In-Flight Characterization of Image Spatial Quality using Point Spread Functions D. Helder, T. Choi, M. Rangaswamy Image Processing Laboratory Electrical Engineering Department South Dakota State University December 3, 2003

Outline Introduction Target Types and Deployment Processing Techniques Lab-based methods In-flight measurements Target Types and Deployment Edge, pulse and point targets Processing Techniques Non-parametric and parametric methods High Spatial Resolution Sensor Examples Edge and point method examples with Quickbird Pulse method examples with IKONOS Conclusions Acknowledgement The authors gratefully acknowledge the support of the JACIE team at Stennis Space Center.

Introduction Resolving spatial objects is perhaps the most important objective of an imaging sensor. One of the most difficult things to define is an imaging system’s ability to resolve spatial objects or its ‘spatial resolution.’ This paper will focus on using the Point Spread Function (PSF) as an acceptable metric for spatial quality.

Laboratory Methods A sinusoidal input by Coltman (1954). Tzannes (1995) used a sharp edge with a small angle to obtain a finely sampled ESF. A ball, wire, edge, and bar/space patterns were used as stimuli for a linear x-ray detector Kaftandjian (1996). Many other targets/approaches exist…

In-flight Measurements Landsat 4 Thematic Mapper (TM) using San Mateo Bridge in San Francisco Bay (Schowengerdt, 1985). Bridge width less than TM resolution (30 meters) Figure 1. TM image of San Mateo Bridge Dec. 31, 1982.

In-flight Measurements TM PSF using a 2-D array of black squares on a white sand surface (Rauchmiller, 1988). 16 square targets were shifted ¼-pixel throughout sub-pixel locations within a 30-meter ground sample distance (GSD). (a) Superimposed over example TM pixel grid (b) Band 3 Landsat 5 TM image on Jan 31, 1986. Figure 2. 2-D array of black squares

In-flight Measurements MTF measurement for ETM+ by Storey (2001) using Lake Pontchartrain Causeway. Spatial degradation over time was observed in the panchromatic band by comparing between on-orbit estimated parameters. Figure 3. Lake Pontchartrain Causeway, Landsat 7, April 26, 2000.

Target Types & Deployment General Attributes For LSI systems—any target should work! Orientation—critical for oversampling Well controlled/maintained/characterized—homogeneity and contrast, size, SNR Time invariance—for measurement of system degradation 1-D or 2-D target? Three target types have been found useful for high resolution sensors: edge, pulse, point

SDSU tarps—pulse target Mirror Point Sources Stennis tarps—edge target Figure 4. Quickbird panchromatic band image of Brookings, SD target site on August 25, 2002.

Edge Targets Figure 5. Edge target Reflectance: exercise the dynamic range of the sensor Relationship to surrounding area Size: 7-10 IFOV’s beyond the edge Make it long enough! Uniformity Characterize it regularly ‘Natural’ and ‘man-made’ targets Optimal for smaller GSI’s (< 3 meters) Figure 5. Edge target

Edge Target Attributes Flat spectral response as shown in Figure 6. Orientation—critical for edge reconstruction Figure 7. Orientation for edge reconstruction Figure 6. Spectral response of Stennis tarps

Pulse Target Another 1-D target More difficult to deploy: 2 straight edges 3 uniform regions More difficult to obtain PSF Optimal for 2-10m GSI Other properties similar to edges Figure 8. Pulse target

Pulse Target Attributes Spatial pulse = Fourier domain sinc( f ) Fourier transform of the pulse should avoid zero-crossing points on significant frequencies. 3 GSI is optimal to obtain a strong signal and maintain ample distance from placing a zero-crossing at the Nyquist frequency as shown in Figure 9. Figure 9. Nyquist frequency position on the input sinc function vs. tarp width

Figure 10. Convex mirror geometry Point Targets Array of convex mirrors or stars, asphalt in the desert, or…? 20 is a good number… Proper focal length to exercise sensor over its dynamic range. Proper relationship to background Is it really a point source? Uniformity of mirrors and background dsat Sun Satellite C f=R/2 v R Convex mirror surface Figure 10. Convex mirror geometry

Mirror Point Sources as viewed by Quickbird Larry is outstanding in his field… of mirrors

Other attributes of point sources: Easy deployment Easy maintenance Very uniform backgrounds possible!

Point Sources Phasing of convex mirror array Figure 12. Distribution of mirror samples in one Ground Sample Interval (GSI) Figure 11. Physical layout of mirror array

Processing Techniques Parametric Approach Assumes underlying model is known Only need to estimate a ‘few’ parameters Less sensitive to noise Will only estimate 1 PSF Generally preferred approach Non-parametric Approach Assumes no underlying model Must estimate entire function More sensitive to noise When no information is available of the PSF. Will estimate ‘any’ PSF May be used for a first approximation

Figure 13. SNR definition for edge, pulse, and point targets Processing Techniques Signal-to-Noise Ratio (SNR) definition Simulations suggest SNR > 50 for acceptable results Figure 13. SNR definition for edge, pulse, and point targets

Figure 14. Parametric edge detection Non-parametric Step 1: Sub-pixel edge detection and alignment A model-based method is used to detect sub-pixel edge locations The Fermi function was chosen to fit transition region of ESF Sub-pixel edge locations were calculated on each line by finding parameter ‘b’ Since the edge is straight, a least-square line delineates final edge location in each row of pixels Figure 14. Parametric edge detection

Non-parametric Step 2: Smoothing and interpolation Necessary for differentiation for Fourier transformation modified Savitzky-Golay (mSG) filtering mSG filter is applicable to randomly spaced input Best fitting 2nd order polynomial calculated in 1-pixel window Output in center of window determined by polynomial value at that location Window is shifted at a sub-pixel scale, which determines output resolution Minimal impact on PSF estimate Figure 15. mSG filtering

Non-parametric Step 3: Obtain PSF/MTF For an edge target: LSF is simple differentiation of the edge spread function (ESF) which is average profile. Additional 4th order S-Golay filtering is applied to reduce the noise caused by differentiation. MTF is calculated from normalized Fourier transformation of LSF. For a pulse target: Since the pulse response function is obtained after interpolation, the LSF cannot be found directly ( a deconvolution problem). Instead the function may be transformed via Fast Fourier Transform and divided by the input sinc function to obtain the MTF after proper normalization.

Figure 16. Point Technique using Parametric 2D Gaussian model approach Parametric Approach (Point source Gaussian example) Step 1: Determine peak location of each point source to sub-pixel accuracy. Step 2: Align each point source data set to a common reference point. Step 3: Estimate PSF from over-sampled 2-D data set. Step 4: MTF is obtained by applying Fourier transform to the normalized PSF. Aligned PSF Modeled PSF MTF PSF Impulse 2D Model Fitting Fourier Transform Alignment Figure 16. Point Technique using Parametric 2D Gaussian model approach

Figure 17. Peak position estimation Peak position Estimation of Point source Mirror image Raw data Figure 17. Peak position estimation 2-D Gaussian model

Figure 18. PSF estimation using 2-D Gaussian model PSF Estimation by 2D Gaussian model Aligned point source data 2-D Gaussian model X Y=0 Y X=0 Figure 18. PSF estimation using 2-D Gaussian model 1-D slice in X direction 1-D slice in Y direction

High Spatial Resolution Sensor Examples Site Layout Figure 18. Brookings, SD, site layout, 2002.

Edge Method Procedure Figure 19. Panchromatic band analysis of Stennis tarp on July 20, 2002 from Quickbird satellite.

Figure 20. LSF & MTF over plots of Stennis tarp target Edge Method Results Quickbird sensor, panchromatic band The FWHM values varied from 1.43 to 1.57 pixels MTF at Nyquist ranged from 0.13 to 0.18 Figure 20. LSF & MTF over plots of Stennis tarp target

Figure 21. IKONOS blue band tarp target on June 27, 2002 Pulse Method Procedure Figure 21. IKONOS blue band tarp target on June 27, 2002

Pulse Method Results IKONOS sensor, Blue band Date 6/27/02 7/3/02 7/22/02 FWHM 2.9149 2.9689 2.8336 MTF 0.4722 0.4511 0.3347 SNR 55.7 102.0 82.1 Figure 22. Over plots of IKONOS blue band tarp targets with cubic interpolation and MTFC

Point source targets using Quickbird panchromatic data (a) Mirror image-4 (b) Pixel values Visually symmetric in cross-track, but shifted in the along-track [0.2pixel]. Also the estimated peak location appears to be shifted in along-track. (c) Raw data (d) 2-D Gaussian model

Peak estimation of September 7, 2002 Mirror 7 data (a) Mirror image-7 (b) Pixel values Blurring is asymmetric in both directions. (c) Raw data (d) 2D Gaussian model

Least Square Error Gaussian Surface for aligned mirror data of August 25, 2002, Quickbird images (a) Aligned mirror data (b) 2-D PSF

Least Square Error Gaussian Surface for aligned mirror data of September 7, 2002, Quickbird images. (a) Aligned mirror data (b) 2-D PSF

Comparison of Aug 25 and Sept 7 , 2002 PSF plots   (a) Sliced PSF plots in cross-track (b) Sliced PSF plots in along-track Blur in aug is more than sept may be due to atmospheric scattering and mir placement errors Humidity on aug is 60% and on sept is 48%. Along-track blur is more than cross-track due to motion of sensor Mirror data Full-Width at Half-Maximum Measurement [FWHM] Overpass Date Cross-track [Pixel] Along-track August 25, 2002 1.427 1.428 September 07, 2002 1.396 1.398 Relative Error (%) 2.17 2.10

Comparison of Aug 25 and Sept 7 , 2002 MTF plots (a) MTF plots in cross-track (b) MTF plots in along-track Mirror data Modulation Transfer Function values @ Nyquist Days / Direction Cross-track   Along-track August 25, 2002 0.163 0.162 September 07, 2002 0.190 0.189 Relative Error (%) 16.60 16.70

Conclusions In-flight estimation of PSF and MTF is possible with suitably designed targets that are well adapted for the type of sensor under evaluation. Edge targets are Easy to maintain, Intuitive, Optimal for many situations. Pulse targets are Useful for larger GSI, More difficult to deploy/maintain, MTF estimates more difficult due to zero-crossings. Point sources are Capable of 2-D PSF estimates, Show significant promise for sensors in the sub-meter to several meter GSI range.

Conclusions (con’t.) Processing methods are critical to obtaining good PSF estimates. Non-parametric methods are Most advantageous when little is known about the imaging system, Better able to track PSF extrema, More difficult to implement, More susceptible to noise. Parametric methods are Superior when system model is known, Easier to implement, Less noise sensitive, Only work for one PSF function. Many other targets types and processing methods are possible…