONFIDENCE Page 181 of 245

182 pointing mirror, on specified assumptions about the associated characterisation methods and basic optics layouts. C Elimination of movements It is possible to eliminate all instruments movements required for in-flight characterisation by a further shift towards part-aperture measurements. As indicated in figure C , diffuser D a (from figure C ) can be simply eliminated; no ratio measurements are made; diffuser D b is sun-illuminated to provide the only in-flight absolute response measurements. Earth view only sunlight in characterisation mode Db fixed sensor Figure C Use of part-aperture only for radiometric characterisation This solution essentially similar to that used for the Sira CHRIS instrument has the crucial advantage that it is very compact, simple and cheap. But it does not provide high confidence because there is no check for degradation of the single fixed source assembly (diffuser, lens and prism), and only part of the main instrument aperture is sampled. For high confidence, at least one movement is probably needed, unless the on-board hardware measurements are supported by vicarious calibration. (However, if vicarious calibration is used as the principle means for absolute response measurement, on-board hardware may be used to measure medium-terms changes in response, in periods between vicarious forays. In this case there are many other simple possibilities for the on-board sub-system, including for example an LED near the detector.) C.3.4 REFLECTING DIFFUSER OPTIONS The ratioing techniques described so far in this chapter use transmitting diffusers. It is also possible in principle to use reflecting diffusers, or even a combination of reflecting and transmitting diffusers. Two designs using reflecting diffusers are sketched in figures C and C March 2001 COMMERCIAL IN CONFIDENCE Page 182 of 245

183 C Example using flat reflecting diffusers In figure C , the two diffusers, D a and D b are flat. They are located on either side of the nadir axis from the pointing mirror, in parallel planes facing each other, so that either can be viewed by rotations of the pointing mirror (outside the range required for across-track Earth views). Either diffuser can be sun-illuminated in this configuration, sun illumination is at oblique angles, so that relatively small slots are required to admit sunlight. The diagram shows both the diffusers illuminated, but in practice we would arrange the sun-illumination slots so that the diffusers are illuminated in different planes of incidence (by platform pitch or by at different latitudes). Direct sun illumination and reflection from diffuser D a, is shown in full lines. Illumination and reflection from diffuser D b, is shown in dotted lines this includes both reflection directly to the sensor and reflection onto diffuser D a. sunlight sunlight baffle Da Db baffle pointing mirror baffle Earth view Figure C System of two flat reflecting diffusers The radiances viewed are then: R a : the radiance of diffuser D a in direct sun-illumination, R b : the radiance of diffuser D b in sun-illumination, R ba : the radiance of diffuser D a when D b is sun-illuminated. We then take a ratio of signals to give the ratio R ba /R b as an indication of reflectance of diffuser D a. As before, the ratio of signals in flight is compared with a ratio of similar signals measured pre-flight, using a sun simulator the percentage change in the ratio is the percentage change in reflectance of diffuser D a, since the pre-flight measurements. Then diffuser D a, in direct sunlight, can be used to characterise the sensor. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 183 of 245

184 There are of course a very wide range of possible arrangements for two diffusers. The logic underlying the flat-diffuser design form shown in figure C includes the following points: flat diffusers in sunlight provide spatially-uniform radiance, in direct reflection towards the sensor, which gives uniform sampling of the sensor aperture, and of the diffuser areas, facing locations, in parallel planes, provides uniform illumination of diffuser D a in reflection from diffuser D b, which is important again for uniform sampling of diffuser D a. C Example using two spherical diffusers The arrangement shown in figure C uses two concave spherical diffusers, which share a common centre of curvature. The two diffusers are placed close together in this case. Diffuser D a is directly sun-illuminated at a selected latitude, and is again used with direct sun illumination for characterisation of the sensor. Diffuser D b is again used only in ratio measurements. It may be sun illuminated for this purpose, directly or via any suitable optics, but it is shown illuminated by a lamp. (The lamp will provide even illumination of diffuser D b, if it located near the notional sphere of which both diffusers form part. The lamp is shown in a common plane with the centres of the diffusers, but would be shifted out-of-plane to avoid obstructing the Earth view.) sunlight pointing mirror Db Earth view L Da Figure C System of 2 spherical reflecting diffusers In an arrangement of two spherical diffusers, with a common centre of curvature, the illumination from either of the diffusers falling on the other is spatially uniform, if the polar reflectance distributions are Lambertian. (This is the basic principle of integrating spheres, and results from the fact that the obliquity-weighted angular subtense of any selected part of a sphere is the same at all other point on the sphere.) This means that the two spherical diffusers can be placed close together, at convenient angles for viewing, without introducing 30 March 2001 COMMERCIAL IN CONFIDENCE Page 184 of 245

185 unacceptable non-uniformity in the illumination of diffuser D a from diffuser D b. Sunillumination of diffuser D a (and hence sampling of the sensor aperture) will be slightly nonuniform due to the curvature of the diffuser. It is necessary for sunlight to be incident nearnormally onto the centre of diffuser Da, in order to minimise this non-uniformity. This requires the sun-illuminating beam to be relatively large. The design in figure C is an attempt to reduce the size of the in-flight characterisation system, using reflecting diffusers, by placing the diffusers close together. However, it is difficult to achieve a substantial reduction of system size, partly because a large sunillumination beam is needed for at least one diffuser. Stray light problems will also generally be worse (because it will be more difficult to baffle stray illumination of diffuser D a from diffuser D b via structures). The curved diffuser option is not favoured. C Geometry of transmitting and reflecting diffuser systems Configurations using reflecting diffusers will tend to be quite different to those using transmitting diffusers, because of differences in their polar scatter characteristics: Efficient transmitting diffusers generally produce a peak of transmission in the same direction as the incident beam. It is desirable to make measurements very near this same-direction peak, for efficiency and also because the peak gives minimum error with misalignment. This leads to the straight-through configurations illustrated in figures C.3.1-1, C and C Typically, the diffusers can be placed close together in parallel planes. Reflecting diffusers present no possibilities for straight-through operation. In a ratioing arrangement, it is necessary to provide large angles between three beam directions at each diffuser, respectively for: sunlight-incidence, sensor viewing and transfer from one diffuser to the other. As indicated by the examples in figures C and C , the two diffusers must be separated by a distance at least comparable with the aperture size, and must be used at a range of incidence and/or reflectance angles. Because the diffusers must be efficient over large angular ranges, they will in practice be selected for Lambertian properties. However, Lambertian properties are much easier for reflecting diffusers. The different geometrical arrangements for transmitting and reflecting diffuser systems present characteristic advantages and disadvantages, summarised in table C In this table, the relative disadvantages are shown shaded, with more serious concerns darker. The points are elaborated below. Size and movements The most obvious advantage of the transmitting diffuser options is that they are more compact; the straight-through configurations make it possible for two diffusers to be placed very close together for ratioing measurements. However, the straight-through geometry requires that one of the diffusers must be moved with respect to the other (as for example in figures C.3.1-1, C and C ) to allow the three measurements needed for ratioing and sensor calibration. The reflecting systems are large because of the large separation of diffusers, which also presents worse potential problems in control of stray light errors. However, the large separation of reflecting diffusers tends to mean that no movements of diffusers are required to make them viewable, provided that the sensor includes a pointing 30 March 2001 COMMERCIAL IN CONFIDENCE Page 185 of 245

186 mirror. But the diffuser movement that is required in a transmitting system will also generally provide diffuser protection and covers. Merit Transmitting diffusers Reflecting diffusers Size more compact larger Movements movement required on at least one diffuser no relative movements of diffusers, but a movement may be needed to cover apertures Stray light minor concern moderate concern Polar distribution errors can check for changes in polar transmission shape cannot easily check for changes in BRDF shape Pointing requirements will work with or without pointing mirror probably considered only with a pointing mirror Flat field capability usable only for small usable for wider fields Heritage sensor fields less used in space and on ground more experience in space and on ground Table C Comparing basic advantages of reflection and transmitting diffusers in ratioing configurations. Stray light The large separation between reflecting diffusers, together with the Lambertian properties of the diffusers, will present detailed problems in control of stray light. In particular, the scatter from diffuser D b will fall mainly on internal structures, and some of this light will be re-scattered onto diffuser D a. This stray light effect can be characterised pre-flight, but changes in the diffuse reflectance of the structures will alter the error, affecting the accuracy of the ratio measurement on the reflectance of diffuser D a. With good baffling particular for light paths between the two diffusers - the stray light errors will probably be tolerable, in configurations like that shown in figure C It will be relatively difficult to control stray light for the arrangement shown in figure C (particularly scatter from D b to D a via structure). Polar distribution shape errors All ratioing methods tend to depend on the assumption that the shapes of polar distributions do not change between pre-flight and in-flight measurements. Errors due to changes in these relative distributions are discussed in section C with reference to the transmitting diffuser options. The problem is not serious for transmitting diffusers, since an in-flight check can be run for changes in the distribution shapes. However, reflecting diffusers are used over much wider angular ranges, so that a valid in-flight check for BRDF changes would be difficult. Flat fielding Reflecting diffusers can have Lambertian properties i.e. they provide near-uniform radiances over large reflected angles. This property is desirable for flat fielding (extension of absolute response characterisation over the sensor field), particularly for wide field sensors. Reflecting diffusers are also less sensitive to errors in relative sun angle when the nominal angle is close 30 March 2001 COMMERCIAL IN CONFIDENCE Page 186 of 245

187 to normal as in figure C , but not in figure C ). However, we are mainly concerned with hyperspectral sensors for land applications, which typically have field angles of <5. For these sensors, the wide-field flat-field capabilities of reflecting diffusers are not essential some transmitting diffusers will provide adequate flat-fielding. The advantage of reflecting diffusers, is therefore marginal in the present context. Heritage It is possible to make a case for reflecting diffusers on the basis of heritage and availability. Because of their radiance uniformity over large angles, reflecting diffusers are much more commonly used in laboratories than transmitting diffusers. For space instruments, reflecting diffusers have usually been preferred; good reasons including heritage and, in a few cases, a real need to cover large fields (for example in MERIS). Considerable work has been done on conditioning of Spectralon reflecting diffusers (a LabSphere product) for space. (However, Spectralon is also a candidate transmitting material.) C Selection between transmitting and reflecting diffusers Based on the comparison summarised in table C , there is a general preference for transmitting diffusers, in ratioing configurations. The most critical factors are size and control of errors due to shapes polar diffuse transmission/reflection distributions. It should be emphasised that this conclusion relates particularly to hyperspectral sensors for land applications, which will have limited fields of view. C.4 RATIOING WITH SPECULAR ATTENUATORS Chapter C.3 deals with use of diffused sunlight for in-flight characterisation of space-based sensors. In this chapter, we are concerned with use of sun images for radiometric response characterisation. The radiance of the sun is 5 orders of magnitude above the typical radiances of Earth targets, for which hyperspectral imagers are designed. The direct sunlight must therefore be reduced in radiance by at least 4 orders of magnitude in this case without scattering the light. The possible non-scattering attenuators in include: Neutral filters, Weak reflections (e.g. from polished glass or quartz surfaces), Sieve plates (opaque plates with small holes). Any of the specular attenuators listed above can in principle reduce the transmitted radiance by five orders of magnitude, to bring the sun image into the dynamic range of a typical Earthobserving instrument. It can be placed in front of the sensor either by use of a pointing mirror or by deploying the attenuator itself. However, as in the case of diffusers, we then need to guarantee the stability of the attenuator, or measure its attenuation factor in flight. In the case of filters, the transmission may be affected by surface contamination and also by changes in bulk absorption coefficients due to ageing, solar UV exposure or space radiation 30 March 2001 COMMERCIAL IN CONFIDENCE Page 187 of 245

188 effects. Weak surface reflections can be altered by surface contamination. It would be unsafe to assume that either filters or weak reflectors will maintain sufficiently stable transmission/reflectance coefficients in orbit, to be relied-on for absolute characterisation to few-percent accuracies. C.4.1 SIEVE PLATES AND FILTERS C Sieve plates Sieve plates, with their very simple construction, are of interest as possible absolute standards for transmission, requiring no independent check in flight. They can be affected by contamination that reduces hole areas, or by erosion that increases hole diameters, but if the holes are large enough at start of life, we may be able to accept that changes through life will produce sufficiently small changes. Measured thicknesses of molecular contamination are much less than 1µm, which would indicate that hole diameters down to 200µm should be acceptable. However, there is some indication, from ground based radiometry (which makes extensive use of small apertures) that the molecular contamination of hole edges can be very much thicker than the measured contamination of flat surfaces. Hole area comparisons have indicated molecular contamination thicknesses of a few microns, which would indicate that we need hole diameters of a few millimetres, to be reasonable confident of sufficiently stable areas in flight. (Relatively large hole diameters are also desirable to limit effects of diffraction, but this is a relatively minor concern.) The transmission factor achieved by a sieve plate is approximately equal to the ratio of total hole area to sensor aperture area. Achievement of a large attenuation depends on limiting hole size to a desirable minimum say 2mm diameter and limiting the number of holes deployed across the sensor aperture at any one time. It is important that the pattern of holes in the sieve plate should provide good sampling of the optical aperture, in order to take account of non-uniform changes in transmission across the aperture. Sampling can be improved by moving the sieve plate across the sensor aperture, since a movement will be required to allow the sensor to view the sun through the sieve plate. However, for calibration at a high confidence level, we would prefer to use at least around 10 holes simultaneously. Given 10 holes, each 2mm in diameter, in a sensor aperture diameter of 100mm, the effective transmission factor would be about 1/250. The attenuation increases with sensor aperture size. A next generation of hyperspectral landimaging instrument, with higher spatial resolution, is likely to have aperture diameters in the region of 200mm (which would give an estimated transmission of 1/1000. However, PRISM would probably have an aperture diameter <100mm for the visible region. In principle, a sieve plate with fewer and smaller holes could provide a transmission in the order 1/50,000, which would allow the attenuated sun radiance to be measured without additional attenuation, at the top end of a typical sensor dynamic range. But this would tend to provide calibration at a low confidence level. Use of a single sieve plate therefore appears unattractive without some added complexity to check the hole diameters in flight. (Sira have suggested a scheme in which a hole diameter is measured in flight by adding a small fixed lens, which allows the main instrument to be used as a microscope for viewing the hole. This 30 March 2001 COMMERCIAL IN CONFIDENCE Page 188 of 245

189 parallels real procedure for using holes in laboratory-based radiometry, and effectively eliminates the contamination risk of using holes well below 1mm in diameter. However, this method is not part of the present study.) C Sieve plate and 2 neutral-density filters Although a sieve plate may not simply be used to provide all of the attenuation required for direct imaging of the sun, it can be used in combination with neutral density filters. In a ratioing method, the sieve plate would be treated as a transmission standard, and used to calibrate the attenuation of two neutral-density filters, in flight. The two calibrated filters may then used in combination to provide sensor characterisation. The method requires: Neutral filter ND1, having transmission T 1, Neutral filter ND2, having transmission T 2, Sieve plate, having effective transmission S. The measurements made are: direct sun image through ND1 and sieve plate, giving signal S a = k.s.t 1 direct sun image through ND2 and sieve plate, giving signal S b = k.s.t 2 direct sun image through ND1 and ND2, giving signal S c = k.t 1.T 2. The value k is assumed constant, since the sun radiance and sensor sensitivity are the same for all measurements (after dark-level correction). The ratios Sc/Sa and Sc/Sb therefore give the transmission values T 1 and T 2 for the two filters in terms of the sieve plate effective transmission S, which is measured pre-flight, and assumed stable. The method requires use of three movements, to provide the three combinations of filters and sieve plate on the instrument line of sight. If a pointing mechanism is included, pointing can provide one of the three movements, as indicated in figure C It will be desirable to use the linear range of the sensor to allow relatively high transmission for the sieve plate (to permit larger and more stable hole areas). For example, the sieve plate may be given a nominal transmission of 1/50, while each filter has a transmission of 1/1000. The attenuated sun radiance produced by the sieve plate and either filter would then be equivalent to an Earth radiance at albedo 1.05 in orthogonal sun-illumination. The radiance imaged through the two filters would be a lower by a factor 20. This requires linearity characterisation to cover the 20:1 range, but this is feasible by a range of supplementary methods. (It will be possible in principle to increase the radiance levels that the sensor can measure by control of integration times, so that even lower sieve plate transmission may be feasible.) With the relatively large hole sizes permitted by a transmission factor in the order 1/50 (for example about 3mm diameter for 20 holes in a 100mm sensor aperture), the sieve plate may well be considered a sufficiently stable reference. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 189 of 245

190 Figure C Ratioing method using a sieve plate and two ND filters C.4.2 MULTIPLE-REFLECTING WINDOWS Low reflectance values can be provided by the polished surfaces of ordinary refracting materials, such as optical glass. If uncoated, the reflectances show only slight variations over wide spectral ranges. The material most likely to be preferred is fused quartz, which, with an index of 1.46, provides a Fresnel reflectance of from one surface, or 0.07 from two surfaces. Four reflections between two flat quartz windows (using both surfaces of each) can reduce the radiance of the sun by the required 5 orders of magnitude. However, surface reflectances may change significantly, due particularly to molecular contamination, so that a ratioing method is desirable to measure reflectances in flight. C Ratioing system designs using fused quartz windows One possible design form is indicated schematically in figure C Here the attenuator is two flat windows, set close together at an angle of about 2, and with reflection factors R 1 and R 2. Sunlight is directly transmitted through the widows, but they also reflect, generating multiple images of the sun. In the transmitted beams, sun images are separated at 4 intervals. If the straight-through transmission factor of the window pair is T, the radiances of the image set are: B s.t, B s.t.r 1.R 2, B s.t.(r 1.R 2 ) 2, B s.t.(r 1.R 2 ) 3 etc. where B s is the solar radiance. The sensor cannot measure the straight-through sun image (at radiance B s.t), and probably will not measure the first double-reflection (at B s.t.r 1.R 2 ). However, the sensor will be able to measure the n th and (n+1) th double-reflected sun images at radiances B s.t.(r 1.R 2 ) n and B s.t.(r 1.R 2 ) n+1. The ratio of the two measured radiances will provide the factor R 1.R 2. The radiance of any of the sun images can then be calculated, assuming knowledge of the solar radiance (as usual) and with a measurement on the straightthrough transmission factor T. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 190 of 245

191 sieve plate sunlight possible movement diffuser 2 windows 3rd double reflection sensor Figure C Full aperture attenuator using multiple reflections The transmission factor of the two windows alone can be high, since the reflectances are low. However, there is some advantage in adding a sieve plate, as indicated in figure C , or a neutral density filter, to reduce the overall transmission factor T, probably to the range 1% to 20%. (This reduces problems of stray light, as outlined in section C ) The transmission factor T can in principle be measured using any external source by viewing the target (a) through the windows and (b) through an open aperture (which may also be the aperture used for Earth imaging, if the platform is agile). The ratio of signals gives the factor T. One suggestion is that the moon should be used for this measurement, since it should have stable radiance over the period required for the two views. (It is not necessary to know the absolute radiance of the moon, or any other selected target.) Because the moon has a relatively low radiance, it may be necessary for the transmission factor T to be relatively high for example 10%. Optical hardware for this arrangement may be particularly simple. Each of the two windows may be made up of two uncoated fused quartz plates, with all four surfaces parallel. Each window will give a total reflectance R 1 ranging from at 2500nm wavelength to at 450nm. The two windows alone will give a transmission between and A sieve plate may be added to reduce the transmission factor T by one order of magnitude, to a nominal range from to This requires a very coarse sieve plate, that is very unlikely to be sensitive to contamination, but the sieve plate transmission does not in any case need to be stable over long periods. With the sieve plate, the transmissions for the first 5 sun images are shown in table C {The combined reflectance R c of any two surfaces, having individual reflectances R a and R b is given by: R c = R a + (1-R a ) 2.R b /(1-R a R b ). This formula can be used sequentially to compute the reflectances of any set of surfaces.} In practice, the measurements would be made on the third and fourth sun images (the second and third double reflection). The third sun image, with an attenuation factor in the region 30 March 2001 COMMERCIAL IN CONFIDENCE Page 191 of 245

192 will provide a radiance towards the top end of a typical sensor dynamic range, equivalent to an albedo around 1 in overhead sunlight. The fourth sun image will provide a radiance equivalent to around 0.01 albedo in normal sunlight. This will give a low signal, but noise is not necessarily a serious problem, given possibilities for summation of signals across the field and over moderate spectral bands (and possibly some increase in integration times for lower radiances). Table C shows transmission factors for multiple sun images in a system with: two windows, each with 4 uncoated quartz plates, sieve plate or neutral filter with 25% transmission. In this case again, the second and third double reflections would be used for ratio measurement. The ratio is smaller, which would reduce any problems of noise on the lower ratio measurement. The higher transmission factor of the sieve plate would also make it slightly easier to measure the transmission factor T, using a low-reflectance target such as the moon. wavelength 2500nm 450nm straight through image st double reflection nd double reflection 1.36E E-05 3rd double reflection 1.78E E-07 4th double reflection 2.33E E-09 Table C Transmission factors for sun images, using 2 windows, each with 2 fused quartz plates, and sieve plate transmission 1/10 wavelength 2500nm 450nm straight through image st double reflection nd double reflection 1.24E E-05 3rd double reflection 5.21E E-06 4th double reflection 2.2E E-08 Table C Transmission factors for sun images, using 2 windows, each with 4 fused quartz plates, and sieve plate transmission 1/4 So, the instrument is pointed to measure the third and fourth sun images in sequence. The ratio of the radiances of these two images gives the factor R 1.R 2 precisely. It is then necessary to measure the direct transmission, T, of the attenuator, for example by recording images of the moon through it and past it, and taking a ratio. The radiance of the third image can then be calculated precisely as B s.t.(r 1.R 2 ) 2, and used to calibrate the instrument. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 192 of 245

193 C C Movements for the reflecting window ratioing method Zero movements option The most distinctive advantage of the reflecting window method is that it can apparently work without any added movements, if the sensor has a pointing mirror and if the platform is agile. The method requires only the window aperture and an open aperture, which can be accessed by a pointing mirror, and an ability to point both apertures at either the sun or the moon. However, it is not clear that a pointing mirror and the required platform agility will be available in the same sensor/platform assembly. To work without added movements, we need pointing rotation and platform rotation on the same axis, but it is unlikely either that (a) pointing will be provided for any other purpose on a pitch axis, or (b) that pointing will be provided on a roll axis if it is feasible to operate the sensor with substantial platform roll. C Window and diffuser deployment In practice, it may be necessary to add a movement that will in be capable of deploying the window assembly. The method can then be used either with or without a pointing mechanism. In this case the same movement could be used to place a transmitting diffuser in the window aperture as indicated in figure C C Stray light errors in the reflecting-window ratioing method The most significant potential error, in the method using multiple reflections between windows, is due to stray light. While the ratio measurements are made, the windows, and possibly the main instrument, will be in direct sunlight a few degrees off the direction instrument boresight. If the solar radiances is B s Watts.m -2.steradian -1, the irradiance, I s Watts.m -2, will be B s.π.sin 2 φ, where φ is the semi-angular subtense of the sun. The stray light radiance produced by the windows and the instrument will typically have a polar distribution: B stray = I s.t.s 0.β -2 where S 0 is a constant, typically between 10-4 and 10-6, and β is angle in radians from the direct sunlight direction. Taking S 0 = 10-5, T = 0.1 (for the case shown in figure C ), β = 0.2 and sinφ = , we get the ratio of stray radiance to solar radiance: B stray /B s = S 0.T.π.sin 2 φ.β -2 = Using the design form shown in figure C , and transmission figures from table C , we would attempt to measure a sun image at a lower radiance in the region of B s. In this case, the stray light will produce an error of 1% in the ratio measurement. This is a significant concern, but indicates that the method can probably be made to work. Note in particular: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 193 of 245

194 It is probably possible to design and make the parallel windows to have a stray light coefficient S 0 <10-5, though <10-6 could be difficult to guarantee. The radiance of the residual stray light can be measured, simply by recording at several points near the weak sun images, so that it is possible to assess the error in flight (which is very important for confidence in calibration), and probably possible to correct the error with accuracy better than ±10%. It is desirable for the sieve plate (or neutral filter) to reduce the straight-through transmission by a substantial factor, since this has a direct effect in reducing the stray light error. But if the sieve plate attenuation is made too large, it may become difficult to use the moon for measurement of the transmission factor T. C Other errors in the reflecting window method This theoretical treatment of sun-image radiances given above ignores the effects of interference between multiple reflections in each window. However, provided that the windows and their separations are millimetres thick, the spectral structure produced by interference will be too coarse to be resolved by the sensor. Any measurable effects can probably be corrected using pre-flight characterisation data. The sun images are transmitted through slightly different areas of the windows. Given very severe non-uniform contamination of the windows, this could produce a significant error. Severe contamination would, however be detected by ratio and straight-through transmission results very different from those recorded in pre-flight characterisation. C.4.3 COMPARISONS OF DIFFUSERS AND SPECULAR ATTENUATORS Relative advantages and disadvantages of diffuser methods and specular attenuator methods are summarised in table C The diffuser methods are represented only by the partaperture ratioing arrangement indicated in figure C Shading is used to indicate the more important relative disadvantages. It is difficult to compare the basic options, since there are several possible variants on each. The sieve plate/filter option appears to be less worth further consideration, mainly because it requires more full-aperture movements to provide sets of ratio and sensor-characterisation measurements and the movements probably make the system larger than the other options. The multiple-reflecting windows option, considered only for absolute response measurement, can in principle require no movements, if the sensor has a pointing mirror and the platform is agile. However a disadvantage of the specular attenuators is that, using only the sun image, they cannot extend absolute characterisation across the field flat-fielding requires a diffuser to be added, although there are no significant requirements on the diffuser stability. The reflecting windows option will probably use one full-aperture movement, as will the selected transmitting diffuser arrangement in principle, these two options will give systems of similar size. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 194 of 245

195 Size Merit Development problems Flat field capability Movements Transmitting diffusers (figure C ) probably the smallest option moderate (some diffuser development) ok for land sensor fields probably 1 (with partaperture ratioing) Multiple-reflecting windows (figure C ) may be small (partaperture diffuser) moderate (plate mounting, diffuser) added diffuser needed probably 1 including diffuser Sieve plates and filters (figure C ) largest (with movements) moderate (neutral filter availability) added diffuser needed 3 or 2 + pointing Platform agility agility agility requirements Errors part aperture effects stray light effects, noise (low signals) sieve plate contamination Added operations check for changes in polar distributions transmission measurement using the moon, stray light check correction for sunspots etc. separate flat-fielding correction for sunspots etc. separate flat-fielding Table C Summary comparison of diffuser and specular-attenuator ratioing methods There is a marginal preference for the transmitting diffuser option, based on the complexity of operations required to complete radiometric characterisation. Again, the specular attenuators do not provide flat-fielding, so that a separate set of measurements is needed. These methods also require correction for non-uniformities in the radiance distribution of the sun. C.5 MEASUREMENTS ON TRANSMITTING DIFFUSERS There are advantages in using transmitting diffusers for ratioing techniques, mainly because they occupy less space, they are less likely to degrade and can be less sensitive to stray light than reflecting diffusers. In order to obtain data on which to base a more detailed consideration of using transmitting diffusers, some experimental measurements have been made with this type of diffuser and the results are described here. Polar scatter measurements were made on glass (BK7) plates with one or both surfaces finely ground with silicon carbide grit of different grades as well as on a commercial opal glass diffuser. From these measurements the Gain of each diffuser was calculated for light scattered in the direction normal to the surface. In addition to this the Gain of various combinations of two or more diffusers was measured. The Gain of the diffuser in these cases is defined as the ratio of the luminance of the diffuser to that of a Lambertian diffuser, for the same illuminance. In all cases measurements were made using light of wavelength March 2001 COMMERCIAL IN CONFIDENCE Page 195 of 245

196 nm and in some cases additional measurements were made at 900 nm to check the effect of changing wavelength. For speed and convenience, measurements were made using a test facility for measuring the MTF of lenses. As a result signal levels were noisier than would have been the case if equipment had been designed specifically for this type of measurements. To some extent this limited the accuracy of the measurements, but in any case this was sufficient to obtain useful data on the behaviour of transmitting diffusers. The arrangement used is illustrated in figure C.5-1. Figure C.5-1 Arrangement used for assessing diffusers The results of some of the polar scatter measurements are illustrated in figure C.5-2. The associated table provides details for each of the diffusers, including the measured Gains. We note in particular the following: by comparing diffusers D and A with diffuser B, that a double sided diffuser increases the scatter angle and by comparing these with H that three diffusing surfaces increases the angle even further. opal diffuser E has a large unscattered component although the scattered component appears to be virtually Lambertian diffuser F uses a fine grade of grinding powder and has a significant unscattered component diffuser C illustrates the effect of insufficient grinding. With more grinding it becomes diffuser D 30 March 2001 COMMERCIAL IN CONFIDENCE Page 196 of 245

197 1.2 1 NORMALISED LUMINANCE F D G C A B H 0.2 E ANGLE OF VIEW Degrees Figure C.5-2 Polar scatter distribution from various transmitting diffusers (λ=546 nm) see Table C.5-1 for details of individual diffusers DIFFUSER TYPE GAIN GRINDING COMMENTS POWDER SIZE CODE A Single sided BK7 B Double sided BK7 C Single sided BK7-220 Insufficient grinding D Single sided BK Diffuser C with more grinding E Single sided - - Opal F Single sided BK7 G Single sided BK7 H B & D Combination of diffusers B & D Table C.5-1 Details of diffusers shown in figure C.5-2 As indicated earlier, some measurements were repeated at a wavelength of 900 nm and a comparison of the 546 nm and 900 nm curves is shown in figure C.5-3. The results show that within experimental error there is no significant difference between the two wavelengths. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 197 of 245

198 1.2 1 NORMALISED LUMINANCE G B ANGLE OF VIEW Degress Figure C.5-3 Comparison of polar scatter at 546 nm (blue curves) and 900 nm (red curves) for diffusers B and G (see Table C.5-1 for details of the diffusers) It is interesting to note that the first part of these polar scatter curves (i.e. up to about 10 ) can be simulated by a Gaussian curve and that this can be extended to larger angles by using the sum of two Gaussian curves. This is useful because in combining two diffusers one is effectively convolving the effect of the two diffusers together. This procedure is simplified by using the Gaussian fit, because the Fourier transform of a Gaussian is another Gaussian. Figure C.5-4 shows the polar response for diffusers D and B as well as the best fit sum-oftwo-gaussians to diffuser D. The figure also shows the theoretical response of B calculated from the Gaussian fit to D, on the assumption that B is a combination of two D s. An important aspect of diffusers is to be able to predict the gain of combinations of diffusers from the gain of the individual diffusers. Measurements of gain were made on several diffuser combinations and various algorithms for predicting their combined gain were tested. Table C.5-2 lists the combinations that were tried, their measured gains and the predicted gains from two different algorithms. The measured data together with the curves representing the two algorithms, are plotted in figure C.5-5 and 5-6. The two best algorithms were: Algorithm 1 Gain =10,2.N -2.1, where N is the number of diffuse surfaces Algorithm 2 Gain = xS , where S is the sum of the reciprocals of individual gains, i.e. S = Σ (1/G n ) where G n is the gain of the nth diffuser and the summation is over all the diffusers. It appears that algorithm 2 gives a better fit to the measurements. Algorithm 1 may in fact work equally well and possibly better, if all the diffuse surfaces were the same. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 198 of 245

199 1.2 1 NORMALISED LUMINANCE B 0.2 D ANGLE OF VIEW Degrees Figure C.5-4 Illustration of using Gaussian curves to fit polar scatter curves. Solid lines are measured curves, triangles are the best fit Gaussian curve for diffuser D and squares are values for diffuser B calculated from the Gaussian fit to D. DIFFUSER COMBINATION TOTAL No. OF DIFFUSE SURFACES MEASURED GAIN PREDICTED GAIN ALGORITHM 1 PREDICTED GAIN ALGORITHM 2 A B D G A+G B+G D+G A+B A+D B+D B+D+G A+B+D A+B+D+G Table C.5-2. Measured and predicted gains for various diffuser combinations (see Table C.5-1 for diffuser details) 30 March 2001 COMMERCIAL IN CONFIDENCE Page 199 of 245

200 GAIN (log scale) NUMBER OF SURFACES Figure C.5-5 Measured Gains plotted against number of diffuse surfaces (squares) and algorithm 1 (solid line) GAIN (log scale) SUM OF RECIPROCAL OF GAIN Figure C.5-6 Measured gains plotted against the sum of the reciprocal of the individual gains (squares) and algorithm 2 (solid line) From the results of these measurements one can conclude that 3 to 4 diffusing surfaces, of the type experimented with, are required to give a gain < 1. The ratioing method using two 30 March 2001 COMMERCIAL IN CONFIDENCE Page 200 of 245

201 diffusers, proposed in the report referred to in the introduction, would require each of the two diffuser discs to have 3 to 4 diffusing surfaces, or to have fewer diffusing surfaces (e.g. 2) and to include an ND filter or coating, or sieve plate, as part of each disc. An alternative is to have a three-disc arrangement as proposed in section C.2 above, where one could consider having either three diffusing discs, or any combination of diffusing disc(s), sieve plates and ND filters. In this case discs with only 2 diffusing surfaces would be satisfactory. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 201 of 245

202 APPENDIX D - IN-FLIGHT SPECTRAL CALIBRATION OF HYPERSPECTRAL SENSORS D.1 INTRODUCTION This appendix describes an investigation on methods for in-flight characterisation of hyperspectral radiometers in Earth orbit, for the wavelengths and wavebands defined by the sensors. We are concerned mainly with characterisation of hyperspectral imaging radiometers with the following performance profiles: spectral range limited to the solar region, in which Earth radiances are dominated by reflected solar radiation particularly the visible/near-ir and short-wave IR (VNIR and SWIR) bands, spectral resolution in the order 10nm and spatial resolution of a few tens of metres from low Earth orbit. Instruments with these characteristics are used principally for imaging land surfaces. They typically have aperture sizes in the region 50 to 250mm, and field angles of a few degrees. D.1.1 THE NEED FOR SPECTRAL CHARACTERISATION OF HYPERSPECTRAL DATA Hyperspectral space instruments having the above performance profile typically include: a telescope, which forms an image of Earth surface on a spectrometer entrance slit, a spectrometer which forms an image of the entrance slit, with spectral dispersion in a direction orthogonal to the slit, and one or two area-array detectors located in the dispersed spectrum image, such that a slit image in each wavelength is formed on a detector row, and the spectrum line associated with each spatially-resolved ground point is formed on a detector column. All or part of the detector array can be read out, to record all or part of the spectrum of spectral radiance of a line of spatially-resolved points on ground. The detailed spectral data provided by the imaging spectrometer system can be used in analysis of the surface chemistry of vegetation, soil etc., to produce a variety of useful data products. It is important for users of hyperspectral data to know the spectral response function (SRF) defined by each detector row. Barycentres of the SRFs will preferably be known to ±0.5nm or better. The width of each SRF (defined as the full-width at half maximum) will preferably be known to ±2nm or better. It will also be highly desirable for the shapes and barycentre positions of the SRFs to remain stable through the sensor life in orbit, so that users are not obliged to modify their algorithms for generation of data products. In the longer term, we may 30 March 2001 COMMERCIAL IN CONFIDENCE Page 202 of 245

203 envisage that constellations of satellites will carry nominally-identical hyperspectral imagers at this stage it will also be desirable for all sensors in a group to define the same SRF barycentres, so that common algorithms can be used to process data from all satellites. SRF centres and shapes will generally be characterised in pre-flight testing. However, the location of the dispersed image on the detectors may be changed after pre-flight testing by movements of spectrometer optics, the slit or the detectors, which will alter barycentres. Movements may be produced by launch vibration or by temperature changes; a 0.5nm barycentre shift will be produced typically by a relative image movement of only 1µm. Temperature-related changes in the refractive indices of dispersing prisms will typically shift barycentres by order of 1nm per K (this figure calculated assuming that fused quartz prisms are used, giving nominal spectral resolution in the region 10nm at 1000nm wavelength). The focus of the dispersed image on the detector may also be altered by movements in the spectrometer, which will change the SRF widths. A 2nm change in SRF width may be produced by a focus shift in the order of 10µm. It may in practice be very difficult to guarantee the stability of the imaging spectrometer optics and detectors to sub-micron levels, so that in-flight characterisation for barycentres will generally be considered necessary. It is much more reasonable to expect stability of focus to order of 10 µm; however, an in-flight check on spectral widths may also be considered desirable. The in-flight characterisation method should provide SRF barycentre positions to ±0.5nm or better. It may also provide a check on SRF widths to about ±2nm. It should be possible to measure barycentre positions: immediately after launch to allow corrections for errors due to launch, and at several subsequent times through life to check for effects of through-life temperature changes, and if necessary allow corrections. It may be possible to prove by analysis and pre-launch testing that short-term changes in spectrometer temperature, due to detection system heat dissipation and orbital variations in platform temperature, will not produce significant SRF shifts. However, ideally it will be possible measure barycentre positions at sub-orbital frequency. D.1.2 SCOPE OF THE INVESTIGATION The investigation of SRF characterisation concentrates in the problem of in-flight measurements, and covers: use of on-board sources and filters, use of solar and atmosphere absorption features sensor optical design methods for inclusion of in-flight SRF characterisation 30 March 2001 COMMERCIAL IN CONFIDENCE Page 203 of 245

204 possibilities for integration of methods for SRF characterisation methods with methods for absolute response characterisation and flat-fielding. D.1.3 SUMMARY OF CONCLUSIONS A large number of different sources and optical configurations can be considered for in-flight spectral calibration of hyperspectral sensors, though some concepts require some further development. Preferred options will depend on other sensor design choices, particularly the pointing method (pointing optics or platform rotation) and the preferred method for radiometric calibration. Some preferred options include:! Where a large diffuser is included for radiometric calibration, sun-illumination of the diffuser through a filter provides a simple method for location of SRF barycentres.! Where the sensor has a pointing mirror, a small fixed spectral source can be scanned across the optical aperture by the pointing mirror, providing both SRF barycentre location and a method for detecting changes of focus in the spectrometer (hence changes in SRF shapes).! Where the sensor has no pointing mirror, part-aperture illumination methods are preferred for spectral calibration, to avoid a requirement for movements two small illumination systems can provide both SRF barycentre location and a measurement of changes in focus of the spectrometer (hence changes in SRF shapes).! A very simple method requires interference filter coatings at both ends of the entrance slit these extremes of the spectrometer field then being dedicated to spectral calibration. (Spectral illumination relayed directly to the entrance slit provides a variety of possible methods, but may generally be found difficult because of constraints on design within the telescope and slit assemblies.)! Where full-aperture spectral illumination is provided, use of a Fabry-Perot etalon provides a method for increasing the resolution of measurements that can be made on SRF shapes in flight.! Use of solar absorption bands and atmosphere absorption bands appears very promising, although experimental verification is desirable. Use of natural features requires no on-board hardware, and will provide at least a good fall-back solution for spectral calibration, if on-board hardware system fail. D.2 BASIC ELEMENTS OF SPECTRAL CALIBRATION In-flight spectral calibration will generally require that the sensor shall receive radiation from one or radiant sources having some distinctive and stable spectral structure, that can be located with respect to detector rows, in analysis of the hyperspectral image data. Possible sources for spectral calibration are listed in Table D.2-1, with very brief comments on advantages and disadvantages. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 204 of 245

205 Sources Method Requirements Advantages Disadvantages Atmospheric absorption features Solar absorption lines Ground-based sources laser, reflected sunlight Rare Earth oxide doped diffuser, sunilluminated, full aperture Rare Earth optical filters On-board diodes and solid state laser Spectral lamps: HCL, ECL, Arc and discharge sources Interference filters Fabry Perot etalon Viewed in Earth scene Viewed in reflection from on-board diffuser Viewed on overpass Typically viewed via pointing mirror Several methods, e.g. sun-illumination and a diffuser Generally viewed via a diffuser Generally viewed via a diffuser Several methods, e.g. sun-illumination and a diffuser Several methods, e.g. sun-illumination and a diffuser View of uniform Earth scene Diffuser (also used for radiometric calibration) Dark background simple tracking apparatus Large diffuser, pointing mirror or other mechanism Simple optics, typically including a diffuser Source; simple optics, typically including a diffuser Source; simple optics, typically including a diffuser Viewed in transmission using sunlight via diffuser Viewed direct with sunlight (possibly diffuser) No hardware required No hardware required No on-board hardware Fairly simple, if a pointing mirror is included for other purposes Simple, if using radiometric calibration equipment Simple, if using radiometric calibration equipment Simple, if using radiometric calibration equipment Vary with viewing method Vary with viewing method; several transmission lines Varies with atmosphere and background Low contrast at typical spectral resolution Single spatiallyresolved pixel; single point(s) in orbit Large mechanism needed Radiation darkening a potential concern Power needed; low intensity; temperature sensitive Power needed; variable intensities Needs qualification for temperature stability Vary with viewing method Table D.2-1 Summary of possible sources for in-flight spectral calibration of hyperspectral sensors In general, we assume that detailed measurements on SRF barycentres and shapes will have been made in pre-flight characterisation of the sensor, covering many representative wavelengths and all field points. The function of in-flight calibration will be to measure changes produced by movements of the spectrometer, after pre-flight characterisation, to allow the pre-flight calibration to be updated. The in-flight measurements will be simplified so far as possible, to measure only the significant changes in the dispersed spectrum image. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 205 of 245

206 D.2.1 SOURCE SPECTRAL FEATURES D Shapes of spectral features In principle, several different types of source spectral structure can be used for spectral calibration, including emission/transmission lines and bands, absorption bands and absorption edges. There is a marginal preference for use sharp emission or transmission lines, produced by spectral lamps or by interference filters, which can be located with respect to detector rows by simple centroiding algorithms. More complex structures, such as the absorption spectra of rare-earth filters, require more complex data processing, but this does not present serious problems, since processing can generally be performed on ground (and correction commands, if required, uploaded to the platform). Stability is essential; it is desirable to avoid spectral features that depend to some extent on sensor or scene variables. Calibration for SRF widths, if required, is likely to present more serious problems. It will probably not be possible to compute wavebands to 2nm accuracy from the apparent widths of fixed spectral features (provided for example by atmosphere absorption bands, stable lasers, or interference filters). It will be difficult in flight to measure wavebands by the method that will be appropriate on ground (likely to include a scanning monochromator). D Minimum number of spectral features required It is unlikely that movements in the spectrometer will produce significant changes in the size and shape of the image formed on detectors the major effects of any movements will be simple shifts of the whole image in the detector plane, and/or simple defocus of the whole image. It will therefore usually be considered sufficient, for the purpose of in-flight calibration, to locate only a single spectral feature with respect to the detector, for each separate optical channel. Hyperspectral imagers covering both the visible/near-ir (VNIR) and short-wave IR (SWIR) bands are likely to use two separate area-array detectors for these two bands, so that at least one distinctive spectral feature will be required in each band. The bands are likely to be roughly 450nm to 1000nm for VNIR, and 1000nm to 2400nm for SWIR. There may be an overlap in the region of 1000nm, where a single spectral feature may serve for calibration of both channels. D Advantage of multiple spectral features However, there is a case for use of several spectral bands. In general, this will provide a check for any changes in size of the dispersed spectrum image. More important, it may provide better data for analysis of SRF shape changes - it will be difficult to infer changes in SRF widths from a single absorption or emission feature, unless the feature can be spectrally scanned. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 206 of 245

207 D.2.2 FIELD COVERAGE Ideally, SRFs will be measurable at all points across the instrument field. However, a simple linear shift of the dispersed image on the detector can be measured at any single point in the field, and a rotation of the image in the detector plane can be measured using two points in the field, with a substantial separation. Two points in the field will be considered an adequate minimum. D.2.3 FULL AND PART-APERTURE COVERAGE In general, all calibration procedures should mimic Earth-imaging conditions so far as possible, to avoid possible sources of calibration error. Ideally, the spectral calibration source should fill the aperture of the sensor that is used for Earth imaging. However, if the source is outside the telescope, this implies that the aperture of the spectral-calibration optics must be large, and that a mechanism must be included to allow the sensor to view the source. There is therefore a case for considering spectral calibration sources that occupy only part of the optical aperture. D Effects of part-aperture illumination In an optical system with measurable aberrations, the centroid positions of images formed in the focal plane can be modified by varying the illumination of the entrance pupil, as illustrated in figure D In normal imaging mode, the whole of the aperture is illuminated, as indicated schematically in figure D (a), and the true location of a monochrome slitimage point, with respect to detector rows, is the image point position produced in this condition. If the spectrometer system has some aberration, for example defocus, and only part of the aperture is illuminated for spectral calibration as shown in figure D (b), the slit-image point will in general be shifted with respect to the true position for normal imaging. This is not a trivial concern:- the transverse ray aberrations of spectrometer optics can easily reach 50% of the spectral resolution interval, introducing potential spectral calibration errors up to a few nanometres. Part-aperture illumination also in general changes the width of the SRF. If the system has substantial aberrations, the effective spectral resolution of the spectrometer will be usually be improved by part-aperture illumination, as indicated by the small spot sizes in figures (b) and (c) (but diffraction will eventually dominate). These are the significant arguments (in simplified terms) for the in-flight spectral calibration source to illuminate the whole aperture of the sensor. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 207 of 245

208 full aperture illumination slit image point (a) detector row entrance slit slit image point (b) part aperture illumation offset in dispersion direction slit image point (c) part aperture illumation offset across dispersion direction Figure D Spectrometer schematic diagrams, showing effects of part-aperture illumination on spectral calibration D Limiting errors due to part-aperture illumination Errors in spectral calibration, due to partial illumination of the aperture, will be stable, if the spectrometer aberrations are stable. Part-aperture illumination may therefore be accepted, provided that the effects of partial illumination are calibrated in pre-flight measurements, and provided that the spectrometer aberrations are believed to be stable. It may be difficult to guarantee that the spectrometer aberrations remain stable after these pre-flight measurements. However, the most likely aberration change after pre-flight calibration will be a simple change of focus. The effects of a simple focus change, associated with part-aperture illumination, can be minimised by using the centre of the aperture, or a part of the aperture offset from centre in the across-track (and across-dispersion) direction, as indicated in figure D (c). In this case, a change of focus in the spectrometer produces no change in spectral calibration. Part-aperture illumination may therefore be acceptable in practice, with pre-flight calibration of the full-aperture to part-aperture shifts, and with sensible selection of part-aperture areas for spectral calibration. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 208 of 245

209 D Use of part aperture illumination for checks on SRF widths The effects of part-aperture illumination, in shifting spectral calibration, can in principle be used to measure changes in aberration of the spectrometer. For example, two part-apertures, separated in the dispersion direction, may be illuminated alternately as indicated in figure D The effect of simple defocus in the spectrometer is to produce a shift in the slit image position, for each source wavelength. The shift can typically be measured to 1-2% of the pixel dimension, by centroiding techniques. This provides a very sensitive method for measurement of spectrometer defocus. (The method can be considered a simplified version of the Shack-Hartman test for aberrations of imaging optics, in which a small aperture mask is scanned over the optics aperture, while a point image position is measured.) Use of two or more small fixed apertures, or a single small aperture that is moved, can therefore be used to measure defocus of the spectrometer since pre-flight calibration. This is of interest as the basis of a method for checking SRF widths in flight. If there is no measurable change of focus between pre-flight and in-flight measurements, there can be high confidence in the pre-flight measurements on SRF widths. If significant focus change is measured, it is in principle possible to use the focus-change measurement to update true values for spectral widths. However, this requires much more extensive pre-flight measurements on spectral widths, quantifying SRFs as a function of spectrometer defocus. entrance slit slit image point (a) part aperture illumation positive offset in dispersion direction detector row slit image point (b) part aperture illumation negative offset in dispersion direction Figure D Use of offset apertures to measure spectrometer defocus D Summary of full-aperture and part-aperture merits Table D presents a brief summary of the relative merits of part-aperture and fullaperture illumination, for spectral calibration methods. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 209 of 245

210 There appears to be a fairly good case for part-aperture illumination. However, it is not reasonable to conclude that either full-aperture or part-aperture methods are superior, without wider considerations. For example, full-aperture illumination can be achieved without large optics and without a movement, if the source is placed at the telescope focal plane, outside the nominal sensor field. Feature Full-aperture illumination Part-aperture illumination size of an on-board large if the source is small source outside the telescope movement of an onboard source required if the source is outside the telescope fixed source(s) may be used wavelength accuracy good needs moderately stable optics and careful location capability for SRF width measurement no impact of source(s) possible methods via defocus-change measurement Table D Full-aperture and part-aperture illumination comparison D.3 USE OF EXTERNAL SOURCES It is desirable in principle to eliminate all requirements for on-board hardware, for in-flight spectral calibration, by use of external sources. The possibilities include both natural sources and artificial targets. D.3.1 ABSORPTION BANDS IN THE SOLAR SPECTRUM. Figure D shows the solar irradiance at 1nm, 2nm and 10nm spectral resolution, derived from MODTRAN 3.7. (The curve for 2nm resolution is raised by 15mw.m -2.(cm -1 ) -1, and the curve for 10nm resolution is raised by 25mw.m -2.(cm -1 ) -1. Note that these curves are plotted in terms of radiance per wave-number interval.) If the absorption bands in the solar spectrum are used for spectral calibration, they are likely to be observed for this purpose in the raw data derived from a sun-illuminated on-board diffuser, that may be also used for radiometric calibration. This raw data from an on-board diffuser will in general include effects of detector response non-uniformity, as well as random noise. However, these effects can be corrected on ground, by using pre-flight absolute radiometric calibration data. The results will then include errors due to changes (after preflight calibration) in optics transmission and diffuser reflectance, but these errors will be expected to vary smoothly with wavelength, and will not mask the structure in the solar spectrum. Dark signal non-uniformities can be corrected by normal in-flight calibration procedures, and detector response non-uniformities will not be expected to change significantly. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 210 of 245

211 The absorption features of the solar spectrum are relatively shallow, compared with atmosphere absorption bands, but have the advantage that they can be expected to be much more stable. There is also in general a minor advantage in that use of the solar spectrum for spectral calibration requires the same data as absolute calibration (if sun-illumination is used for absolute calibration), so that it is not necessary to collect additional images for spectral calibration. 100 Solar irradiance at 1nm and 10nm resolution irradiance mw.m-2.cm wavelength (nm) Figure D Solar irradiance plotted at 1nm and 10nm wavelength resolution We are mainly concerned with location of spectral features that can be detected at spectral resolution in the region of 10nm, which is typical of requirements on spectrometers applied to land imaging. Figure D shows simulated sensor data at 10nm spectral resolution, for the band from 500nm to 900nm, with 0 and 5nm shifts in spectral calibration. (I.e. one of the data sets has a simulated 5nm calibration errors with respect to the wavelength scale, due to a 5nm shift of the spectrum with respect to the detectors, equivalent to half a detector-row shift.) The wavelength shift can be measured by comparing sensor data measured in flight with theoretical results that would be obtained over a range of wavelength shifts. Several approaches are possible, including uses of regression analysis and look-up tables (LUTs). In general, it is necessary to pre-process the data to suppress low-order terms in the signal/wavelength distributions, including pedestal levels and gradients. For the results shown in figure D.3.1-3: 30 March 2001 COMMERCIAL IN CONFIDENCE Page 211 of 245

212 (a) a solar irradiance curve is computed at 10nm spectral resolution by convolution of MODTRAN irradiance data with a triangular function having a 10nm half width (approximately correct for good spectrometer response), (b) this curve is sampled at 10nm intervals to produce each of 11 data sets, with 1nm shifts between sets over a range 5nm to +5nm, (c) pedestal and gradient terms are suppressed by subtracting from each data point the average of the neighbouring 6 points (range of ±30nm), (d) the convolution of each data set with the zero-shift set is formed, and plotted against the wavelength shift, for 4 different spectral regions as shown in figure D simulated solar irradiance data at 10nm resolution, with 0 and 5nm wavelength shifts nominal irradiance, W.m-2.cm wavelength, nm Figure D Computed data sets, with zero and 5nm nominal wavelength errors 30 March 2001 COMMERCIAL IN CONFIDENCE Page 212 of 245

213 Correlation of solar irradiance data at 10nm resolution nm to 2370nm 1500m to 1750nm 1000nm to 1490nm 600nm to 990nm Figure D Correlation of solar irradiance data at 10nm resolution The results provide an indication of the possible precision of a method based on use of the solar irradiance spectrum, the peak of the correlation function providing a nominal true wavelength error. The curve for wavelengths >2000nm is very shallow, associated with a lack of solar spectral features in this region. There are systematic errors up to few nanometres for this and some other bands. However, it should be possible to correct systematic errors by selection of appropriate sub-bands and by appropriate weighting of data. The very simple algorithm used here gives good results for the selected spectral band between 1500nm and 1750nm the curve for this band has a well-defined peak, indicating that calibration accuracy better than ±0.5nm is probably feasible a least in this region. The peaks appear to be stable when fixed pattern noise is added. Figure D shows results of the same calculation with an assumed 5% peak-to-peak random variation in detector row response (much larger than any likely response non-uniformity, after row-averaging and use of pre-flight calibration data). 30 March 2001 COMMERCIAL IN CONFIDENCE Page 213 of 245

214 0.003 Correlation of solar irradiance data at 10nm resolution nm to 2370nm 1500m to 1750nm 1000nm to 1490nm 600nm to 990nm Figure D Correlation of solar irradiance data at 10nm resolution with 5% response non-uniformity, peak-to-peak The method would require elaboration for any particular space mission. It would be necessary to take account of specific sensor characteristics, including spectral resolution (which generally varies over the range), spectral ranges and numbers of bands that can be read. It is also of course likely that a more sophisticated basic algorithm would be developed to reduce systematic errors. It is relevant that sensors using prism spectrometers generally have higher spectral resolution capability at short visible wavelengths, due to the non-uniform dispersion of refracting materials with wavelength. For example, there is an option to calibrate the Sira CHRIS sensor using the solar spectral feature at spectral resolution at 432nm, where the sensor has 1.6nm spectral sampling interval (although baseline is to use the oxygen absorption band at 760nm, where it has a spectral sampling distance of 7nm). Figure D shows the correlation of theoretical data, at 1nm steps in wavelength shift over a ±5nm range, calculated for 2nm spectral resolution, using the same simple method described above. It is clear that accuracy <0.25nm is likely to be feasible, for CHRIS, using the fine solar spectrum structure at short visible wavelengths. However note that this does not imply similar wavelength accuracies at longer wavelengths because of the non-uniform dispersion of the prism spectrometer, a 0.25nm error at 415nm is produced by an image shift which gives a 1nm error at 760nm. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 214 of 245

215 Correlation of solar irradiance data at 2nm resolution 500nm to 600nm 450nm to 500nm 410nm to 450nm wavelength shift, nm Figure D Correlation of solar irradiance data at 2nm resolution D.3.2 USE OF ATMOSPHERE ABSORPTION BANDS Atmosphere absorption bands generate a large number of sharply-defined spectral features in Earth scenes, that can in principle be used for spectral calibration of space instruments. The main problem expected in use of Earth scenes is that in general the spectral features vary considerably with atmosphere conditions and with the surface scene content. There is a perceived need: to select surface backgrounds that provide very consistent reflectance, to avoid unpredicted biases in the spectral locations of atmosphere absorption bands, and to select spectral features that are relatively consistent as a function of atmosphere conditions. One option for the VNIR band, which has been refined and investigated in detail by Geoff Settle and Paul Darling at Reading University, is to use oxygen absorption band at 763nm, measured in an open ocean scene. The logic here is: (a) that there is relatively little variation in oxygen mass over ocean, so that the shape of the absorption band is fairly consistent, and (b) open ocean gives very low reflectance in this region, without significant absorption features, which might bias the effective location of the oxygen band. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 215 of 245

216 There is an implication that atmosphere absorption will be measured in a background generated mainly by atmosphere scatter, but this background has a smooth spectral distribution, unlikely to bias absorption feature locations. Most of the variations in the spectrum of ocean, as seen from space, are generated by variations in water vapour absorption and aerosol scatter, but the oxygen band is located in a region free from significant water vapour absorption. Figure D shows differences in radiance, measured in PRISM instrument bands, produced: 1. by a 1nm shift in the sensor spectral calibration (a wavelength error), 2. by a 40% change in water vapour content, and 3. by a change from 23km to 20km in visibility. ra dia nc e err or, W. m- 2.s r- 1.n m effects for errors in wavelength, and assessment of visibility and water vapour 20% water vapour error 3km visibility error 1nm wavelength error wavelength, nm Figure D Comparison of effects of wavelength calibration shift with effects of errors in estimation of water vapour (40%) and visibility (23km to 20km) VNIR band The data are computed using MODTRAN, based on a standard mid-latitude Summer atmosphere, with zero ground reflectance. Sharp oscillations in the wavelength-error curve shows the locations of sharp spectral features that can in principle be used (at typical landsurface spectrometer resolution) to make sensitive measurements on shifts in the instrument spectral calibration. Many of these variations are of course associated with water vapour absorption, and correlate with features in the water-vapour-change curve. However, the region of the oxygen absorption band at 763nm is free from significant water vapour absorption features. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 216 of 245

217 The effect of visibility change, shown in figure D.3.2-1, includes the oxygen absorption feature, since all radiances and radiance-differences in this calculation are due to atmosphere scatter. The wavelength-shift curve in figure D also shows the effect of solar absorption bands, which are relatively strong at short visible wavelengths, and are strongly represented in this band due to Rayleigh scatter effects for errors in wavelength, and assessment of visibility and water vapour radiance error, W.m-2.sr-1.nm % water vapour error 3km visibility error 1nm wavelength error wavelength, nm Figure D Comparison of effects of wavelength calibration shift with effects of errors in estimation of water vapour (40%) and visibility (23km to 20km) SWIR2 band Figure D provides a similar comparison of the effects of wavelength-error, visibility-error and water-vapour error for the SWIR2 band (wavelengths >2000nm). There is a CO 2 absorption band at 2060nm, that is relatively unaffected by water vapour, and may perhaps be used for spectral calibration of SWIR channels. The SWIR1 band (1000nm to 1800nm) is less promising. Scattered radiance levels in the SWIR2 band are much lower, so that in this band the effects of a 1nm wavelength shift, against a 23km visibility background, are comparable with the noise-equivalent radiance specified for PRISM. In general, it will be desirable to average signal levels over large image areas, to reduce errors due to random temporal noise. D.3.3 ANALYSIS FOR CHRIS IN-FLIGHT SPECTRAL CALIBRATION This section provides a brief summary of the investigation carried out by Paul Darling at Reading University, on use of the oxygen absorption band for in-flight spectral calibration of the Sira CHRIS sensor. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 217 of 245

218 Two basic methods were investigated for retrieval of sensor wavelength calibration shifts: a) linear regression and b) a lookup table method, to determine the detector-row address of the oxygen absorption line at 763nm. In the linear regression method, coefficients are derived that relate the centre wavelength of a detector element, in the vicinity of the absorption band, to the observed radiances on those elements. In the look-up table method, the detector signals are compared with computed signal patterns stored in a look-up table to find the closest entry. The analysis was based on TOA radiances computed using MODTRAN4.0, for the US 1976 standard atmosphere, with a water vapour content of 2.55 g/cm 2. The robustness of algorithms against variation in aerosol loading was tested using data for 13 different visibilities from 10km to 50km 10, 11, 13, 15, 17, 19, 21, 24, 26, 32, 35, 38, and 50 km. The solar zenith angle with respect to the sensor was 40 and the target view angle at the ground was 45. The sun was at a relative azimuth angle of 90 with respect to the sensor-target line of sight. The reflectance of the ground was been set to zero to simulate the low albedo of the open ocean. Detector signal levels were computed for a set of 5 detector rows, nominally centred around the 763nm oxygen absorption line, assuming a triangular spectral response function, and 7nm spectral sampling intervals. The signal levels were computed for wavelength shifts in the range 3.5nm to +3.5nm (± half row width) in 0.1nm steps. Detector response non-uniformity was assumed to be corrected in calibration. Figure D shows the simulated detector signal for a range of atmospheric visibilities, at zero wavelength shift. 2.5 Simulated detector response for View Angle=45 Solar Zenith=40 degrees Detector Response uw/cm^2/sr/nm km 13km 15km 17km 19km 21km 26km 32km 35km 38km 50km Wavelength nm Figure D Simulated detector signals for a range of visibilities 30 March 2001 COMMERCIAL IN CONFIDENCE Page 218 of 245

219 D Linear regression method Multiple linear regression determines best-fit coefficients a p such that signals L p, varying with wavelength shift λ, on each of p detector rows, can be related to λ by the simple linear relationship: λ = p a p L p The coefficients were first determined for 26km visibility. The robustness of the algorithm was then checked by using these coefficients to compute wavelength shifts at other visibilities, and comparing the results with true wavelength shifts. Very poor results are obtained unless the signals L p are pre-processed to compensate the effects of large changes in absolute levels, associated with different aerosol scatter densities. The results shown in Table D were obtained when the five signals at each shift were normalised to the average, and the central values eliminated, (reducing the number of independently variable coefficients from 5 to 4). Better results, indicated in Table D , were obtained by combining data at extreme visibilities. Wavelength errors at visibilities: 10 km 26 km 50 km minimum -1.4 nm nm 0.3 nm maximum -0.5 nm nm 0.98 nm Table D Regression analysis results using normalised signal levels coefficients derived at visibility 26km and applied at visibilities 10km, 26km and 50km Wavelength errors at visibilities: 10 km 26 km 50 km minimum nm nm nm maximum 0.29 nm 0.19 nm 0.52 nm Table D Regression analysis results using normalised signal levels coefficients derived from combined data at 10km and 50km visibilities and applied at visibilities 10km, 26km and 50km These results come close to the target of calibration to 0.5nm accuracy. Addition of random noise degrades the results seriously, if noise appropriate to single detector elements is assumed, but noise would not be expected to have a significant effect large numbers of samples are averaged (for example over a 100 x 100 pixel image). However, it is clear that simple regression analysis is not an ideal tool for extracting wavelength errors form data, without relatively complex processing to take account of different aerosol scatter signal levels. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 219 of 245

220 D LUT method In a LUT method, sets of 5 detector-row signals, representing five rows closest to the 763nm wavelength and the two either side, were computed using MODTRAN data as before, for wavelength shifts from 3.5nm to + 3.5nm in 0.05nm steps, and for 12 equispaced optical depths from 0.56 to 0.1 (corresponding to visibilities from 7.3km to 142km. The 5-point data sets were stored in a 141 x 12 matrix of wavelength shifts and optical depths. 5-point rowsignal data for any given conditions were then compared with this LUT to find a closest match on a root-mean square basis, and the nominal wavelength shift (and visibility) recorded. When the LUT is tested against data computed for similar viewing conditions and without noise, but for optical depths different from those in the table, it gives maximum errors of 0.25nm in wavelength shift retrieval. More significantly, the method was checked for robustness against a range of nominal ocean reflectance values from zero to (using a LUT computed for zero reflectance). At a nominal optical depth of 0.15, this gave the results shown in Table D Surface reflectance Maximum wavelength retrieval error nm nm nm nm nm Table D Robustness of the look-up table method to variation in surface reflectance, at optical depth 0.15 Smaller errors are generated at higher optical depths (lower visibilities) since the surface reflectance variation has less influence compared with that of aerosol scatter. At optical depth 0.31 (15km visibility), the maximum recorded wavelength-retrieval error was 0.28nm. The robustness of this method was tested by adding 500 examples of random noise, at an rms level of W.m -2.sr -1.nm -1, to computed radiance levels, and testing at a range of visibilities and for a 1.3nm true wavelength shift. The results are shown in Table D Fairly large errors are computed at low radiance levels, associated with high visibility. However, the noise levels introduced are appropriate for single pixels noise effects can probably be negligible when relatively large image areas are used. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 220 of 245

221 Visibility Wavelength shift Minimum error Maximum error 13 km 2.6 nm -0.5 nm 0.4 nm 13 km 0.0 nm -0.6 nm 0.6 nm 26 km 3.2 nm -0.8 nm 0.5 nm 26 km 0.0 nm -1.2 nm 1.0 nm 38 km 2.7 nm -1.0 nm 0.9 nm 38 km -0.5 nm -1.2 nm 1.5 nm 50 km 2.9 nm -1.5 nm 0.6 nm 50 km -1.5 nm -1.3 nm 1.7 nm Table D Wavelength retrieval errors from LUT methods effects of random noise at W.m -2.sr -1.nm -1 In general, the investigation shows that adequate spectral calibration can be achieved for an instrument operating in the VNIR band, using the atmosphere oxygen absorption line. Use of observations over open ocean, with retrievals by a LUT-based method, is the likely approach. D.3.4 ARTIFICIAL GROUND TARGETS It should be possible to set up bright targets on ground that can be used to provide spectral calibration of a sensor in space. For example, in the VNIR band, the sensor will be designed to measure maximum target radiances in the order 1 W.m -2.sr -1.nm -1, and typical radiances in the order 0.1 W.m -2.sr -1.nm -1. In a 10nm spectral band, the typical target radiance will be 1 W.m -2.sr -1. The radiant intensity from a 1000 m 2 ground pixel will be in the order 1000 W.sr -1. So for example a 1W laser directed into a 1/1000 steradian beam about 2 beam angle will provide a signal well within the sensor dynamic range. For the sensor to receive the beam, it is necessary only for the laser to be in the sensor ground track, and to point the laser at the sensor with ±1 accuracy as the sensor passes overhead. Other schemes can make use of reflected sunlight, with suitable spectral filters. The radiance of the sun is six orders of magnitude higher than that of a ground area with 5% reflectance (in near-direct sunlight). So, if the sensor has a ground sampling distance of 30m, it is possible to produce a measurable signal by reflecting sunlight towards the sensor from a flat mirror only 30mm square. In this case, it is necessary to direct the reflected sunlight with an accuracy of ±<0.25, since the sun subtends 0.5. Even this moderate requirement could be relaxed by using a larger area of curved mirror, or several small mirrors at slightly different angles. In general, a relatively dark background will be preferred, for example a small lake, extending over at least 9 ground-pixel areas. Use of mirror-directed sunlight provides greater flexibility in choice of wavelengths for calibration. One option is to use a Fabry-Perot etalon providing a set of lines in both VNIR and SWIR bands. This may provide a method for assessment also of SRF widths, as further discussed in section D March 2001 COMMERCIAL IN CONFIDENCE Page 221 of 245

222 Ground sources can probably be used, but require some further investigation and development. In particular, there are possible problems due to effects of atmosphere turbulence on the outgoing beam scintillation of the point image received at the sensor, during the integration period, will bias the effective centroid of the source image on the spectrometer entrance slit, which will bias the SRF location. It is probably possible to overcome scintillation problems (if they prove significant on further investigation) by using an array of sources, but note that the solution is likely to become more complex. A basic disadvantage is that a single ground installation will check the sensor spectral calibration at only one point in the orbit several installations at widely separated geographical locations would be needed to check for orbital variations in spectral calibration. D.4 USE OF ON-BOARD SOURCES D.4.1 SPECTRAL LAMPS There are several types of lamp that emit line spectra and are frequently used as laboratory wavelength references. These are discharge lamps, in which radiation is emitted from a plasma created in an enclosed bulb. The lamps contain two main constituents, a metal vapour and an inert gas. When the lamp is energised, depending on the lamp type various processes occur which cause excitation of the metal atoms, which then emit specific wavelengths according to the energy levels associated with their basic atomic structure. The basic interaction, in all the lamp types, is between flowing electrons in the plasma which excite the metal atoms. Depending mainly on the inert gas pressure, the conditions for the interaction are different: In low pressure lamps, the pressure of the inert filler is typically 2 torr, while in high pressure lamps it is typically 760 torr (1 atmosphere). The metal vapour pressure is typically ~10-3 torr. Low pressure lamps having electron temperatures between 11000K to 13000K with the gas temperature typically 40 to 60 C, but in a high pressure lamps, both temperatures are in the region ~4000K to 6000K, the high gas temperature creating a much higher collision rate. In high pressure lamps, the emitting region is typically an arc with a central high intensity filament while at low pressure a more uniform glow is emitted. The plasma conditions in low pressure lamps produce relatively little line broadening with only limited pressure and Doppler broadening and some self absorption back into the atomic ground state. Line broadening is more significant in high pressure lamps, which also produce a continuum background associated with the higher gas temperature. The spectral stability of low pressure lamps is exceptionally good, but total radiant output and radiance are generally low. High pressure lamps also provide stable spectral features, though with broader lines. They are generally operated at high input powers to produce high temperature, and at these high input powers, produce high total output. High pressure compact arcs produce the highest radiances possible from lamps. However, the efficiency of high pressure lamps is somewhat lower than that of low-pressure lamps, due to greater heat dissipation. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 222 of 245

223 Type High pressure sodium Other high pressure arcs Low pressure lamps, maximum Miniature low pressure lamps HCL, maximum power Metal halide lamps Electrodeless discharge lamp Typical optical Emitting output area >10 W total visible 30mm x 10mm > 5 W total visible arc lengths <1mm typical visible line gives radiant intensity: 10 mw.sr -1 typical visible line gives radiant intensity: 2 mw.sr -1 typical visible line gives radiant intensity: 1 mw.sr -1 8mm x 20mm ~2mm x 10mm 5 mm diameter 10 W total visible arcs up to 4mm 20 W total visible tubular several cm 2 Bulb Envelope > 150mm x 50mm x 50mm > 100mm x 50mm x 50mm 100mm x 20mm diam. 60mm x 6mm diam. 150mm x 40mm diam. 50mm x 30mm diam. 150mm x 150mm x 60mm Power, (life) >100W (20000h) >50W (10000h) ~10W to 50W (<500h) <10W (<300h) <10W (<1000h) >35W (3000h) >50W (years) Notes Power too high not preferred High power probably not preferred Possible preferred options Possible preferred option used in space High pressure lamps with halogens RF excited discharge Table D Spectral lamp summary Table D summarises types and typical properties of spectral lamps. In general, there is a preference for low-pressure lamps, which provide high efficiency and narrow spectral lines, without significant continuum between lines. The high pressure lamps dissipate more power than we should prefer to assign to a spectral calibration system their higher output powers may be considered only to illuminate large diffusers. D.4.2 LOW PRESSURE LAMPS A typical low pressure glow discharge lamp comprises a glass bulb within which is pumped an inert gas at low pressure, typically neon at 10 torr. The cathode is made including a sufficient amount of the element whose emission spectrum is required. In the special case of hollow cathode lamps (HCLs), the cathode is formed into a cylinder with the anode just above. The bulb has a window or lens at the top through which the emission can be seen. Figure D shows a generic HCL construction from Hamamatsu photonics. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 223 of 245

224 Figure D Typical HCL construction When a voltage is applied across the lamp, an electron current from the cathode produces ionisation of the filler gas. Positive ions flow to the cathode and produce sputtering. This forms of a metallic vapour which is excited by the electrons accelerating to the anode and spectral emission of the metallic element occurs. The spectrum is dominated by the energy transitions of the main cathode element, with some emission also from minor cathode constituents and the filler gas, and a large number of lines are generally emitted. Because of the conditions in the discharge line broadening is generally well below the nanometre scale. Many types of single element and several multi element lamps are available. Almost all metallic elements can be incorporated. Multi element lamps can provide more spectral lines but usually at the expense of the intensity of specific dominating lines. In their common application, of atomic absorption spectroscopy, only a few specific analytical lines are used, but the spectra of low pressure lamps are rich in the UV and VNIR regions up to 900nm. Figure D shows the spectrum from 240nm to 800nm for a PtCr(Ne) HCL, as tested for the GOME mission. 30 March 2001 COMMERCIAL IN CONFIDENCE Page 224 of 245

225 Figure D Spectra from the PtCr(Ne) HCL as tested for the GOME mission. D Space use of low pressure lamps HCLs have been used in at least the three recent space missions listed in Table D In general, they have been used where spectral resolution is below 1nm, and particularly in short wave and UV applications. The basic construction method was not extensively modified in any of the space applications. The base and socket were ruggedised and specific window materials and lenses were used where normally a UV transmitting flat window is used. Examples of HCL have been space qualified by thermal cycling and vibration testing at NASA Goddard space flight centre; their results showed brightness changes <3% and wave length changes < Agency Mission Instrument HCL Manufacturer NASA IUE IUE Pt (Ne) Westinghouse (US) NASA Space telescope FOS PtCr(Ne) Westinghouse (US) ESA GOME PtCr(Ne) Cathodeon (UK) Table D Space use of HCLs 30 March 2001 COMMERCIAL IN CONFIDENCE Page 225 of 245

226 D Emission characteristics There is little published data on the absolute intensity or radiance levels that can be obtained from low pressure lamps, but some estimates can be made from limited measurement data, together with general observations derived from discussions with manufacturers. Reported measurements show maximum UV line (306.5nm) photon intensity for a Pt HCL at 2.5x10 15 photons.sec -1.sr -1 when run at a maximum current of 60mA, corresponding to a radiant intensity of 1.6 mw.sr -1. A typical emitting area is 5mm diameter, giving a calculated line radiance of 80 W.m -2.sr -1. In the visible region, line strengths are typically higher than in the UV, so that we would expect some line radiances to be in the order 150 W.m -2.sr -1, at maximum current. There is very little data available for the SWIR band, but caesium is known to provide lines in the NIR/SWIR region. For most low-pressure lamps, radiation emerges over large solid angles, only partially restricted by electrode and other structures. In the special case of HCLs, due to the cathode structure, light emerges from the device in a limited cone angle of order 10 full angle, so that total usable output power in the VNIR band, in a single line, may be limited to order of 70 µw. However, the radiance of the HCL lamp, in it s preferred direction, is slightly higher than that of the other low-pressure lamps with similar elements, size and power. Radiance is the most significant parameter for direct illumination of a spectrometer entrance slit total output power is more important if the lamp is used to illuminate a large diffuser. D Output and life variations with current Lamp output varies typically with the 2 nd to 3 rd power of lamp current, depending on whether the vapour pressure for the element is high or low, as shown in Table D Maximum current is typically 10 to 12mA for high vapour pressure, and 15 to 20mA for a low vapour pressure. Lifetime is affected by mean operating current, typically lifetimes being between 3000 ma.hours and 5000 ma.hours. Failure mode is usually a fall in gas pressure as the sputtered atoms are absorbed, with the gas, into the bulb glass. There may be variations of intensity and current and discharge will eventually stop. Table D also shows variations in life with current and output for HCLs. Current 10mA (nominal for higher vapour pressure) 15mA (nominal for low vapour pressure) 60mA typical max current for either Radiance (estimated VNIR, single line) 1 W.m -2.sr -1 (relates to 3 rd power of current) 10 W.m -2.sr -1 (relates to 2 nd power of current) Lifetime 500 hrs 2W 330 hrs 3W 150 W.m -2.sr hrs 12W Power consumption Table D Typical output and life variations with current for HCLs 30 March 2001 COMMERCIAL IN CONFIDENCE Page 226 of 245

227 A possible way to increase lifetime is to modify the bulb to allow constant recharging of the inert filler gas to reduce the ageing process. Life will then be restricted by removal of the metal from the cathode and absorption into the bulb glass. D.4.3 USE OF SOLID STATE LASER DIODES Semiconductor diodes have a distinct advantage of over other laser sources in size, ruggedness and power requirements. They can provide wavelengths in both the VNIR and SWIR band, or, perhaps most conveniently, in a VNIR/SWIR overlap region. Their most serious disadvantage is generally considered to be temperature sensitivity of the spectral characteristics. The most common devices are based on III-V semiconductor alloys: GaAs, GaP and InSb. Wavelengths from 0.63 to 1.55µm are commonly available with powers from 1 to 100mW. A wide range of wavelengths is possible using materials listed in Table D Materials base Wavelength nm ZnSSe/CdZnSe/ZnSe/GaAs InGaN/AlGaN/GaN/Sapphire AlGaInP/GaAs AlGaAs/GaAs InGaAsP/GaAs InGaAs/GaAs InGaAsP/InP InGaAsSb/AlGaAsSb/GaSb Pb-Chalcogenide (eg PbSnTe) CMT 3400 Table D Solid state laser types and wavelengths D Output characteristics The output from a laser diode is a set of longitudinal modes, spaced in wavelength by half integers of the laser cavity length, within the gain bandwidth for the materials. This appears as a set of closely spaced lines within a Gaussian profile as indicated in figure D March 2001 COMMERCIAL IN CONFIDENCE Page 227 of 245

228 Figure D Typical laser diode spectral output distribution Increasing temperature causes the spectrum to shift to longer wavelengths, as also indicated in figure D In general, temperature control will be important if these devices are selected for spectral calibration. Tables and show typical ranges of operating parameter, and the sensitivity of spectral characteristics to temperature and current. Optical power outputs 1-100mW Emitting area 1-5 µm 2 Beam divergence 10 to 40 max angle (3:1 astigmatism) Polarisation Linear 100:1 Fibre coupled exit numerical aperture Lifetime 50,000 to hrs Operating current 50 to 500mA (using 50 to 10V dc) Table D Typical laser diode operating parameters Wavelength 850nm 1300nm 1550nm δλ (mode width) 0.27nm 0.6nm 0.9nm λmax (gain bandwidth) 2.0nm 5.0nm 7.0nm dλ p /dt 0.22nm/ C 0.5nm/ C 0.73nm/ C dλ m /dt 0.06nm/ C 0.12nm/ C 0.18nm/ C dλ m / current 0.2nm/mA 0.2nm/mA 0.2nm/mA Table D Temperature coefficients of spectral characteristics for laser diodes 30 March 2001 COMMERCIAL IN CONFIDENCE Page 228 of 245