Customer : Contract No : WP No : ESA/ESRIN 21125/07/1-OL 210 Document Ref : Issue Date : Issue : 04 March 2008 0.2 Title : Abstract : ARMINES's contribution to Author : Philippe BLANC Approval : Accepted : Distribution : Hard Copy File: Filename: -Ed0.2.doc Copyright All rights reserved. No part of this work may be disclosed to any third party translated reproduced copied or disseminated in any form or by any means except as defined in the contract or with the written permission of VEGA Group PLC. ARMINES / Ecole des Mines de Paris West Park, 4 rue Paul Mesplé, 31100 Toulouse, France Tel: +33 (0)5.67.77.19.99 Fax: +33 (0)5.67.77.19.98 www.vega-group.com GEN.CTF.007, Issue 6
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TABLE OF CONTENTS 1. APPLICABLE AND REFERENCE DOCUMENTS...6 1.1 Reference Documents...6 2. EXISTING SITES FOR ON-ORBIT MTF ASSESSMENTS...8 2.1 Edge targets...8 2.2 Impulse targets...9 2.3 Pulse targets...9 2.4 Periodic targets...11 2.5 Summary table of permanent MTF sites...13 3. EXISTING SITES FOR ON-ORBIT SNR ASSESSMENTS...17 APPENDIX A EXTENDS OF A POINT SPREAD FUNCTION...18 APPENDIX B MINIMUM SURFACE FOR SNR ESTIMATION...19 B.1.1 RELATIVE ERROR OF THE MEAN ESTIMATOR...19 B.1.2 RELATIVE ERROR OF THE STANDARD DEVIATION ESTIMATOR...20 B.1.3 RELATIVE ERROR OF THE SNR ESTIMATOR...21
AMENDMENT POLICY This document shall be amended by releasing a new edition of the document in its entirety. The Amendment Record Sheet below records the history and issue status of this document. AMENDMENT RECORD SHEET ISSUE DATE DCI No REASON Ed0.1 04 Mar 2008 N/A Initial Issue Page 4 of 22
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1. APPLICABLE AND REFERENCE DOCUMENTS The following is a list of documents with a direct bearing on the content of this report. Where referenced or applicable in the text, these are identified as RD.n or AD.n, where 'n' is the number in the list below 1.1 Reference Documents ID document [RD1] Document reference. Technical proposal. VEGA- SPA.PRO.070197 [RD2] Choi, T., 2002. IKONOS Satellite on Orbit Modulation Transfer Function (MTF) Measurement using Edge and Pulse Method. Master of Science thesis, South Dakota State University, 189 pages. [RD3] Delvit, J.M., D. Léger. 2003. Modulation Transfer Function and Noise Assessment. In: Proceedings of IEEE International Geoscience and Remote Sensing Symposium, July 2003, Vol. 7, pp. 4500-4502. [RD4] Hearn, D.R. 2002. Earth Observing-1 Advanced Land Imager: Imaging Performance On-Orbit. Project report for the National Aeronautics and Space Administration under Air Force Contract F19628-00-C-0002. 105 pages. [RD5] Helder, D., T. Choi, M. Rangaswamy. 2004. In-flight characterization of spatial quality using point spread function. Post-launch Calibration of Satellite Sensors. Taylor and Francis Group, London, ISBN 90 58 09 693 9. pp. 151-170. [RD6] Honkavaara, E., J. Jaakkola, L. Markelin, J. Peltoniemi, E. Ahokas, S. Becker. 2006. Complete photogrammetric system calibration and evaluation in the Sjökulla test field case study with DMC. In: Proceedings of the International Calibration and Orientation Workshop EuroCOW 2006. 6 pages. [RD7] Honkavaara, E., J. Peltoniemi, E. Ahokas, R. Kuittinen, J. Hyyppä, J. Jaakkola, H. Kaartinen, L. Markelin, K. Nurminen, J. Suomalainen. 2008. A Permanent Test Field for Digital Photogrammetric Systems. Photogrammetric Engineering & Remote Sensing, Vol. 74(1), pp. 95-106. [RD8] Kohn, K. 2004. Modulation Transfer Function measurement method and results for the ORBVIEW-3 High Resolution imaging satellite. In: Proceedings of XXth ISPRS Congress. Istanbul. pp. 7-13. Page 6 of 22
[RD9] Kubik, P. E. Breton, A. Meygret, B. Cabrières, P. Hazane, D. Léger. 1998. SPOT 4 HRVIR first inflight Image Quality results. In: Proceedings of the EUROPTO Conference on Sensors, Systems and Next-Generation Satellites, September 1998. Vol. 3498, pp. 376-389. [RD10] Léger, D., F. Viallefont, E. Hillairet, A. Meygret. 2002. In-flight refocusing and MTF assessment of SPOT5 HRG and HRS cameras. In: Proceedings of SPIE of Sensors, Systems, and Next-Generation Satellites VI, April 2003, Vol. 4881, pp. 224-231. [RD11] Léger, D., F. Viallefont, P. Deliot. C. Valorge. 2004. On-orbit MTF assessment of satellite cameras. Post-launch calibration of satellite sensors. Taylor and Francis Group, London, ISBN 90 58 09 693 9, pp. 67-75. [RD12] Léger, D., J. Duffaut, F. Robinet. 1994. MTF Measurement Using Spotlight. In: Proceedings of IEEE Geoscience and Remote Sensing Symposium. Passadena, U.S., Vol. 4, pp. 2010-2012. [RD13] Nelson N. R., P. S. Barry. 2001. Measurement of HYPERION MTF from On-Orbit Scenes. In: Proceedings of the IEEE Geoscience and Remote Sensing Symposium. Vol. 7, pp. 2967-2969. [RD14] Rangaswamy, M. K., 2003. Two dimensional on-orbit Modulation Transfer Function analysis using convex mirror array. Master of Science thesis, South Dakota State University. 149 pages. [RD15] Reulke, R., S. Becker, N. Haala, U. Tempelmann. 2006. Determination and improvement of spatial resolution of the CCD-line-scanner system ADS40. ISPRS Journal of Photogrammetry & Remote Sensing, 60, pp. 81-90. [RD16] Saunier, S., R. Santer, P. Goryl, A. Gruen, K. Wolf, M. Bouvet, F. Viallefont, G. Chander, Y. Rodriguez, A. Mambaimba. The contribution of the European Space Agency to the ALOS PRISM / AVNIR-2 commissioning phase. http://earth.esa.int/pub/esa_doc/alos014.pdf [RD17] Storey, J. C. 2001. Landsat 7 on-orbit modulation transfer function estimation. In: Proceedings of the SPIE Sensors, Systems, and Next-Generation Satellites V, Vol. 4540 (2001), pp 50-61. Table 1: Table of the Reference Documents.
2. EXISTING SITES FOR ON-ORBIT MTF ASSESSMENTS In this sub-section, we present different sites that have been used, owing to bibliography, for on-orbit MTF assessments of different spaceborne imagery systems. Those different specific sites have at least one artificial or natural target dedicated to MTF assessment (cf. [RD5]): Edge targets Impulse targets Pulse targets Periodic targets The aim of the sub-sections is to briefly describe those different types of targets and to precise their main intrinsic parameters. More details on techniques for MTF assessments based on those specific target will be given in the WP224 [RD1]. 2.1 Edge targets An edge target corresponds to an high contrast Heaviside edge. The acquisition of this target by an imagery system enables to obtain an accurate Edge Response Function (ESF). This 1D ESF is then derived to an assess of the 1D MTF profile on the direction perpendicular to the edge transition. Those targets can be: Artificial thanks to painted surfaces or specific dark and bright tarps. Natural with agriculture fields, parking lots, ground / building transitions, water / ice shelf transitions, dark space / moon transitions, etc. Surrounding background α L H Direction of the MTF profile L W Figure 1: Schematic Edge targets. Helder et al. [RD5] give some rules of thumb for an appropriate edge target: Page 8 of 22
The target should be large enough to be able to extract an included edge target that is not affected by the surrounded background. The transition distance of the figure 1 should be greater than the radius extend of the PSF. Helder et al. [RD5] suggest that a rough order of this radius is between 3 and 5 GSD of the system. The figure 6 in the appendix a gives an estimation of the radius extend of the PSF, defined as the 95 % encircled energy radius, depending on the MTF value at Nyquist. The included target (without the sides, possibly affected by the surrounded background) should be greater than one extend radius beyond the edge: the width (in the direction of the MTF profile) of the target, called L W, should be greater than twice the radius of the PSF, between 6 to 10 GSD. The height of the target (perpendicular to the MTF profile) should be large enough to stack and oversample the ESF in order respectively improve the SNR budget and to increase its sampling frequency. Helder et al. suggest that this height, called L H, should be greater than 20 GSD. The angle of the edge with respect to the direction of the MTF profile, called α, should be around 90. A slight difference of α from 90 is important to be able to oversample the ESF. Helder et al. suggest that a difference of 8 degrees from 90 is nearly ideal. Dark / bright contrast: Owing to Helder et al., the difference of the bright and dark responses divided by the noise s standard deviation should be greater than 50. 2.2 Impulse targets An impulse target corresponds to a point source or a set of point sources used to directly obtain an acquisition of the sampled Point Spread Function (PSF) with one or different sampling grids (spatially or temporally). The artificial targets can be active sources such as Xenon lamps or passive sources, such as convex mirrors. The ONERA s experimental site of Faugac-Mauzac have (two) Xenon spotlights that can be aimed at spaceborne imagery systems. Those artificial Impulse targets have been used for SPOT 5 to assess its absolute MTF, as described in [RD10] and [RD12]. Owing to Léger, those lamps can be used for remote sensing system up to 30 m GSD. Rangaswamy in [RD14] has tested 1.2 m convex mirrors to create array of artificial passive point sources. This array of point source targets has been used to assess the MTF of Quickbird II (61 cm GSD) and IKONOS (1 m GSD). Stars can be excellent natural impulse targets provided agile maneuvering satellite platforms. Owing to [RD4], one of the different method used to assess the MTF of the Earth Observing-1 Advanced Land Imager (10 m GSD) consisted in scanning different stars by using a slower than nominal angular scan speed. Stars in the Pleiades and the star Vega in the Lyrae was found to be excellent natural impulse targets in term of radiance contrast: they have been used to assess the PSF, and therefore the MTF of EO- 1 ALI for its different spectral bands. 2.3 Pulse targets A Pulse target consists of a bright region surrounded by dark regions. Those target can be specific target such as painted on concrete surfaces, or dark and bright specific tarps.
They can also be artificial landscape s elements such as long bridges, white stripes on runway, etc.. Surrounding background α L H Direction of the MTF profile L W W Figure 2: Schematic Impulse target The dimensions L W and and the angle α follow the same rules of thumb as described in the sub-section 2.1 dedicated to the edge targets. The width W of the tarp with respect to the Ground Sampling Distance is critical for the effectiveness of the pulse target method. Indeed, the Fourier transform of the pulse is a sinc whose zero-crossing frequencies are multiple of the inverse of W. Therefore, to have a sufficient Fourier contrast at the Nyquist frequency 1/(2GSD), the width of the pulse target should be outside the red region of the figure 3. For sub-pixel pulse targets, the Fourier contrast at Nyquist frequency is high but the strength of the signal received by the sensor, linear with the width W, could be not enough for a good SNR budget. This fact can be circumvented by the selection of a very bright pulse target and/or a very large length target L H that would enables to stack a very large number of pulse responses to improve the SNR budget. In other cases, as stated by Helder et al. in [RD5], a pulse width of 3 GSD ± 20 % is optimal (see figure 3). Page 10 of 22
1 Contrast at the Nyquist Frequency 1GSD 2GSD 3GSD Width W Figure 3: Fourier contrast of the W width pulse target at the Nyquist frequency. 2.4 Periodic targets A periodic target consists of specific patterns (edges, pulses, impulses) that are periodized. Even if numerical MTF assessment is possible, those targets are in fact meant to direct and quick visually assessment of the resolving power of the imagery system. The periodic patterns can be the standard USAF three-bar pattern or the Siemens radial stars pattern (cf. [RD15]). 2L 5L Rmin Rmax L ηl Np brigth patterns η 3 L (a) 6 Figure 4: Example of periodic targets: (a) three-bar pattern (typically η = 1 2 ). (b) Siemens-star pattern. (b) Roughly, a the three-bar pattern of width L is appropriate for GSD in the order of L/3 up to L.
As far as the Siemens star pattern is concerned, if it haves Np bright patterns and a radius varying between Rmin and Rmax, the appropriate GSD are: πrmin πr max < GSD < (Eq. 1) 2Np 2Np Page 12 of 22
2.5 Summary table of permanent MTF sites Name Type of the target(s) Location Main characteristics Corresponding MTF Cal/Val mission Appropriate GSD (rough order) Salon de Provence checkerboard (ONERA) Artificial Edge targets (2x2 checkerboard) Salon de Provence, France 43 36 21"N, 5 07'13"E 60 m x 60 m CN ~ 1:14 (reflectance) ALOS PRISM (10 m) [RD16] SPOT 5 HRG (2.5 m / 5 m) [RD11], [RD10] GSD < 5-10 meters Big Spring Edge checkerboard (Space Imaging) Artificial Edge targets (2x2 checkerboard) Big Spring airport, Texas, U.S. 32 13 14 N, 101 30 45 W 40 m x 40 m CN ~ 1:5 (PAN) IKONOS (1 m / 4 m) [RD15], [RD2] GSD < 5-10 meters Stennis Space Center Edge Targets (NASA) Artificial Edge targets (SSC painted Targets) Stennis Space Center, Mississippi, U.S. 30 23 12 N, 89 37 43 W 20 m x 20 m CN ~ 1:6 (PAN) QUICKBIRD (61 cm / 2.44 m) [RD14] ORBVIEW (1 m) [RD8] GSD < 2.5-5 meters Maricopa Fields Natural Edge targets (Fields transitions) Maricopa, Arizona, US 32 23'N, 112 33'W Typical Field Width: 400 m to 800 m SPOT 4 (10 m / 20 m) [RD9] SPOT 5 HRS (10 m) [RD11] 10-20 m < GSD < 100-200 m Ross Ice Shelf Natural Edge targets (Sea/Icefield transitions) Ross Ice Shelf Antartica 81 30S, 175 00W Edge Width > 5 km EO-1 HYPERION (30 m) [RD13] 10-20 m < GSD < 500 m Lake Ponchartrain Causeway "Natural" Double Pulse target Lake Ponchartrain Louisiana, U.S. 30 01'19"N, 90 09'14"W Bridge width: 10 m Distance between bridges: 24.4 m CN ~ 1:4 (PAN) Landsat 7 ETM+ (15 m / 30 m ) [RD17] EO-1 ALI (10 m / 30 m ) [RD4] EO-1 HYPERION (30 m) [RD13] 5-10 m < GSD < 30 m Page 13 of 22
Bronx Whitestone bridge "Natural" Pulse target Bronx Whitestone bridge, New York City, U.S. 40 48 05 N, 73 49 46 W Bridge width: 26 m CN ~ 1:2 (PAN) EO-1 ALI (10 m / 30 m ) [RD4] 10 m < GSD < 60 m Fauga-Mauzac site (ONERA) Active Impulse Target (Xenon Lamps 1kW, 3kW) Fauga-Mauzac, France 43 23'02''N, 01 17'28''E Beam divergence ~ 6 SPOT 5 HRG (2.5 m / 5 m) [RD11], [RD10] 1 m < GSD < 30 m Pleiades stellar site Natural Impulse Target (Stars as unresolved point sources) - - EO-1 ALI (10 m / 30 m ) [RD4] - Fort Huachhuka USAF Pattern (USAF) Artifical painted Three-bar pattern Fort Huachuka Arizona, US 31 35'47"N, 110 18'26"W Bar width: 15 cm to 3 m Inadequate for SPOT 5 HRG (2.5 m) [RD11] 10-15 cm < GSD < 1-3 m Stennis Space Center Radial Pattern (NASA) Artifical painted Siemens-star pattern Stennis Space Center, Mississippi, U.S. 30 23 07 N, 89 37 42 W Radius: Rmax 130 m Np bright patterns: 88 (4x22) Inadequate for SPOT 5 HRG (5 m) [RD11] SPOT 5 HRG-THR (2.5 m) [RD11] GSD < 2-3 m Sjökulla site (Finnish Geodetic Institute) Artificial Edge targets Artificial Pulse targets Three-bar patterns Siemens star patterns Sjökulla, Finland 60 14 31"N, 24 23 03"E Bar width: 3 cm to 1.5 m CN ~ 1:8 (reflectance) Airborne digital image systems [RD7], [RD6] HR / EHR spaceborne systems (Defense) GSD from 3 cm to 50 cm Table 2: Summary table of permanent MTF sites. Page 14 of 22
Salon de Provence checkerboard Big Spring Edge checkerboard Stennis Space Center Edge Targets Maricopa Fields Ross Ice Shelf Lake Ponchartrain Causeway Page 15 of 22
Page 16 of 22 Bronx Whitestone bridge Fauga-Mauzac site Pleiades stellar site Fort Huachhuka USAF Pattern Stennis Space Center Radial Sjökulla site
3. EXISTING SITES FOR ON-ORBIT SNR ASSESSMENTS SNR assessment methods requires the use Lambertian surfaces. The characteristics of SNR sites are therefore strongly close to those of radiometric calibration site. Nevertheless, it is important to note that accurate SNR assessments require accurate assessments of the measure noise s standard deviation. Statically, as presented in the appendix b, for typical remote sensing systems, the standard deviation assessment on an homogeneous surface needs a larger number of independent measures than the mean radiance assessment: In other words, the minimum surface of homogeneous regions required for SNR assessment is typically larger than the one required for the mean radiance assessment. The figure 9 gives the required minimum surface for a given relative SNR precision. The figure 6 is also of interest for the SNR assessment site: the extend of the PSF gives the minimum distance between the homogeneous region and the surrounding background to avoid surrounding contaminations on the standard deviation assessment. With the notation of the figure 5: should be greater than the radius extend of the PSF; L H x L W should be greater than the required minimum surface. Surrounding background L H L W Figure 5: Homogeneous region for SNR assessment. Page 17 of 22
APPENDIX A EXTENDS OF A POINT SPREAD FUNCTION For the MTF and the SNR assessments, it is useful to know the extend of the PSF. This knowledge enables to determine: The minimum size of the MTF target that should be at least twice the radius of the PSF extend. The minimum distance with the target surrounding region to determine the inclusive region in the target that is not contaminated by the surrounding background. This minimum distance should be at least the radius of the PSF extend. A common criterion to quantify the PSF extend is the energy encircled (EE) radius. For the purpose of MTF target extension and non surrounding contamination, we propose to determine the PSF extend as the 95 % energy encircled radius. The figure 6 shows the 95 % energy encircled radius in pixels versus the MTF value at the Nyquist Frequency. This calculation is based upon a MTF analytic model proposed by Delvit et al. [RD3]. 95 % Encircled Energy radius (pixel) 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 FTM at Nyquist frequency Figure 6: PSF extend, defined as 95 % energy encircled radius in pixels, versus the MTF value at the Nyquist Frequency. Page 18 of 22
APPENDIX B MINIMUM SURFACE FOR SNR ESTIMATION The SNR assessment on a homogeneous surface can be viewed as the jointed estimation 2 of the mean m and the variance v = σ of a random gaussian white noise n. Let s call 2 2 m e, v = σ and SNR e respectively the estimation of m, v = σ and e e SNR = m v = m σ. The aim of this appendix is to determine the minimum number N of independent measures of the random gaussian white noise n to obtain a good accuracy of the SNR assessment. In the remote imagery domain, this minimum number N is related to a minimum homogenous surface of N.GSD 2. Let consider { n k } k [ 1, N N independent measures of a random gaussian white noise n ] whose mean m and variance v = σ are both unknown. The unbiased optimal estimators m e and v e are, in this case: 2 m e 1 N nk N k = 1 = (Eq. 2) and N 1 v ( ) 2 e = nk me 1 (Eq. 3) N k = 1 The SNR estimation SNR e is then defined by: SNR e me me = = (Eq. 4) v σ e e B.1.1 Relative error of the mean estimator From Student t-distribution T N-1 with N-1 degrees of freedom, the 95 % confidence interval 0.95 (CI) relative error of the mean estimator ε m can be derived: where N ε 0.025 0.95 1 m tn σe 2 ( N ) = (Eq. 5) N m N > 30 SNR N t α is defined as the point that gives ( N ) P T > t α = α. 1 N 1 1 The relative error of the mean estimator depends on the number independent measures N but also on the signal to noise ratio. Most spaceborne imagery systems have a SNR greater than, let say, 50. Therefore, as illustrated by the figure 7, the relative error of the mean estimator is better than 0.4 % so long as the surface of the homogeneous region exceeds 10x10 pixel 2. Page 19 of 22
10 % ε m 0.95 (SNR=10) ε m 0.95 (SNR=50) ε m 0.95 (SNR=100) 95 % CI Relative error of the mean estimator (%) 1 % 0.1 % 0.01 % 10 1 10 2 10 3 10 4 Surface of the homogeneous region in pixel 2 Figure 7: 95 %-CI relative error of the mean estimator versus surface of the homogeneous region in pixel 2, for three different SNR. B.1.2 Relative error of the standard deviation estimator 2 From χ -distribution with N-1 degrees of freedom, the 95 % confidence interval relative error of the standard deviation ε 0.95 σ can be derived: 2 χ N 1,0.025 ( N ) (Eq. 6) N 0.95 σ 1 ε 2 where χ N, α Inverse of the chi-square cumulative distribution function with N degrees of freedom at the values in α. One can note that the relative error does not depends on the SNR: it only depends on the number N of the independent measures available. It is also interesting to note that the relative error of the standard deviation estimator is more than 30 times greater than the relative error of the mean estimator for the same surface, for SNR greater than 50. As illustrated by the figure 8, a relative error better than 1 % requires a surface of the homogeneous region greater than 140x140 pixel 2. Page 20 of 22
100 % 95 % CI Relative error of the standard deviation estimator ε σ 0.95 (%) 10 % 1 % 0.1 % 10 1 10 2 10 3 10 4 10 5 10 6 Surface of the homogeneous region in pixel 2 Figure 8: 95 %-CI relative error of the standard deviation estimator versus surface of the homogeneous region in pixel 2 B.1.3 Relative error of the SNR estimator For small mean and standard deviation estimation errors, dm and dσ, the corresponding SNR estimation error is given by: 1 m dsnr = dm dσ σ 2 σ (Eq. 7) Thus, the relative error dsnr/snr can be written as: dsnr 1 m dm m dσ = SNR SNR σ m σ σ dm dσ = m σ (Eq. 8) Then, 0.95 0.95 0.95 0.95 SNR m σ σ SNR> 50 ε ε ε ε (Eq. 9) In other words, for typical spaceborne imagery system (SNR > 50), the 95%-CI relative error of the SNR estimator presented in the figure 9, is close to the 95%-CI relative error of the standard deviation estimator. Page 21 of 22
100 % 95 % CI Relative error of the standard deviation estimator ε σ 0.95 (%) 10 % 1 % 0.1 % 10 1 10 2 10 3 10 4 10 5 10 6 Surface of the homogeneous region in pixel 2 Figure 9: 95 %-CI relative error of the SNR estimator versus surface of the homogeneous region in pixel 2 (SNR > 50). Page 22 of 22