Stennis Space Center
Parameters Describing Earth Observing
Remote Sensing Systems
Robert Ryan
Lockheed Martin Space Operations - Stennis
Programs
John C. Stennis Space Center
December 2-4, 2003
1
Contributors
Stennis Space Center
NASA Stennis Space Center
Vicki Zanoni
Mary Pagnutti
NASA Goddard Space Flight Center
Brian Markham
Jim Storey
2
Introduction
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• 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.
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Introduction (Continued)
Stennis Space Center
• 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.
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Introduction (Continued)
Stennis Space Center
• 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.
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Specifying a Digital Imagery Product
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•Spatial
– Spatial/Frequency Domain
– Aliasing
•Spectral (Sensor)
– Panchromatic or Multispectral
•Radiometry
– Relative
– Absolute
– Signal-to-Noise Ratio
•Geolocational Accuracy
– Circular Error
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Some Spatial Product Parameters
Stennis Space Center
•
•
•
•
•
Ground Sample Distance
Point Spread Function
Edge Response
Line Spread Function
Optical Transfer Function
– Modulation Transfer Function (MTF)
• Aliasing
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Ground Sample Distance
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• 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
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0.2 m GSD
0.4 m GSD
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0.6 m GSD
1.0 m GSD
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GSD 0.2 m
GSD 0.2 m 2x2
GSD 0.2 m 3x3
GSD 0.2 m 4x4
Stennis Space Center
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Point Spread Function
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• Scene is considered to be a collection of point
sources
• Each point source is blurred by the point spread
function (PSF).
System
Point source
A
A ( x  xo , y  yo )
Impulse Response (PSF) Displaced Point Spread Function
So
ASo
PSF  x, y 
APSF ( x  xo , y  yo )
PSF  x, y   A ( x  xo , y  yo )
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Image Formation
Stennis Space Center
• Image is convolution of point spread
function (PSF) with input scene

I i ( x, y )    I o ( x, y ) PSF ( x xo , y  yo )dxo dyo

where Ii (x, y) is the image
I o (x, y) is the input object
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Optical Transfer Function
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• An equivalent measurement of the PSF is
the Optical Transfer Function via a two
dimensional Fourier Transform
– Consists of Magnitude and Phase Terms
OTF (  ,  )  FT PSF ( x, y ) MTF (  ,  ) Exp( j (  ,  ))
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Modulation Transfer Function
Stennis Space Center
• MTF is a measure of an imaging system’s
ability to recreate the spatial frequency
content of scene
MTF is the magnitude of the
Fourier Transform of
the Point Spread Function / Line
Spread Function.
1.0
Cut-off
Spatial frequency
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Stennis Space Center
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Spatial/Frequency Domain Stennis Space Center
• Most specifications are written in terms of MTF
as a function of spatial frequency
– Dominant parameter is typically MTF @ 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
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Edge Response and Line Spread Function
Stennis Space Center
E( x )
l( x )
x
d
dx
x
OTF (  ,  )  FT PSF ( x, y ) MTF (  ,  ) Exp( j (  ,  ))
OTF (  ,0)  FT l ( x)  MTF (  ,0) Exp( j (  ,0))
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Relative Edge Response
Stennis Space Center
1.2
Ringing
Overshoot
1
0.8
0.6
0.4
Region where
mean slope is
estimated
Slope is
approximately
inversely
proportional to
width of PSF
0.2
0
Ringing
-0.2
Undershoot
-2.5 -2.0 -1.5 -1.0 -0.5
0
0.5
Pixels
1.0
1.5
2.0
2.5
Edge slope is a simple description applicable
for well behaved systems
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Stennis Space Center
Aliasing
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Assessing Levels of Aliasing
1
L
0
1
GSD/L= (GSD) (Slope) << 1 No Aliasing
GSD
L
0
1
Stennis Space Center
GSD/L= (GSD) (Slope) ~ 1 Moderately Aliased
GSD
PSF
L
GSD/L= (GSD) (Slope) > 1 Severely Aliased
0
GSD
Nyquist Sampling: Need to sample at least twice the highest spatial frequency to reconstruct image
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CIR Images of SRS Synthesized Products
Stennis Space Center
Savannah River Site - 28.8 GSD Simulations
AVIRIS 3.2 m GSD
28.8 m PSF, Slope 0.035 m-1
9.6 m PSF, Slope 0.10 m-1
16 m PSF, Slope 0.06 m-1
35.2 m PSF, Slope 0.028 m-1
41.6 m PSF, Slope 0.024 m-1
22.4 m PSF, Slope 0.045 m-1
48 m PSF, Slope 0.021 m-1
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Landsat Spatial Resolution Trade Study
Stennis Space Center
NDVI
1.0
0.8
AVIRIS: ~3 m GSD, ~3 m PSF
After ETM+ Band Synthesis
After 3x3 Boxcar Averaging:
~10 m GSD, ~10 m PSF
Actual Landsat 7 ETM+:
30 m GSD, ~36 m PSF
0.6
0.4
0.2
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
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Spatial Parameter Summary
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• Basic Description Well Behaved Systems
– In track and cross track
• GSD, Edge Slope
• GSD,PSF FWHM
• GSD, MTF @ Nyquist
• Full Description
– GSD and 2 D PSF or OTF
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Spectral
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• Basic 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
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Spectral Characteristics: BandsStennis Space Center
IKONOS Relative Spectral Response
Relative Spectral Responsivity
1
0.9
0.8
Pan
0.7
0.6
Blue
0.5
Green
0.4
Red
0.3
NIR
0.2
0.1
0
350
450
550
650
750
850
950
1050
Ba
Re nd-t
gi o-B
st
ra an
tio d
n
Wavelength (nm )
NIR
•
System Spectral Response
R
•
B
•
•
G
Band-to-Band Registration
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Radiometry Specification
Stennis Space Center
• Three Types
– Linearity
– Relative
• Pixel-to-Pixel
• Band-to-Band
• Temporal
– Absolute
• SNR
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Radiometry: Linearity
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Linear and non-linear response to input radiance
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Radiometry: Relative
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Normalized Average Row Values for Antarctica
IKONOS Image of Antarctica – RGB, POID 52847
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Includes material © Space Imaging LLC
Radiometry: Absolute
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NIR Band Calibration Summary
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Radiance [W/(m2sr)]
25
20
15
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
SI Radiance = DN/84.3
10
5
0
0
200
400
600
800
1000
DN
1200
1400
1600
1800
2000
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Signal-to-Noise Ratio
Stennis Space Center
• 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
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Pan Band MTFC
Pan Kernel
Stennis Space Center
Pan Kernel Column Section
Pan Kernel Row Section
5
5
4.5
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Cycles/ Pixel
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
Cycles/ Pixel
Row MTFC slightly stronger
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Noise Gain
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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 OFF SNR 25
MTFC ON SNR 13
NIR Kernel Applied to Simulated Imagery
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Spatial Resolution: SNR
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Original Maricopa IKONOS
Imagery
SNR ~ 100
Maricopa IKONOS Imagery
with Noise Added
SNR ~ 2
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Includes material © Space Imaging LLC
Geolocation Accuracy
Stennis Space Center
• Basic Description
– RMSE
– Circular Error (CE 90, CE 95)
• Full Description
– Distribution Functions
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CE90 Geolocational Accuracy
Stennis Space Center
• 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 welldefined points tested must
fall within a certain radial
distance.
Includes material © Space Imaging LLC
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CE 90 Example
Stennis Space Center
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.
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Summary
Stennis Space Center
• 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.
37