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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

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Stennis Space CenterContributors

NASA Stennis Space Center

Vicki Zanoni

Mary Pagnutti

NASA Goddard Space Flight Center

Brian Markham

Jim Storey

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Stennis Space CenterIntroduction

• 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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Stennis Space CenterIntroduction (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.

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Stennis Space CenterIntroduction (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.

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Stennis Space CenterSpecifying 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

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Stennis Space CenterSome Spatial Product Parameters

• Ground Sample Distance • Point Spread Function• Edge Response • Line Spread Function• Optical Transfer Function

– Modulation Transfer Function (MTF)

• Aliasing

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Stennis Space CenterGround 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

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1.0 m GSD

0.2 m GSD 0.4 m GSD

0.6 m GSD

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Stennis Space CenterGSD 0.2 m GSD 0.2 m 2x2

GSD 0.2 m 3x3 GSD 0.2 m 4x4

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Point Spread Function

• Scene is considered to be a collection of point sources

• Each point source is blurred by the point spread function (PSF).

Displaced Point Spread Function

System

Point source Impulse Response (PSF)A

),( oo yyxxA

oS oAS

),( ,

,

oo yyxxAyxPSF

yxPSF

),( oo yyxxAPSF

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Stennis Space CenterImage Formation

• Image is convolution of point spread function (PSF) with input scene

objectinput theis y)(x,I

image theis y)(x,I where

),(),(),(

o

i

oooooi dydxyyxxPSFyxIyxI

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Stennis Space CenterOptical 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

)),((),(),(),( jExpMTFyxPSFFTOTF

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Stennis Space CenterModulation Transfer Function

• 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 ofthe Point Spread Function / LineSpread Function.

1.0

Cut-off

Spatial frequency

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Stennis Space CenterSpatial/Frequency Domain

• 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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Stennis Space Center

Edge Response and Line Spread Function

dx

d

)x(E

)x(l

x x

))0,(()0,()()0,(

)),((),(),(),(

jExpMTFxlFTOTF

jExpMTFyxPSFFTOTF

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Relative Edge Response

-2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5-0.2

0

0.2

0.4

0.6

0.8

1

1.2RingingOvershoot

RingingUndershoot

Region where mean slope is estimated

Ed

ge

Res

po

nse

Pixels

Edge slope is a simple description applicable for well behaved systems

Slope is approximately inversely proportional to width of PSF

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Aliasing

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Stennis Space CenterAssessing Levels of Aliasing

0

1

0

1

GSD/L= (GSD) (Slope) ~ 1 Moderately Aliased

GSD/L= (GSD) (Slope) << 1 No Aliasing

Nyquist Sampling: Need to sample at least twice the highest spatial frequency to reconstruct image

0

1GSD/L= (GSD) (Slope) > 1 Severely AliasedL

GSD

GSD

L

GSD

L

PSF

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Stennis Space CenterCIR Images of SRS Synthesized Products

AVIRIS 3.2 m GSD 16 m PSF, Slope 0.06 m-1

28.8 m PSF, Slope 0.035 m-1 35.2 m PSF, Slope 0.028 m-1 41.6 m PSF, Slope 0.024 m-1 48 m PSF, Slope 0.021 m-1

22.4 m PSF, Slope 0.045 m-19.6 m PSF, Slope 0.10 m-1

Savannah River Site - 28.8 GSD Simulations

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Landsat Spatial Resolution Trade Study

AVIRIS: ~3 m GSD, ~3 m PSFAfter 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

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Stennis Space CenterSpatial Parameter Summary

• 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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Stennis Space CenterSpectral

• 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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IKONOS Relative Spectral Response

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

350 450 550 650 750 850 950 1050

Wavelength (nm)

Rel

ativ

e S

pec

tral

Res

po

nsi

vity

Pan

Blue

Green

Red

NIR

Spectral Characteristics: Bands

System Spectral Response

•

•• •B

R

G

NIR

Band-to-Band Registration

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Stennis Space CenterRadiometry Specification

• Three Types– Linearity– Relative

• Pixel-to-Pixel• Band-to-Band• Temporal

– Absolute

• SNR

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Stennis Space CenterRadiometry: Linearity

Linear and non-linear response to input radiance

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Stennis Space CenterRadiometry: Relative

IKONOS Image of Antarctica – RGB, POID 52847

Normalized Average Row Values for Antarctica

Includes material © Space Imaging LLC

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Stennis Space CenterRadiometry: Absolute

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5

10

15

20

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30NIR Band Calibration Summary

SSC, Big Spring, TX, 6/22/01SSC, Big Spring, TX, 8/5/01SSC, Lunar Lake, NV, 7/13/01SSC, Lunar Lake, NV, 7/16/01SSC, Maricopa, AZ, 7/26/01SSC, Stennis, 52 tarp, 1/15/02SSC, Stennis, 3.5 tarp, 1/15/02SSC, Stennis, 22 tarp, 1/15/02SSC, Stennis, Concrete, 1/15/02SSC, Stennis, Grass, 1/15/02SSC, Stennis, 52 tarp, 2/17/02SSC, Stennis, 3.5 tarp, 2/17/02SSC, Stennis, 22 tarp, 2/17/02SSC, Stennis, Concrete, 2/17/02SSC, Stennis, Grass, 2/17/02UofA/SDSU, Brookings, SD, 7/3/01UofA/SDSU, Brookings, SD, 7/17/01UofA/SDSU, Brookings, SD, 7/25/01UofA, Lunar Lake, NV, 7/13/01UofA, Lunar Lake, NV, 7/16/01UofA, Railroad Valley, NV, 7/13/01UofA, Railroad Valley, NV, 7/16/01UofA, Ivanpah, CA, 11/19/01SI Calibration Curve, Post 2/22/01

DN

Ra

dia

nc

e [

W/(

m2 s

r)]

SI Radiance = DN/84.3

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Stennis Space CenterSignal-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

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Stennis Space CenterPan Band MTFC

Row MTFC slightly stronger

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Pan Kernel Column Section

Cycles/ Pixel-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Cycles/ Pixel

Pan Kernel Row Section

Pan Kernel

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Stennis Space CenterNoise Gain

SNR decreases with MTFC processing and the noise displays a spatial frequency dependence that did not exist at the

sensorBand 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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Stennis Space CenterSpatial Resolution: SNR

Original Maricopa IKONOS Imagery

SNR ~ 100

Maricopa IKONOS Imagery with Noise Added

SNR ~ 2

Includes material © Space Imaging LLC

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Stennis Space CenterGeolocation Accuracy

• Basic Description– RMSE– Circular Error (CE 90, CE 95)

• Full Description– Distribution Functions

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Stennis Space CenterCE90 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

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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.

CE 90 Example

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Stennis Space CenterSummary

• 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.