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
 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
Stennis tarps—edge target
Mirror Point
Sources
Figure 4. Quickbird panchromatic band image of
Brookings, SD target site on August 25, 2002.
Edge Targets
 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 zerocrossing 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
Point Targets
 Array of convex mirrors
or stars, asphalt in the desert, or…?
20 is a good number…
Sun
Satellite
 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
v
R
f=R/2
Convex
mirror
surface
C
Figure 10.
Convex mirror
geometry
Larry is outstanding in his field… of mirrors
Mirror Point
Sources as
viewed by
Quickbird
Other attributes of point sources:
Easy deployment
Easy maintenance
Very uniform backgrounds possible!
Point Sources
 Phasing of convex mirror array
Figure 11. Physical layout
of mirror array
tan  
x
1.25
 tan 1
y
10.2
  7 o ; D  7.20m
Figure 12. Distribution of
mirror samples in one Ground
Sample Interval (GSI)
Processing Techniques
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
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
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
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
f ( x) 
Figure 14. Parametric edge detection
a
d
 ( x  b) 
exp 
 1
c


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.
L S F (n)  ESF (n)  ESF (n  1) .
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.
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.
2D
Model
Fitting
Alignment
Impulse PSF
Aligned PSF
Fourier
Transform
Modeled PSF
MTF
Figure 16. Point Technique using Parametric 2D Gaussian model approach
Peak position Estimation of Point source
Mirror image
Raw data
Figure 17. Peak position
estimation
2-D Gaussian model
PSF Estimation by 2D Gaussian model
Aligned point source data
2-D Gaussian model
Y=0
X=0
Figure 18. PSF
estimation using 2-D
Gaussian model
X
1-D slice in X direction
Y
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.
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
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
351
354
339
337
342
(a) Mirror image-4
(c) Raw data
359
438
521
384
336
365
927
1787
456
323
366
450
539
383
349
352
356
347
351
344
(b) Pixel values
(d) 2-D Gaussian model
Peak estimation of September 7, 2002 Mirror 7 data
305
312
317
306
303
(a) Mirror image-7
(c) Raw data
296
371
410
325
310
255
781
1315
385
315
294
674
972
358
310
324
290
211
304
296
(b) Pixel values
(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
Mirror data
(b) Sliced PSF plots in along-track
Full-Width at Half-Maximum Measurement
[FWHM]
Overpass Date
Cross-track
[Pixel]
Along-track
[Pixel]
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
Mirror data
(b) MTF plots in along-track
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…