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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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Contributors

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

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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)

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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)

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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 6

Some Spatial Product Parameters

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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 0.6 m GSD 0.4 m GSD

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1.0 m GSD 9

GSD 0.2 m GSD 0.2 m 2x2

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GSD 0.2 m 3x3 GSD 0.2 m 4x4

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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

A

Point source Impulse Response (PSF)

S o

Displaced Point Spread Function

AS o A

 (

x



x o

,

y



y o

)

PSF PSF

  

A

   (

x



x o

,

y



y o

)

APSF

(

x



x o

,

y



y o

) 11

Image Formation

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

I i

(

x

,

y

)

     

I o

(

x

,

y

)

PSF

(

x



x o

,

y



y o

)

dx o dy o

where I

i

(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

 (  ,  )) 13

Modulation Transfer Function

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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.

Spatial frequency Cut-off

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Spatial/Frequency Domain

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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 16

Edge Response and Line Spread Function

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E ( x ) l ( x ) x d dx

OTF OTF

(  ,  (  , 0 ) )  

FT FT



l PSF

(

x

, 

y

)

MTF

  ( 

MTF

, 0 ) (  , 

Exp

(

j

)

Exp

(  ( 

j

, 0 ))  (  ,  )) x 17

Relative Edge Response

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1.2

1 0.8

0.6

0.4

Region where mean slope is estimated 0.2

Ringing Overshoot Slope is approximately inversely proportional to width of PSF 0 -0.2

Ringing Undershoot -2.5 -2.0 -1.5

-1.0 -0.5

0 0.5

1.0

1.5

2.0

2.5

Pixels Edge slope is a simple description applicable for well behaved systems

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Aliasing

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Assessing Levels of Aliasing

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1 0 L GSD/L= (GSD) (Slope) << 1 No Aliasing GSD 1 L GSD/L= (GSD) (Slope) ~ 1 Moderately Aliased 0 GSD

PSF

1 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

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Savannah River Site - 28.8 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 0.045 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

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Landsat Spatial Resolution Trade Study

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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 NDVI 1.0

0.8

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 23

Spectral

• •

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: Bands

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0.9

1 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 350 450

IKONOS Relative Spectral Response

550 650 750

Wavelength (nm )

850 950 1050 Pan Blue Green Red NIR

System Spectral Response Ba n d -t Re o g -Ba is n tra d ti o n

B • R • • NIR G •

Band-to-Band Registration

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Radiometry Specification

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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 Includes material © Space Imaging LLC 28

5 30 25 20 15 10

Radiometry: Absolute

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

SI Radiance = DN/84.3

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0 0 200 400 600 800 1000

DN

1200 1400 1600 1800 2000 29

Signal-to-Noise Ratio

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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 30

Pan Band MTFC

Pan Kernel

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Pan Kernel Row Section 5 4.5

4 3.5

3 2.5

2 1.5

1 -0.5 -0.4 -0.3 -0.2 -0.1

0 0.1 0.2 0.3 0.4 0.5

Cycles/ Pixel Pan Kernel Column Section 5 4.5

4 3.5

3 2.5

2 1.5

1 -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 31

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 Green Red NIR Pan 1.59

1.63

1.68

1.81

4.16

MTFC OFF SNR 25 MTFC ON SNR 13 NIR Kernel Applied to Simulated Imagery 32

Spatial Resolution: SNR

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

Geolocation Accuracy

• •

Basic Description

– RMSE – Circular Error (CE 90, CE 95)

Full Description

– Distribution Functions

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CE90 Geolocational Accuracy

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• 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 35

Additionally, the CE 90

CE 90 Example

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Summary

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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.

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