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

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

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.

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.

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.

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

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

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

0.2 m GSD 0.4 m GSD 0.6 m GSD 1.0 m GSD

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

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

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

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

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

Spatial/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

Edge Response and Line Spread Function

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

Aliasing

Assessing Levels of Aliasing 1 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

CIR Images of SRS Synthesized Products 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 1

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

Spatial 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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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.