1. 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

2. 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.

3. 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.

4. 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…

5. 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.

6. 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

7. 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.

8. 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

9. 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.

10. 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

11. 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

12. 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

13. 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

14. 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

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

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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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.

23. 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

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

25. 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

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

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

28. 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

29. 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

30. 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

31. Point source targets using Quickbird panchromatic data
(a) Mirror image (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

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

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

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

35. 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

36. 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

37. 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.

38. 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…