1. Parameters Describing Earth Observing Remote Sensing Systems
Robert Ryan
Lockheed Martin Space Operations - Stennis Programs
John C. Stennis Space Center
December 2-4, 2003

2. Contributors NASA Stennis Space Center Vicki Zanoni Mary Pagnutti
NASA Goddard Space Flight Center
Brian Markham
Jim Storey

3. Introduction
Standard definitions for spatial, spectral, radiometric, and geometric properties are needed describing passive electro-optical systems and their products.
Sensor parameters are bound by the fundamental performance of a system, while product parameters describe what is available to the end user.

4. Introduction (Continued)
Because detailed sensor performance information may not be readily available to an international science community, standardization of product parameters is of primary importance.
User community desire as a few parameters as possible to describe the performance of a product or system.

5. Introduction (Continued)
Guidelines and standards are of little use without standardized terms.
Studies that describe the impact of parameters on various applications are critically needed.
This presentation is going to emphasize spatial.

6. Specifying a Digital Imagery Product
Spatial
Spatial/Frequency Domain
Aliasing
Spectral (Sensor)
Panchromatic or Multispectral
Radiometry
Relative
Absolute
Signal-to-Noise Ratio
Geolocational Accuracy
Circular Error

7. Some Spatial Product Parameters
Ground Sample Distance
Point Spread Function
Edge Response
Line Spread Function
Optical Transfer Function
Modulation Transfer Function (MTF)
Aliasing

8. Ground Sample Distance
Ground Sample Distance (GSD) is the distance between the center of pixels in an image
Products are typically resampled and do not completely agree with intrinsic sensor sampling
Most commonly used spatial parameter
Does not tell the whole story

9. 0.2 m GSD
0.4 m GSD
0.6 m GSD
1.0 m GSD

10. GSD 0.2 m
GSD 0.2 m 2x2
GSD 0.2 m 3x3
GSD 0.2 m 4x4

11. Point Spread Function
Scene is considered to be a collection of point sources
Each point source is blurred by the point spread function (PSF).
System
Point source
Impulse Response (PSF)
Displaced Point Spread Function A

12. Image Formation
Image is convolution of point spread function (PSF) with input scene

13. Optical Transfer Function
An equivalent measurement of the PSF is the Optical Transfer Function via a two dimensional Fourier Transform
Consists of Magnitude and Phase Terms

14. Modulation Transfer Function
MTF is a measure of an imaging system’s ability to recreate the spatial frequency content of scene
1.0
MTF is the magnitude of the
Fourier Transform of
the Point Spread Function / Line
Spread Function.
Cut-off
Spatial frequency

16. Spatial/Frequency Domain
Most specifications are written in terms of MTF as a function of spatial frequency
Dominant parameter is typically Nyquist frequency
Nyquist frequency depends on GSD
Nyquist frequency = 1/(2*GSD)
MTF at Nyquist is a measure of aliasing
Edge Response is more intuitive
RER (Relative Edge Response)
Ringing

17. Edge Response and Line Spread Function

18. Relative Edge Response
-2.5
-2.0
-1.5
-1.0
-0.5
0.5
1.0
1.5
2.0
2.5
-0.2
0.2
0.4
0.6
0.8 1
1.2
Ringing
Overshoot
Region where mean slope is estimated
Slope is approximately inversely proportional to width of PSF
Edge Response
Ringing
Undershoot
Pixels
Edge slope is a simple description applicable
for well behaved systems

19. Aliasing

20. Assessing Levels of Aliasing1 L
GSD/L= (GSD) (Slope) << 1 No Aliasing
GSD 1 L
GSD/L= (GSD) (Slope) ~ 1 Moderately Aliased
GSD
PSF 1
GSD/L= (GSD) (Slope) > 1 Severely Aliased L
GSD
Nyquist Sampling: Need to sample at least twice the highest spatial frequency to reconstruct image 1

21. CIR Images of SRS Synthesized Products
Savannah River Site GSD Simulations
AVIRIS 3.2 m GSD
9.6 m PSF, Slope 0.10 m-1
16 m PSF, Slope 0.06 m-1
22.4 m PSF, Slope m-1
28.8 m PSF, Slope m-1
35.2 m PSF, Slope m-1
41.6 m PSF, Slope m-1
48 m PSF, Slope m-1 1

22. Landsat Spatial Resolution Trade Study
AVIRIS: ~3 m GSD, ~3 m PSF
After ETM+ Band Synthesis
0.2
0.4
0.6
0.8
1.0
After 3x3 Boxcar Averaging:
~10 m GSD, ~10 m PSF
After Additional 3x3 Filtering:
~10 m GSD, ~30 m PSF
After Additional 3x3 Decimation:
~30 m GSD, ~10 m PSF
After Additional 3x3 Averaging:
~30 m GSD, ~30 m PSF
Actual Landsat 7 ETM+:
30 m GSD, ~36 m PSF
NDVI

23. Spatial Parameter Summary
Basic Description Well Behaved Systems
In track and cross track
GSD, Edge Slope
GSD,PSF FWHM
GSD, Nyquist
Full Description
GSD and 2 D PSF or OTF

24. Spectral Basic Description Full Description Center Wavelength
Full width half maximum
Slope edge at 50% points
Others
Ripple
Out-of-band rejection
Full Description
Spectral response functions with units

25. Spectral Characteristics: Bands
Band-to-Band Registration
System Spectral Response

26. Radiometry Specification
Three Types
Linearity
Relative
Pixel-to-Pixel
Band-to-Band
Temporal
Absolute
SNR

27. Radiometry: Linearity
Linear and non-linear response to input radiance

28. Radiometry: Relative Normalized Average Row Values for Antarctica
IKONOS Image of Antarctica – RGB, POID 52847
Includes material © Space Imaging LLC

29. Radiometry: Absolute NIR Band Calibration Summary Radiance [W/(m2sr)]
200
400
600
800
1000
1200
1400
1600
1800
2000 5 10 15 20 25 30
NIR Band Calibration Summary
SSC, Big Spring, TX, 6/22/01
SSC, Big Spring, TX, 8/5/01
SSC, Lunar Lake, NV, 7/13/01
SSC, Lunar Lake, NV, 7/16/01
SSC, Maricopa, AZ, 7/26/01
SSC, Stennis, 52 tarp, 1/15/02
SSC, Stennis, 3.5 tarp, 1/15/02
SSC, Stennis, 22 tarp, 1/15/02
SSC, Stennis, Concrete, 1/15/02
SSC, Stennis, Grass, 1/15/02
SSC, Stennis, 52 tarp, 2/17/02
SSC, Stennis, 3.5 tarp, 2/17/02
SSC, Stennis, 22 tarp, 2/17/02
SSC, Stennis, Concrete, 2/17/02
SSC, Stennis, Grass, 2/17/02
UofA/SDSU, Brookings, SD, 7/3/01
UofA/SDSU, Brookings, SD, 7/17/01
UofA/SDSU, Brookings, SD, 7/25/01
UofA, Lunar Lake, NV, 7/13/01
UofA, Lunar Lake, NV, 7/16/01
UofA, Railroad Valley, NV, 7/13/01
UofA, Railroad Valley, NV, 7/16/01
UofA, Ivanpah, CA, 11/19/01
SI Calibration Curve, Post 2/22/01 DN
Radiance [W/(m2sr)]
SI Radiance = DN/84.3

30. Signal-to-Noise Ratio
Several definitions exists
For well behaved systems (Very few bad detectors) Basic Description
Temporal Noise or Shot Noise Limited
SNR for an extended uniform radiance scenes
Advanced Description
Includes both detector nonuniformity, processing and shot noise components

31. Pan Band MTFC Row MTFC slightly stronger Pan Kernel
Pan Kernel Row Section
-0.5
-0.4
-0.3
-0.2
-0.1
0.1
0.2
0.3
0.4
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
Pan Kernel Column Section
Cycles/ Pixel 5
4.5 4
3.5 3
2.5 2
1.5 1
-0.5
-0.4
-0.3
-0.2
-0.1
0.1
0.2
0.3
0.4
0.5
Cycles/ Pixel
Row MTFC slightly stronger

32. Noise Gain
SNR decreases with MTFC processing and the noise displays a spatial frequency dependence that did not exist at the sensor
Band
Noise Gain
Blue
1.59
Green
1.63
Red
1.68
NIR
1.81
Pan
4.16
MTFC ON SNR 13
MTFC OFF SNR 25
NIR Kernel Applied to Simulated Imagery

33. Spatial Resolution: SNR
Original Maricopa IKONOS
Imagery
SNR ~ 100
Maricopa IKONOS Imagery
with Noise Added
SNR ~ 2
Includes material © Space Imaging LLC

34. Geolocation Accuracy Basic Description Full Description RMSE
Circular Error (CE 90, CE 95)
Full Description
Distribution Functions

35. CE90 Geolocational Accuracy
A standard metric often used for horizontal accuracy in map or image products is circular error at the 90% confidence level (CE90). The National Map Accuracy Standard (NMAS) established this measure in the U.S. geospatial community. NMAS (U.S. Bureau of the Budget, 1947) set the criterion for mapping products that 90% of well-defined points tested must fall within a certain radial distance.
Includes material © Space Imaging LLC
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.

36. CE 90 Example
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.
Data scatter plot showing the geolocational errors present in this imagery. Additionally, the CE90 (calculated by the FGDC standard method and by a percentile method) and the typical pixel size are shown on this plot.

37. Summary
For “well behaved” systems and products a few simple well chosen parameters can describe the system or product.
Derived products can be significantly different than their intrinsic sensor data
Studies that describe the impact of parameters on various applications are critically needed.