Keywords: interferometer, spectroscopy, remote sensing, calibration, radiometric performance

Transcription

1 Applications of high spectral resolution FTIR observations demonstrated by the radiometrically accurate ground-based AERI and the Scanning HIS aircraft instruments Henry E. Revercomb, Robert O. Knuteson, Fred A. Best, David C. Tobin, William L. Smith*, Wayne F. Feltz, Ralph A. Petersen**, Paolo Antonelli, Erik R. Olson Daniel D. LaPorte, Scott D. Ellington, Mark W.Werner, Ralph G. Dedecker, Ray K. Garcia, Nick N. Ciganovich, H.Benjamin Howell, Ken Vinson, and Steven A. Ackerman University of Wisconsin-Madison, Space Science and Engineering Center 1225 West Dayton Street, Madison Wisconsin, * NASA Langley Reseach Center ** NOAA/NCEP ABSTRACT Development in the mid 80s of the High-resolution Interferometer Sounder (HIS) for the high altitude NASA ER2 aircraft demonstrated the capability for advanced atmospheric temperature and water vapor sounding and set the stage for new satellite instruments that are now becoming a reality [AIRS (2002), CrIS (2006), IASI (2006), GIFTS (2005/6)]. Follow-on developments at the University of Wisconsin-Madison that employ interferometry for a wide range of Earth observations include the ground-based Atmospheric Emitted Radiance Interferometer (AERI) and the Scanning HIS aircraft instrument (S-HIS). The AERI was developed for the US DOE Atmospheric Radiation Measurement (ARM) Program, primarily to provide highly accurate radiance spectra for improving radiative transfer models. The continuously operating AERI soon demonstrated valuable new capabilities for sensing the rapidly changing state of the boundary layer and properties of the surface and clouds. The S-HIS is a smaller version of the original HIS that uses cross-track scanning to enhance spatial coverage. S-HIS and its close cousin, the NPOESS Airborne Sounder Testbed (NAST) operated by NASA Langley, are being used for satellite instrument validation and for atmospheric research. The calibration and noise performance of these and future satellite instruments is key to optimizing their remote sensing products. Recently developed techniques for improving effective radiometric performance by removing noise in post-processing is a primary subject of this paper. Keywords: interferometer, spectroscopy, remote sensing, calibration, radiometric performance 1. INTRODUCTION The AERI and the S-HIS provide up-looking and down-looking observations with high spectral resolution (0.5 cm -1 ) and broad infrared spectral coverage (3- up to 25 µm). Both realize high standards of radiometric accuracy by following and expanding on the calibration approaches developed for the HIS aircraft instrument. 1, 2 This accuracy has made possible a wide range of applications and products, including spectroscopy for improved radiative transfer models, high vertical resolution remote sensing of temperature and trace gases, surface emissivity and temperature, cloud radiative properties, satellite data validation, and related higher level products including atmospheric stability and water fluxes from combination with wind observations. The AERI instruments are also robust and well suited to continuous observing. 3-5 Multiple AERI instruments have successfully demonstrated autonomous operation for several years without any regular operator intervention, and routinely provide fully calibrated data through an internet link to the ARM science team. This robustness makes AERI an attractive candidate for broad deployment to detect detailed changes in the conditions of the planetary boundary layer. 6-7 Multispectral and Hyperspectral Remote Sensing Instruments and Applications, Allen M. Larar, Qingxi Tong, Makoto Suzuki, Editors, Proceedings of SPIE Vol (2003) 2003 SPIE X/03/$

2 This paper includes a brief discussion of the AERI and the S-HIS with some sample observations in Sections 2 and 3, and then concentrates on exciting new techniques for substantially reducing noise in Fourier Transform IR (FTIR) observations. Considerable attention is given to these noise reduction techniques, because radiometric noise, like calibration uncertainty, influences the accuracy of all of the downstream products. Section 4 discusses an effective technique for removing random uncorrelated spectral noise and Section 5 presents corrections for interferometric noise that can arise from vibration-induced mirror tilts, creating spectrally correlated random noise. 2. AERI: BRIEF DESCRIPTION AND SAMPLE RESULTS The AERI instrument was transformed from a new research tool to a robust instrument capable of operational applications under the Instrument Development effort of the DOE ARM Program. The standard AERI sampling provides one temperature and water vapor sounding of the boundary layer (0-3 km without ancillary data) every 8-10 minutes. 6, 8 This detailed view of the boundary layer is a major augmentation to the normal radiosonde view that operationally is limited to two soundings per day. For ARM, five AERIs are deployed at the Southern Great Plains (SGP) Oklahoma/Kansas site, as well as one each in Alaska and on Nauru in the Tropical Western Pacific. In addition to applications for atmospheric remote sensing and spectroscopy, the AERI in its marine configuration (M-AERI) has led to a significant improvement in the measurement accuracy of sea surface skin temperature from shipboard, 9 and its land surface version (S-AERI) offers new capabilities for characterizing land emissivity and temperature The instrument is based on a 4-port interferometer from the Bomem Michelson Series that was designed for use on a factory floor. The Optical Path Difference (OPD) scanning mechanism uses corner-cube reflectors mounted on a balanced wishbone arm that rotates about a flex-spring pivot. The detector system is a two-band sandwich of InSb over PC HgCdTe, cooled to between 68 and 78 K by a Litton Stirling cooler. The interferometer is mounted on an optical bench that also supports a pair of high emissivity calibration blackbodies (one ambient and one normally at 60 C), and a 45 scene selection mirror that is used to point up to the sky at zenith, to the blackbodies, and down to an LN 2 or ice blackbody for testing. Other configurations customized for marine and surface applications also allow viewing at selected up-looking and down-looking angles for deriving surface emissivity and temperature. The basic AERI system also includes an extensive real-time housekeeping system that provides a comprehensive instrument health display. This display is presented in the form of a collection of stoplights that are easily interpreted by non-experts (normally green, they turn yellow if a parameter goes slightly out of bounds and red if there is a real problem). Current radiance spectra are also displayed along with time sequences of selected brightness temperatures. In addition to controlling basic system operation, a PC computer performs complete radiometric and spectral calibration (including non-linearity correction, removal of self apodization, and standardization of the spectral scale). It also provides a network interface that allows data to be automatically transferred to a central site via the internet. Although not fully implemented, the same computer is capable of performing temperature and water vapor profile retrievals in real time. The AERI instruments have helped to set a new standard in radiometric calibration for high spectral resolution observations. 13, 14 This standard has been verified by tests with a NIST maintained blackbody reference. 14 AERI in its ground-based application is also immune to the vibration-induced interferometric noise discussed in Section 5 for the aircraft-based S-HIS. However, the implications for AERI sampling rate and other considerations of the noise filtering techniques discussed in Section 4 are currently under investigation. One possibility is to make use of noise filtering to allow the sky sampling rate to be increased for special cloud studies. Figure 2-1 shows an example of 24-hour water vapor time sequences for the network of five AERI instruments deployed for the Southern Great Plains site of the ARM Program is shown for 10 December The lowest 2.5 km are shown with winds from co-located Microwave Profiler instruments overlaid. Recent results of this type from the SGP network have been used to demonstrate the potential for new meteorological applications for the identification of precursors to severe weather. 15, 16 Future applications for weather service or naval surface sounding systems and for support of airport weather are envisioned. 12 Proc. of SPIE Vol. 4897

3 Vici, OK Altitude Hillsboro, KS ARM Central Facility Morris, OK Mixing Ratio Purcell, OK Time, UTC Figure 2.1. Time-height cross-sections of water vapor mixing ratio shown as contour plots with wind vectors from co-located NOAA wind profilers overlaid. The four outlying sites are located about 100 km from the Central Facility on the boundaries of the extended Southern Great Plains site that represents one grid cell of a Global Circulation Model. 3. SCANNING HIS: BRIEF DESCRIPTION AND APPLICATIONS The S-HIS instrument flies on a number of aircraft platforms including the NASA ER-2, the NASA DC-8 and soon the Proteus. 17, 18 The S-HIS uses cross-track scanning to provide spatial imaging that expands significantly on the original nadir-only sampling of the HIS. On the Proteus aircraft, an upward view will also be added for calibration verification and for studies of upper level water vapor. The S-HIS is also easier to operate in the field than the original HIS, because it employs a mechanical detector cooler in place of a cryogenically-cooled dewar requiring both LHe and LN 2. The S-HIS was initially designed to fly aboard an unmanned aircraft vehicle (UAV) with limited payload capacity. This drove it to be small, light-weight, and to have low power consumption. The S-HIS uses a dynamically aligned Planemirror Michelson interferometer with laser-controlled sampling from Bomem of Quebec, Canada. Due to the initial design constraints on size, the S-HIS instrument uses a novel "3-color" detector configuration with the shortwave detector positioned in front of the side-by-side long- and mid-wave detectors that share the available aperture. All of the detectors share the same field stop and therefore, see the same spot on the ground. This arrangement allows cooling to be provided by a single mechanical cooler and eliminates the need for dichroic beamsplitters. The cooler is the same 0.6 W, split-cycle Stirling cooler from Litton that is used on the AERI instrument. The S-HIS 45 scene mirror allows the instrument to image using cross-track scanning. It executes a sequence consisting of multiple views of the earth and two calibration sources, one at ambient and another controlled to a fixed temperature (typically 310 K). The raw interferograms from each view are compressed in real time to reduce the volume of data. A complex numerical filter is applied using a digital signal processor (DSP), while a second DSP is used for controlling the instrument. The S-HIS uses calibration techniques that were developed for the HIS and AERI to 2, 4, 5, 13, 14 achieve the high radiometric accuracy needed for atmospheric state retrieval and spectroscopic applications. The ER2 aircraft configuration for S-HIS currently exposes the instrument to vibration conditions that introduce interferometric errors that can be as large or even larger than the detector noise equivalent radiance. While steady progress has been made in reducing the instrument sensitivity to vibrations, this situation has led to the study of a correction technique for interferometric noise that may prove useful for other FTIR instruments. This technique, the subject of Section 5, makes use of measurements of vibration-induced wavefront tilts. To monitor wavefront tilts, the S-HIS system records wavefront phase differences between pairs of separated laser beams for both the x- and y- axes of Proc. of SPIE Vol

4 the dynamic alignment system. These phase differences are both sampled for every eighth HeNe laser fringe (8.4 KHz sampling rate). This gives a tilt measurement with one-to-one correspondence to every point of the stored intererferograms (numerically filtered) for each band. While the phase error sampling system has a Nyquist frequency of 4.2 khz, the system is filtered to a 2 khz cut-off to suppress noise aliasing. The highest resonant frequencies normally observed occur in the region khz. The primary resonances are largely contained between Hz. Examples of two interesting results from S-HIS observations are given in Figures 3-1 to 3-2. Figure 3-1. Image of the Okavanga Delta in southern Africa on 27 August 2000 from Scanning HIS at cm -1 on the NASA ER2 during the SAFARI mission (left) and from MODIS on Tera (right). Clearly S-HIS is not primarily an imager, but the key is that there is a detailed IR spectrum for every pixel of the S-HIS image. The example spectra contrast the signature of an unvegetated surface (top) with a vegetated or water surface. The combination of observations from a high spectral resolution instrument like the S-HIS or the current AIRS on the NASA Aqua platform with high spatial resolution instruments like the MODIS or its aircraft simulator offer many new opportunities. 350 T(K) Wavenumber (cm -1 ) 2800 Figure 3-2. Infrared fire signature known as the blue spike observed for fires in Africa during the NASA SAFARI mission (7 September, 2000). The signature requires the presence of heated air over a cooler surface. 14 Proc. of SPIE Vol. 4897

5 4. PRINCIPAL COMPONENT NOISE FILTERING: SCANNING HIS EXAMPLE For any measurement, the sensitivity (or signal-to-noise ratio) is limited by the instrument signal throughput and the noise associated with the basic physical principles of detection. Sensitive, cryogenically cooled semi-conductor detectors are used for infrared spectral observations to enhance the sensitivity, but maximizing the signal-to-noise ratio is still a challenge for achieving a high sensitivity to atmospheric state retrieval. Usually, we think of the sensitivity as being a basic limit to the utility of the observations. However, infrared emission spectra are a good example of inherently redundant measurements for which the effective signal-to-noise ratio for the radiance at a chosen wavenumber can actually be improved by using noise filtering during data processing. Because the number of independent sources of spectral variation (e.g. resolvable atmospheric temperature and trace gas distributions) can be substantially smaller than the number of spectral channels observed, the information content of spectra can be represented by fewer variables than the number of channels. The approach used here 19, 20 is to use Principal Component Analysis (PCA) to map the spectral channel basis set into a smaller set of orthogonal principal components (or eigenfunctions) that are chosen to represent the actual variance of the observations. By limiting the number of principal components used, a significant fraction of the random uncorrelated noise can be eliminated from the representation of the information content. This can significantly improve the sensitivity of individual spectral channels. 4.1 Theory The procedure of representing spectra with eigenfunction expansions is not at all new, and it has been widely recognized as a technique for reducing data volume. However, the effectiveness for increasing the sensitivity of individual channels to some atmospheric effects is quite striking and it seems that the power of the approach for noise filtering has not been fully recognized. The approach described here minimizes the error in representing the signal by using eigenfunctions derived from the observations themselves. The steps followed for this dependent-set noise filtering for a set of M observed spectra with N channels each are: 1. Divide each observed spectrum by the estimated Noise Equivalent Radiance (NER) to create effectively white noise, 2. Create the NxN covariance matrix of the M spectra (subtract the mean of the M spectra from each spectrum, form an MxN matrix with each spectral deviation from the mean being one of the M rows, and right-multiply that matrix by its transpose), 3. Derive eigenfunctions of the covariance matrix, 4. Create the NxN noise-filtering matrix (select the first N s eigenfunctions, form an NxN s restricted eigenfunction matrix with each selected eigenfunction being one of the N s columns, and left-multiplying this matrix by its transpose), 5. Reconstruct each noise-filtered spectrum (row vector) by left-multiplying by the noise-filtering matrix, and 6. Multiply by the NER to return to radiance space. Normalizing by NER before noise filtering puts all of the channels on a common signal-to-noise scale. This prevents regions with unusually large noise from being fit as if they have large signal. The noise filtering effect of this procedure can be explained as follows. Following normal procedures for eigenfunction determination, the first eigenfunction fits the largest amount of variance over the sample set, the second eigenfunction fits the largest amount not explained by the first, and so forth. Therefore, the early eigenfunctions preferentially fit real signal variations that are correlated in wavenumber, not random uncorrelated noise. Fitting uncorrelated noise is very inefficient such that fitting all of the random uncorrelated noise on N channels requires N eigenfunctions. Therefore, for a sample variance that can be represented by N s eigenfunctions, not all of the random noise will be reproduced. This leads to a noise filtering benefit. If, on the average, each eigenfunction fits the same amount of random noise, the noise filter will reduce the level of random noise by the factor sqrt(n s /N) for a very large sample set (M ). Simulations of realistic infrared spectra have demonstrated this noise reduction factor to be realized on the average across the spectrum. To realize a large noise reduction factor that is close to the ideal sqrt(n s /N), it is both important for the sample size to be large and for the atmospheric variations of the sample to be relatively limited (making the necessary N s small). For the results shown here, N s is between 10 and 20 and N is order 1000 of each of the 3 S-HIS spectral bands. Also, it is important for the sample size M to be large (here, M= 4700). For a sample size of 5,000-10,000, the eigenvalues for Proc. of SPIE Vol

6 random uncorrelated noise are all nearly equal, whereas, if the sample size is too small, the limited statistics cause the lowest eigenvalues to be substantially larger than subsequent values even for random uncorrelated noise. Poor statistics make it possible for early eigenfunctions to fit a larger fraction of the uncorrelated noise, leading to less efficient noise filtering. Inadequate statistics may be one reason this technique has not been fully exploited in the past. More work is needed to explore criteria for selecting N s and effective sample size. However, it seems likely that a key concept to keep in mind is that the right choice for optimum noise filtering is likely to differ from the choice for other applications like temperature and water vapor retrieval. In general, for retrieval it desirable to use a relatively large number of eigenfunctions to make the conditions of applicability as large as possible, and for optimum noise reduction N s should be as small as possible. 4.2 Sample Results Noise filtering has been applied to data collected by the S-HIS onboard the NASA DC8 aircraft during the AFWEX experiment over the DOE Atmospheric Radiation Measurement (ARM) central facility in Oklahoma on 10 December The observations used were largely cloud free and were all nadir viewing from a fixed altitude of 10.7 km. Four 150 mile legs of about 20 minutes each centered on the ARM site were spread over about a 5 hour time period. An example of 100 consecutive filtered and unfiltered individual brightness temperature spectra are compared in Figure 4.1. This is just a small section of the longwave window portion of the spectra, but a detailed look is required to make the important small effects visible. Examples could be shown from many parts of the spectrum. The effect of the filtering is clearly dramatic, but the question of whether the spectra are distorted or forced to agree with the mean naturally arises. Figure 4.1. Overlays of 100 consecutive brightness temperature spectra covering cm -1 (records ). Those on the left are filtered and those on the right are the original spectra (the vertical scale is from 266 to 278 K). That the spectra are not all driven to the mean is illustrated in Figure 4.2. The 100 sample means of filtered and of unfiltered spectra selected from different time periods are compared to each other and to the mean of most of the spectra (4100 out of 4700). Note that these means from different portions of the flight differ significantly from each other and from the overall mean. Also, they are in reasonable agreement with the 100-sample means of unfiltered data, but actually demonstrate better physical consistency. Figure sample mean spectra compared to the mean of 4100 spectra (third from the top). Those on the left are filtered and those on the right are the unfiltered original spectra (the vertical scale is from 271 to 278 K). Finally, an example from the shortwave band of the spectrum is used to show that filtered spectra exhibit good agreement with calculated line-by-line spectra. First, Figure 4.3 shows the region of interest for an individual spectrum 16 Proc. of SPIE Vol. 4897

7 that agrees well with the mean over 4100 spectra to illustrate the large difference between an individual filtered and unfiltered spectrum. H 2 O CO 2 CO CO 2 Figure 4.3. Radiance spectrum from 2020 to 2140 cm -1, illustrating the large difference between an individual filtered and unfiltered spectrum. The dark narrow curves are large sample means and the individual filtered spectrum from record These spectra are all tightly grouped throughout. The lighter curve is the original, unfiltered record 2347 spectrum. Figure 4.4 shows the same spectral region as a brightness temperature spectrum compared to a calculated spectrum. H 2 O CO 2 CO CO 2 Figure 4.4. Comparison of filtered observed brightness temperature spectra (single and mean of 16) to a spectrum calculated using the ARM line-by-line radiation transfer model (LBLRTM) with a microwave-scaled sonde atmospheric state. The excellent agreement demonstrated the physical reasonability of noise filtered spectra. These examples seem to provide clear examples of the effectiveness of PCA for removing random noise from observed high spectral resolution spectra. For this case, the noise is reduced by factors of between 5 and 10. One subtlety that should be remembered is the resulting correlation of the residual noise with spectral features. However, if this correlated noise is kept to a small fraction of the original noise, it should be quite acceptable for most applications. 5. INTERFEROMETRIC NOISE REMOVAL: SCANNING HIS EXAMPLE Interferometric noise can result from vibration-induced wavefront tilts between the two interfering beams of a Michelson interferometer, especially in the environment of an aircraft platform. Unlike noise from the detector or extraneous electrical noise, this type of noise is correlated in wavenumber, since it is really a small modification of the signal interferogram itself, induced by time-dependent tilts. For the type of vibration spectra experienced with S-HIS, Proc. of SPIE Vol

8 the interferometric noise is a low resolution perturbation, originating dominantly from low OPD regions where the interferogram is largest. It is desirable to limit this source of noise to a level substantially smaller than other fundamental noise sources. Mechanical design providing vibration isolation and avoiding resonances that can be stimulated by unshielded vibrations contribute toward this goal. Also, the dynamic alignment on the S-HIS suppresses a significant band-pass of low frequency vibrations. However, even using these techniques the goal of negligible interferometric noise is not always easily accomplished in harsh environments. Therefore, we have implemented accurate measurements of the dynamic wavefront tilt in the Scanning HIS to form the basis for a correction in ground processing. This section presents our correction approach and preliminary evidence that it is quite effective. 5.1 Theory Tilt-related interferometric noise can arise from two basic effects, (1) amplitude modulation from the effective smearing of optical path difference (OPD) for non-parallel wavefronts and (2) sample-position errors related to the variation of OPD as a function of position in the signal beam for non-parallel beams. Our correction technique for amplitude modulation effects has been presented in another recent SPIE publication. 21 This subsection summarizes that result and presents the theoretical basis for correction of related sample position errors on the S-HIS. The first step in both types of correction is to remove the effects of onboard numerical filtering. After S-HIS interferogram points are initially sampled at the metrology laser fringe rate, a complex numerical filter is convolved with the interferogram to reduce the data volume (by factors of 8 or 16) without information loss or noise aliasing. Since this convolution combines points sampled with somewhat different wavefront tilts, the most accurate correction should start by first reconstructing an approximation to the original unfiltered interferogram. The filter effects can be removed by the following steps, because the numerical filter convolution is equivalent (by the convolution theorem) to multiplication by a real, asymmetric function in the spectral domain: A. Fourier transform to spectral domain (complex interferogram to complex spectrum). B. Divide the spectrum by the spectral equivalent of the numerical filter (real, but asymmetric). C. Condition the bounds of the spectra to reduce ringing, D. Place the unfiltered spectrum into a wavenumber scale zero-filled out to the original Nyquist wavenumber. E. Make the complex spectrum symmetric about ν = 0. F. Fourier transform to obtain a real, asymmetric interferogram. The effect of amplitude modulation is based on the well-known relationships that wavefront tilts θ t reduce the amplitude of a monochromatic beam by the following factors: 2 J 1 (z)/z [1- z 2 /8 + z 4 /192 - ], circular beam (1) sin(z)/z [1- z 2 /6 + z 4 /120 - ], square beam (2) where J 1 is a first order Bessel function, z = 2πνRθ t, R is the radius (or ½ side of the square) of the beam, and ν is the wavenumber. For S-HIS, the total tilt θ t is a combination of the vibration induced jitter tilt in each of two orthogonal directions (θ x and θ y ) and a small static tilt (θ ox and θ oy ) arising from the refractive effects of wedges in the beamsplitter and compensator substrates that are slightly mismatched. This causes the proper wavefront alignment of the IR beam to differ a small amount from that established by the interferometer dynamic alignment system that establishes alignment based on HeNe laser beams. The total tilt squared can be written as θ t 2 (x,ν)= [θ x0 (ν)+ θ x (x)] 2 + [θ y0 (ν)+ θ y (x)] 2 = [θ x0 2 (ν) + θ y0 2 (ν)] + [θ x 2 (x) + θ y 2 (x)] + 2 [θ x0 (ν) θ x (x) + θ y0 (ν) θ y (x)] = A(ν) + B(x) + 2 [θ x0 (ν) θ x (x) + θ y0 (ν) θ y (x)]. (3) where x is the optical path difference. Note the mixed wavenumber and OPD dependence caused by the delay dependence of the jitter tilts and the wavenumber dependence of the static tilts. Writing out the first modulation term in the Taylor series expansion for a circular beam (Equation 1) gives 18 Proc. of SPIE Vol. 4897

9 -½[π ν R θ t(x, ν)] 2 = -½ (πr) 2 [ν 2 A(ν)+ν 2 B(x)+2ν 2 θ x0 (ν) θ x (x)+2ν 2 θ y0 (ν) θ y (x)] -½ (πr) 2 G i (ν) H i (x) (4) where G 1 = ν 2 A(ν) = ν 2 [θ 2 x0 (ν) + θ 2 y0 (ν)] H 1 = 1 G 2 = ν 2 H 2 = B(x) = [θ 2 x (x) + θ 2 y (x)] G 3 = 2ν 2 θ x0 (ν) H 3 = θ x (x) G 4 = 2ν 2 θ y0 (ν) H 4 = θ y (x). Note that this representation of the effect of tilt modulation makes the ν- and x-dependences mathematically separable, which will be important to representing our corrections in terms of Fourier transforms. Now, this formulation for the modulation effects of a tilt on a monochromatic signal in a circular beam can be substituted into the representation of an interferogram F(x) as the Fourier transform of a complex, unfiltered spectrum Cc, yielding F(x) = dν C c {1-½[π ν R θ t(x, ν)] 2 }exp(i2πνx) = dν C c exp(i2πνx) - ½(π R) 2 [H i (x) dν G i (ν) C c exp(i2πνx) = FT (C c ) - ½ (πr) 2 [H i (x) FT (G i (ν) C c )] (5) where Fourier transformation is indicated by FT and can be accomplished using FFTs. The equation describing how to correct a raw, uncalibrated spectrum Co (Fourier transform of the uncorrected interferogram F(x)) can be obtained from Equation 5 by taking the Fourier transform and rearranging to yield C c = C 0 + ½(π R) 2 FT [H i (x) FT (G i (ν) C c )] C 0 + ½(π R) 2 FT [H i (x) FT (G i (ν) C 0 )]. (6) The final expression is given completely in terms of C 0, by replacing C c with C 0 in the second term. This is justified because the second term is a reasonably small correction (mathematically, the justification can be proven by iteratively substituting the expression for Cc into itself, creating an infinite series with the indicated first two terms). Note that for small tilts, this is a rigorous correction that is expressed entirely in terms of true Fourier transfomations. In addition to affecting interferogram amplitudes, tilts cause sample-position errors. Depending on the detailed optical design, this effect can actually be substantially larger than modulation effects because it is linear in the tilt, rather than quadratic. On the S-HIS this effect is substantial because the design makes use of aperture sharing for spectral band separation. Since the center of the IR beams in the interferometer for the longwave (LW) and midwave (MW) bands are displaced from the location of the laser beam for the sample-triggering detector by a distance d (on the order of 1 cm), tilt causes the mean OPD for each sample of these bands to differ from the uniformly-spaced sample positions triggered by laser signal zero crossings. The error is just δx = θ d (x) d (7) where θ d (x) is the component of the jitter tilt (not the total tilt including static tilt) in the direction from the sampletriggering beam center to the IR beam center. The tilt θ d (x) is defined by θ d (x) = +θ x (x) cos γ - θ y (x) sin γ, for the longwave detector (8) -θ x (x) cos γ + θ y (x) sin γ, for the midwave detector Proc. of SPIE Vol

10 where γ is the angle between the x-axis and the vector to the longwave detector from the interferometer beam center, nominally 45. The correction for sample-position errors is conceptually simple, just requiring interpolation to equally spaced points from the known, unequally spaced sample points. In this case, linear interpolation is sufficiently accurate, because the interferogram resulting from numerical filter removal is very highly over-sampled. The interferogram correction can therefore be expressed simply as F c (x i ) = F(x i ) - ½[F(x i+1 ) - F(x i-1 )] (δx/ x) (9) where x is the OPD spacing between points and δx is the sample-position error from Equation 7. While the implementation of this correction has not been fully demonstrated, preliminary results shown in the next subsection demonstrate the viability of the approach discussed here. This sample-position error effect and correction technique can be an important consideration for designing interferometer systems. The effect can also result when offaxis detectors are used for imaging, depending on the optical design (the effect can be minimized by putting the aperture stop or its image close to the interferometer mirrors). 5.2 Sample Results The S-HIS has been through a series of improvements to reduce the level of vibration-induced interferometric noise. These changes have included (1) improved immunity to high level acoustic forcing for operation on the NASA DC8 (including shielding, housing resonance modification and damping, and optical bench vibration isolation), (2) replacement of the original porch-swing Michelson mirror drive carriage with a custom linear-bearing carriage, (3) modification of dynamic alignment mechanism to remove a resonance, and (4) electrically controlled static tilt offset to reduce the amplification effect of a non-zero static tilt contribution. Here we are showing data from two classes of performance aboard the NASA ER2 aircraft, one from February of 2000 before the Michelson drive was changed, and one from a period in 2000 shortly after the drive was changed. The sample magnitude spectra of wavefront tilt errors shown in Figure 5.1 demonstrate the reduction realized after incorporation of the new Michelson drive. Figure 5.1. Sample tilt magnitude spectra for the S-HIS aboard the NASA ER2, before (top 2) and after replacement of Michelson porchswing drive with linear bearing mechanism (bottom 2). 20 Proc. of SPIE Vol. 4897

11 Figure 5.2 demonstrates the consistency of S-HIS tilt measurements with the relationships presented above for the impact on the infrared spectrum. The data used was collected from views of the hot calibration blackbody (310 K) during the flight on 27 February 2000, before the porchswing drive was replaced. The very large infrared amplitude effect of the tilts present in this data are useful to demonstrate the effect of tilt corrections. The plot on the left shows the fractional variation of the infrared signal near ZPD (determined from an average over much of the uncalibrated IR spectrum) plotted as a function of the total tilt (scattered points), compared to the expectation from Equation 4. The band-average static tilt (θ x0 = 6.3, θ x0 = -8.2 µrad) was determined by optimizing this agreement. The effect of applying the correction of Equation 6 is shown on the right. 1- Modulation Modulation Correlation Total Wavefront Tilt, microrad (with estimated static tilts) 1-Mod Fit(tilt) Figure 5.2. Demonstration of tilt modulation effects and the correction approach (Equation 6) applied to early S-HIS data for which the effects are very large. The residual variation after correction (shown on the right) is comparable to the uncorrelated detector noise. Similar results have verified the principles needed to correct for interferometric noise from sample position errors. Near ZPD, the effect of low frequency sample position errors from vibration approximates a translation of the interferogram (an effective translation by δx causes the phase to change by 2πν δx ). The result of using this effect to verify the principles needed to correct for sample position errors is shown in Figure 5.3. The figure compares the component of the tilt responsible for creating sample position errors derived from the phase of the infrared spectrum to the measured tilt. The agreement is clearly very good Tilt(gamma) Tilt(LWphase 1) Diff HBB Record Number Figure 5.3. Verification of the effect of vibration-induced sample position errors on infrared observations. The good agreement of the measured tilt and the tilt calculated from the effects of OPD perturbation on the phase demonstrate the validity of the relationships needed to correct for this type of interferometric noise. Proc. of SPIE Vol

12 6. CONCLUSIONS Effective techniques for removing noise from high spectral resolution infrared observations have been defined and demonstrated. For random noise that is uncorrelated with wavenumber, Principal Component Analysis (based on eigenfunctions of the observed spectra themselves) can remove a large fraction of instrument noise without serious loss of signal, when applied to large data sets with limited amounts of atmospheric variation. Examples of practical data sets include 6-10 minute portions of polar orbiting sounder data, significant fractions of research aircraft flights with S- HIS, or several days of AERI ground-based data. This technique is possible because high-resolution infrared spectra are highly redundant, in the sense that the number of spectral channels is much larger than the number of independent atmospheric variables responsible for spectral variations. It seems likely that other techniques with higher numerical efficiency for representing the basic information content of infrared spectra may also be capable of a similar noise reduction. Techniques are also defined to reduce vibration-induced interferometric noise that can result from wavefront tilt jitter and is correlated in wavenumber space. Depending on detailed instrument design factors, tilts can cause both signal amplitude-modulation errors or errors in optical path difference. Correction techniques that make use of real-time tilt measurements in post-processing algorithms are defined for both types of interferometric noise. The same relationships also provide the basis for implementing hardware to make real-time corrections in the instrument analog and digital processing chain. These noise reduction techniques provide higher signal-to-noise ratio spectra to improve a wide range of products that have been demonstrated with the S-HIS and AERI instruments, including spectroscopy, remote sensing of temperature and trace gases, surface emissivity and temperature, cloud radiative properties, and related higher level products. ACKNOWLEDGEMENTS We gratefully acknowledge support for this work by the DOE Atmospheric Radiation Measurement (ARM) program, the NASA EOS program, and the NPOESS Integrated Project Office (IPO) under contract number 50-SPNA REFERENCES 1. Smith, W. L., H. E. Revercomb, H. B. Howell, H. M. Woolf, D. LaPorte, H. Buijs, J. N. Berube, F. Murcray, and D. Murcray, HIS - Remote Sensing from the NASA U-2 Aircraft. Second Conference on Satellite Meteorology/Remote Sensing and Applications, Williamsburg, Virginia, May, Revercomb, H.E., H. Buijs, H.B. Howell, D.D. LaPorte, W.L. Smith, and L.A. Sromovsky, Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder, Appl. Opt., 27, , Revercomb, H.E.; Best, F.A.; Dedecker, R.G.; Dirkx, T.P.; Herbsleb, R.A.; Knuteson, R.O.; Short, J.F., and Smith, W.L., Atmospheric Emitted Radiance Interferometer (AERI), 4 th Symposium on Global Change Studies, Anaheim, CA, Boston, MA: American Meteorological Society; 46-49, Revercomb, H.E.; Best, F.A.; Knuteson, R.O.; Whitney, B.A.; Dirkx, T.P.; Dedecker, R.G.; Garcia, R.K.; van Delst, P.; Smith, W.L., and Howell, H.B., Atmospheric Emitted Radiance Interferometer, part I: Status, basic radiometric accuracy, and unexpected errors and solutions, Proceedings of the Sixth Atmospheric Radiation Measurement (ARM) Science Team Meeting, San Antonio, TX, 4-7 March Washington, DC: US Department of Energy, Office of Energy Research, Office of Biological and Environmental Research, Environmental Sciences Division; , Revercomb, H.E.; Best, F.A.; Knuteson, R.O.; Smith, W.L.; Dirkx, T.P.; Dedecker, R.G.; Feltz, W.F.; Garcia, R.K.; Whitney, B.A., and Howell, H.B., Downwelling IR radiance spectra for the ARM Program: Capabilities and status of the Atmospheric Emitted Radiance Interferometer (AERI), IRS 96: Current problems in atmospheric radiation. Proceedings of the International Radiation Symposium, Fairbanks, Alaska, August Hampton, VA: A. Deepak Publishing; , Feltz, W. F., W.L. Smith, R.O. Knuteson, H.E. Revercomb, H.M. Woolf, and H.B. Howell, Meteorological applications of temperature and water vapor retrievals from the ground-based atmospheric emitted radiance interferometer (AERI), J. Appl. Meteor., 37, , Feltz, W. F. and J. R. Mecikalski, Monitoring High Temporal Resolution Convective Stability Indices Using the Ground-based Atmospheric Emitted Radiance Interferometer (AERI) During the 3 May 1999 Oklahoma/Kansas Tornado Outbreak, Wea. Forecasting, 17, , Proc. of SPIE Vol. 4897

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