Spatial Stray Light Correction for Imaging Instruments Using Matrix Method Yuqin Zong
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1 CORM 2007 Annual Conference, Gaithersburg, Maryland, May 8-11, 2007 Spatial Stray Light Correction for Imaging Instruments Using Matrix Method Yuqin Zong
2 Outline 1) Introduction 2) Principle of spatial stray light correction 3) Validation of spatial stray light correction 4) Examples of applications 5) Summary
3 Outline 1) Introduction 2) Principle of spatial stray light correction 3) Validation of spatial stray light correction 4) Examples of applications 5) Summary
4 Logarithmic SPD normalized to FEL lamp's peak Si Detector Delative Responsivity SPECTRAL stray light (Spectrometer measures a point source) 1.0E E K FEL lamp 1 1.0E E E-03 Si detector Rel. Resp. Deuterium Lamp E Wavelength (nm) 0
5 SPATIAL stray light in imaging instruments for measurements of extended sources Size-of-source effect (radiometry) Out-of-field sensitivity or veiling glare (photometry) Wire character contrast Display contrast
6 Methods for dealing with stray light 1) Improve instruments by hardware - limited, low signal, 2) Avoid it, by matching the spectrum power distribution of the calibration source and that of the test source. - need to know the source to be measured - need many standard sources, and a reference instrument 3) Correct it mathematically - Spectral - Spatial
7 Outline 1) Introduction 2) Principle of spatial stray light correction 3) Validation of spatial stray light correction 4) Examples of applications 5) Summary
8 Logarithmic LSF [a. u.] Characterization of a spectrometer for Line Spread Functions (LSF) for Spectral Stray-light Correction Pixel Index i Wavelength (nm)
9 Relative Signal Relative Signal Relative Signal Relative Signal Result of a Spectral Stray-light Correction using a 1024x1024 Correction Matrix A Broadband Source A Green LED 1.0E E E+00 log 1.0E+00 log 1.0E E E E E E E E E E E E-07 1 count 1.0E E E E E E E E E E E E E-04 1 count linear Wavelength (nm) 9.0E E E E E E E E E E E-04 linear Wavelength (nm)
10 Principle of Spatial Stray-light Correction LSF 1-D Line Spread Function (LSF) 2-D Stray light Correction Matrix PSF 2-D Point Spread Function (PSF) 3-D Stray light Correction Matrix Problem! 3-D matrix inversion!
11 Point Spread Function (PSF) at Pixel (3, 3) Stray-light Distribution Function (SDF) at Pixel (3, 3) y 1,1 y 1,2 y 1,3 y 1,4 y 1,5 y 2,1 y 2,2 y 2,3 y 2,4 y 2,5 y 3,1 y 3,2 y 3,3 y 3,4 y 3,5 d i, j i, j y scatter, i, j y true, i, j IR(3,3) d 1,1 d 1,2 d 1,3 d 1,4 d 1,5 d 2,1 d 2,2 d 2,3 d 2,4 d 2,5 d 3,1 d 3,2 d 3,3 d 3,4 d 3,5 y 4,1 y 4,2 y 4,3 y 4,4 y 4,5 d 4,1 d 4,2 d 4,3 d 4,4 d 4,5 y 5,1 y 5,2 y 5,3 y 5,4 y 5,5 d 5,1 d 5,2 d 5,3 d 5,4 d 5,5 d 1,1 d 1,2 d 1,3 d 1,4 d 1,5 d 2,1 d 2,2 d 2,3 d 2,4 d 2,5 d 3,1 d 3,2 d 3,3 d 3,4 d 3,5 d 4,1 d 4,2 d 4,3 d 4,4 d 4,5 d 5,1 d 5,2 d 5,3 d 5,4 d 5,5 d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 d 9 d 10 d 11 d 12 d 13 d 14 d 15 d 16 d 17 d 18 d 19 d 20 d 21 d 22 d 23 d 24 d 25
12 D = d 1.. d 1.. d 2.. d 2.. d 3.. d 3.. d 4.. d 4.. d 5.. d 5.. d 6.. d 6.. d 7.. d 7.. d 8.. d 8.. d 9.. d 9.. d 10.. d 10.. d d d d d d.. 16 d 16.. d 17.. d 17.. d 18.. d 18.. d 19.. d 19.. d 20.. d 20.. d.. 21 d 21.. d.. 22 d 22.. d 23.. d 23.. d 24.. d 24.. d 25.. d 25 d 1 d 2 d 3 d 4 d 5 d 6 d 7 d 8 d 9 d 10 d 11 d 12 d 13 d 14 d 15 d 16 d 17 d 18 d 19 d 20 d 21 d 22 d 23 d 24 d 25 d 11 d 12 d 13 d 14 d 15
13 m,..., k,...,5,4,3,2,1 m,..., k,...,5,4,3,2,1 2D Point Spread Function (PSF) 1, 2, 3, 4, 5, 6,, l,, n 2D Stray-light Distribution Function (SDF) 1, 2, 3, 4, 5, 6,, l,, n d k, l i y scatter, k, l IR y true, k, l 2D SDF:(k, l) i = (k-1) n +l 1D SDF (i)
14 D The SDF matrix, D (m n) (m n) d d.. d.. d d 1,1 1,2 1, J 1,n 1 1,n d d.. d.. d d 2,1 2, 2 2, J 2, n-1 2, n d d.. d.. d d i,1 i, 2 i, J i, n-1 i, n d d.. d.. d d n-1,1 n-1, 2 n-1, J n-1, n-1 n-1, n d d.. d.. d d n,1 n, 2 n, J n, n-1 n, n i = (k-1) n +l 2-D Y meas 1-D Y meas Y s = D Y IR Y meas = Y IR + Y s = Y IR + D Y IR Y IR A 1 Y meas C spat Y meas = [I + D] Y IR = A Y IR Correction Matrix Any problem! A image A trillion element matrix! 128 Gbytes memory Windows Vista 64
15 Dealing with huge number of pixels (binning) raw sig 3 3 binned raw sig 3 3 binned corrected sig Y IR C spat Y meas Y spat Y meas Y IR Y IR Y meas - Y spat 3 3 binned stray light sig Yspat 2-D Surface Interp stray light sig Yspat corrected sig
16 Outline 1) Introduction 2) Principle of spatial stray light correction 3) Validation of spatial stray light correction 4) Examples of applications 5) Summary
17 An imaging radiometer/photometer: 2-D CCD array: 1392x1040 CCD size: 4.65 µm 4.65 µm A/D: 12 bits Lens: 55 mm No TE-cooler PSF test conditions: Distance: 2 m Pin hole size: 0.2 mm diameter Iris: F2.8 Signal Dynamic range: > 6 orders
18 A measured Point Spread Function (PSF)
19 Relative Signal Relative Signal Relative Value Relative Value Results of Spatial Stray-light Corrections (4096x4096 Correction Matrix) A White Spot A Black Spot 1.0E E E E E E E-02 log 1.0E E E E E E E E E Position (mm) Measured Sig Corrected Sig linear Position (mm) Measured Sig Corrected Sig
20 Outline 1) Introduction 2) Principle of spatial stray light correction 3) Validation of spatial stray light correction 4) Examples of applications 5) Summary
21 Remote Sensing (S. W. Brown, J. Rice, B. C. Johnson) Gerhard Meister, NASA, The MODIS Aqua Point-Spread Function for Ocean Color Bands, ISPRS, Vol XXXVI (7/W20) Figure 2. MODIS Aqua band 11 PSF in track direction (solid line) and scan direction (dashed line). Figure 3. Contamination of top-of-atmosphere radiances over ocean due to a large cloud (semi-infinite) for band 11.
22 Display measurements (E. F. Kelley, P.A. Boynton, EEEL, NIST)
23 IR Radiometry and Imaging (Sergey Mekhontsev)
24 Traffic Signs (signals) Measurements (Cameron Miller)
25 Quantitative medical imaging (Maritoni Litorja)
26 Hyperspectral Image Projector (HIP) (Joe Rice, Steve Brown) Spectral Engine Spatial Engine Reference Instrument Unit Under Test DMD2 DMD1 J.P. Rice
27 Summary A simple, practical method has been developed for correcting spatial stray-light errors in imaging instruments (array detector or scanning) using stray light correction matrixes. This method can be used to correct stray light errors in imaging instruments with large number of pixels. The spatial stray light correction also eliminates other types of errors such as detector read-out smearing, and detector window reflection, etc. The errors are reduced by 1 to 2 orders of magnitude. This technique can be used in many fields and measurement uncertainty can be reduced significantly.
28 References [1] ZONG Y., BROWN S. W., JOHNSON B. C., LYKKE K. R., and OHNO Y., Simple spectral stray light correction method for array spectroradiometers, Appl. Opt., 2006, 45, [2] ZONG Y., BROWN S. W., JOHNSON B. C., LYKKE K. R., and OHNO Y., Correction of stray light in spectrographs: implications for remote sensing, Proc. SPIE, 2005, 5882, to [3] Yuqin Zong, Steven W. Brown, Keith R. Lykke, and Yoshi Ohno, CORRECTION OF STRAY LIGHT IN SPECTRORADIOMETERS AND IMAGING INSTRUMENTS, Proc. 26 th of the CIE, Beijing, 2007.
29 Acknowledgements Yoshi Ohno, Steve Brown, Keith Lykke, and Many.
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