DTIC ADA429774: Enhanced Spectral Modeling of Sparse Aperture Imaging Systems

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Enhanced Spectral Modeling of
Sparse Aperture Imaging Systems

by

Robert E. Introne

B.S., Massachusetts Institute of Technology, 1989
M.S., Georgia Institute of Technology, 1990

A dissertation submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy
in the Chester F. Carlson Center for Imaging Science

College of Science

Rochester Institute of Technology

2004

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CHESTER F. CARLSON
CENTER FOR IMAGING SCIENCE
COLLEGE OF SCIENCE
ROCHESTER INSTITUTE OF TECHNOLOGY
ROCHESTER, NEW YORK

CERTIFICATE OF APPROVAL

Ph.D. DEGREE DISSERTATION

The Ph.D. Degree Dissertation of Robert E. Introne
has been examined and approved by the dissertation
committee as satisfactory for the dissertation
requirement for the Ph.D. degree in Imaging Science

// Original Signed //
Dr. John R. Schott, Dissertation Advisor

// Original Signed //
Dr. Roger L. Easton

// Original Signed //
Dr. Robert D. Fiete

// Original Signed //
Dr. Michael W. Richmond

1 Sep 04
Date
DISSERTATION RELEASE PERMISSION
ROCHESTER INSTITUTE OF TECHNOLOGY
COLLEGE OF SCIENCE
CHESTER F. CARLSON CENTER FOR IMAGING SCIENCE

Title of Dissertation:

Enhanced Spectral Modeling of Sparse Aperture Imaging Systems

I, Robert E. Introne, hereby grant permission to the Wallace Memorial Library of the
Rochester Institute of Technology to reproduce my thesis in whole or in part. Any
reproduction will not be for commercial use or profit.

Signature // Original Signed //

Date 1 Sep 04
Enhanced Spectral Modeling of
Sparse Aperture Imaging Systems

by

Robert E. Introne

Chester F. Carlson Center for Imaging Science
Rochester Institute of Technology

Abstract

The remote sensing community continues to pursue advanced sensor designs and post-
processing techniques that improve upon the spatial quality of collected overhead imagery.
Unfortunately, spaceborne applications frequently encounter launch vehicle fairing and
weight constraints that limit the size of the primary aperture that can be utilized for a given
application. Sparse aperture telescopes provide a potential avenue for overcoming some of
the size and weight issues associated with deploying a large monolithic mirror system. These
telescope systems are constructed of smaller subapertures which are phased to form a
common image field and thereby synthesize a larger effective primary diameter to obtain
higher spatial resolution than that achievable with a single subaperture.

Much of the research conducted to date in this sparse aperture arena has focused on the
panchromatic image quality performance of various optical configurations through
approaches that make use of resampled, gray-scale imagery products. The research effort
performed in conjunction with this dissertation focused on laying the groundwork for
synthetic model-based approaches for evaluating the optical performance of sparse aperture
collection systems with enhanced spectral fidelity and a polychromatic object scene. It
entailed a fundamental investigation and demonstration of the first-principles physics
required to model such imaging systems. This theoretical development ultimately led to the
generation of a modeling concept that more rigorously addresses the spectral characteristics
of classic sparse aperture optical configurations used in remote sensing applications. To
demonstrate the proposed theoretical foundation, a proof-of-concept digital model was
implemented that incorporates essential components of the fundamental physical processes
involved with typical sparse aperture collection systems, including any potential spectral
effects unique to these design configurations.

In addition to modeling the detected imagery derived from the collection system, there was
also an interest in exploring the quality implications of image restoration techniques typically
required for sparse aperture imaging systems. Several variations of the classic Wiener-
Helstrom filter were implemented and investigated in response to this research objective.
The basic restoration methodologies pursued in this effort provide a foundation for research
into more advanced techniques in the future. Finally, a top-level sensitivity study of the
image quality performance of various sparse aperture pupil configurations subjected to
varying levels of subaperture dephasing and/or aberrations was performed. This exploration
of the trade space focused on a panchromatic detection scenario and attempted to bound the
performance region where unique spectral quality issues are observed for the unconventional
collection telescopes targeted through this research effort.
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The views expressed in this dissertation are those of the author and do not reflect the
official policy or position of the United States Air Force, Department of Defense, or
the U.S. Government.

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Contents

List of Figures.........................................................................................................................ix
List of Tables........................................................................................................................xix
Nomenclature.......................................................................................................................xxi
1 Introduction........................................................................................................................1
2 Objectives............................................................................................................................5
2.1 Success Criteria..............................................................................................................5
2.2 Goals..............................................................................................................................7
3 Theory.................................................................................................................................9
3.1 Imaging Linear Systems Theory....................................................................................9
3.2 Incoherent Imaging System..........................................................................................12
3.3 Scene Radiance and Detected Signal...........................................................................16
3.4 System Pupil Function.................................................................................................27
3.4.1 Conventional Apertures.......................................................................................28
3.4.2 Sparse Aperture Configurations..........................................................................30
3.5 Optical Transfer Function............................................................................................34
3.6 Point Spread Function..................................................................................................43
3.7 Aberrated Aperture MTF.............................................................................................48
3.8 Detector Sampling........................................................................................................56
3.9 Detector Carrier Diffusion...........................................................................................59
3.10 Image Motion.............................................................................................................60
3.10.1 Smear................................................................................................................60
3.10.2 Jitter..................................................................................................................62
3.11 Atmospheric Turbulence............................................................................................63
3.12 System Transfer Function..........................................................................................69
3.13 Polychromatic MTF...................................................................................................70
3.14 System Noise..............................................................................................................74
3.14.1 Photon Noise....................................................................................................75
3.14.2 Dark Current.....................................................................................................76
3.14.3 Read and Signal Chain Noise...........................................................................77
3.14.4 Quantization Noise...........................................................................................78
3.14.5 Total Noise.......................................................................................................78
3.14.6 Signal-to-Noise Ratio.......................................................................................80
3.15 Image Restoration......................................................................................................82
3.16 Sparse Aperture System Issues..................................................................................86
3.16.1 Effective Collection Aperture..........................................................................86
3.16.2 Fill Factor.........................................................................................................89
3.16.3 Integration Time vs. Fill Factor........................................................................90
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4 Approach...........................................................................................................................95
4.1 Theoretical Development.............................................................................................96
4.2 Modeling Approach.....................................................................................................97
4.2.1 Modeling Overview.............................................................................................97
4.2.2 Nominal Collection Scenario............................................................................103
4.3 Imagery Collection Geometry....................................................................................107
4.4 Atmospheric Modeling..............................................................................................111
4.5 Scene Spectral Radiometry........................................................................................114
4.6 Imaging System Characterization..............................................................................121
4.6.1 Pupil Phase Profile............................................................................................121
4.6.2 Aperture OTF Evaluation..................................................................................128
4.6.3 Aperture PSF Evaluation...................................................................................133
4.6.4 System OTF Evaluation....................................................................................135
4.7 Quasi-Monochromatic Signal....................................................................................138
4.8 Integrated Detected Signal.........................................................................................141
4.9 System Noise Evaluation...........................................................................................144
4.10 Image Restoration....................................................................................................148
4.11 Gray-World Comparison..........................................................................................154
4.12 Data Analysis Metrics..............................................................................................159
4.12.1 Signal-to-Noise Ratio.....................................................................................160
4.12.2 Relative Edge Response.................................................................................162
4.12.3 Noise Gain......................................................................................................168
4.12.4 Normalized rms Error.....................................................................................169
5 Results.............................................................................................................................171
5.1 Transfer Function Character......................................................................................172
5.2 Quasi-Monochromatic Simulation.............................................................................183
5.3 Integrated Panchromatic Simulation..........................................................................199
5.4 Polychromatic versus Gray-World Model.................................................................209
5.4.1 WASP-Based Object Description.....................................................................209
5.4.2 HyMap-Based Object Description....................................................................220
5.4.3 DIRSIG-Based Object Description...................................................................231
5.5 Alternative Wiener Filter Options..............................................................................239
5.6 Analysis Excursions...................................................................................................245
5.6.1 Filtering Under Different Noise Levels.............................................................245
5.6.2 Integration Time vs. Fill Factor.........................................................................252
5.6.3 Phase Knowledge Sensitivity............................................................................257
5.6.4 Subaperture Dephasing vs. Optical Aberrations...............................................264
6 Conclusions.....................................................................................................................269
6.1 Findings......................................................................................................................270
6.2 Limitations.................................................................................................................275
6.3 Recommendations......................................................................................................278
6.3.1 Sensitivity Studies.............................................................................................278
6.3.2 Advanced Filter Techniques..............................................................................281
6.3.3 Interferometric Investigation.............................................................................283
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