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RANGE COMPRESSED HOLOGRAPHIC APERTURE LADAR Dissertation Submitted to the School of Engineering of the UNIVERSITY of DAYTON In

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RANGE COMPRESSED HOLOGRAPHIC APERTURE LADAR Dissertation Submitted to the School of Engineering of the UNIVERSITY of DAYTON In RANGE COMPRESSED HOLOGRAPHIC APERTURE LADAR Dissertation Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Doctor of Philosophy in Electro-Optics By Jason Wade Stafford UNIVERSITY OF DAYTON Dayton, Ohio December 2016 RANGE COMPRESSED HOLOGRAPHIC APERTURE LADAR Name: Stafford, Jason Wade APPROVED BY: Bradley D. Duncan, Ph.D. Joseph W. Haus, Ph.D. Advisory Committee Chairman Committee Member Executive Director Professor Graduate Academic Affairs Electro-Optics and Photonics Professor Electro-Optics and Photonics David J. Rabb, Ph.D. Matthew P. Dierking, Ph.D. Committee Member Committee Member Technical Advisor, Laser Radar Branch Graduate Faculty Air Force Research Laboratory Electro-Optics and Photonics Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Dean Research and Innovation School of Engineering Professor School of Engineering ii ABSTRACT RANGE COMPRESSED HOLOGRAPHIC APERTURE LADAR Name: Stafford, Jason University of Dayton Advisor: Dr. Bradley D. Duncan 3-D holographic ladar uses digital holography with frequency diversity to allow the ability to resolve targets in range. A key challenge is that since individual frequency samples are not recorded simultaneously, differential phase aberrations may exist between them making it difficult to achieve range compression. Specific steps for this modality are described so that phase gradient algorithms (PGA) can be applied to 3-D holographic ladar data for phase corrections across multiple temporal frequency samples. Substantial improvement of range compression is demonstrated in a laboratory experiment where our modified PGA technique is applied. Additionally, the PGA estimator is demonstrated to be efficient for this application and the maximum entropy saturation behavior of the estimator is analytically described. Simultaneous range- compression and aperture synthesis is experimentally demonstrated with a stepped linear frequency modulated waveform and holographic aperture ladar. The resultant 3D data has high resolution in the aperture synthesis dimension and is recorded using a conventional low bandwidth focal plane array. Individual cross-range field segments are coherently combined using data driven registration, while range-compression is performed without iii the benefit of a coherent waveform. Furthermore, a synergistically enhanced ability to discriminate image objects due to the coaction of range-compression and aperture synthesis is demonstrated. Two objects are then precisely located in 3D space, despite being unresolved in two directions, due to resolution gains in both the range and azimuth cross-range dimensions. iv ACKNOWLEDGEMENTS I would like to thank Dr. Bradley Duncan for guiding me through this research project and for patiently editing my writing. Thank you to Dr. Dave Rabb and Dr. Matthew Dierking for technical assistance, encouragement and guidance, especially in the experimental portion of this project. I also wish to thank Dr. Joseph Haus for serving on my committee as well as Bob Feldman and Brian Ewert for giving me a job and letting me keep it while I conducted this research. Thank you to Andy Stokes, who has been my homework and lab partner in every graduate level course I’ve taken and to Doug Jameson, whose digital holography expertise I tapped when I began this research so long ago. Thank you to my wife and family for supporting me unfailingly throughout this process and giving me something to look forward to every day. I wouldn’t have made it without you. This effort was supported in part by the United States Research Laboratory. The views expressed in this dissertation are those of the author and do not reflect on the official policy of the Air Force, Department of Defense, or the United States government. Jason Stafford November 2016, Dayton, Ohio v TABLE OF CONTENTS ABSTRACT ....................................................................................................................... iii ACKNOWLEDGEMENTS ................................................................................................ v LIST OF FIGURES ........................................................................................................... ix LIST OF TABLES ........................................................................................................... xiv CHAPTER 1 INTRODUCTION ........................................................................................ 1 1.1 Historical Background ............................................................................................... 2 1.2 Dissertation Overview ............................................................................................... 6 CHAPTER 2 BACKGROUND .......................................................................................... 8 2.1 Circular and Inverse-Circular HAL ........................................................................... 8 2.2 Range Compression ................................................................................................. 15 2.3 Single Aperture, Multi-λ Imaging ........................................................................... 23 2.4 Simultaneous Range Compression and HAL .......................................................... 29 CHAPTER 3 THE PHASE GRADIENT ALGORITHM METHOD FOR 3D HOLOGRAPHIC LADAR IMAGING ................................................................ 37 3.1 Introduction ............................................................................................................. 37 3.2 3D Holographic Ladar: Range Resolution and Ambiguity ..................................... 39 3.3 Application of Phase Gradient Autofocus Algorithms ........................................... 41 3.3.1 Assemble complex image plane data cube .................................................... 43 3.3.2 Apply a cross-range target support mask ...................................................... 43 vi 3.3.3 Range compress (1D IDFT) .......................................................................... 43 3.3.4 Centershift brightest range values ................................................................. 43 3.3.5 Window in the range dimension.................................................................... 44 3.3.6 Decompress in range (1D DFT) .................................................................... 45 3.3.7 Compute the phase gradient estimate ............................................................ 45 3.3.8 Integrate the phase gradient to recover the phase aberration estimate .......... 46 3.3.9 Detrend .......................................................................................................... 46 3.3.10 Apply phase correction to complex image plane data................................... 47 3.3.11 Corrected? ..................................................................................................... 47 3.4 Experiment and Results ........................................................................................... 47 3.5 PGA Performance for 3D Holographic Data .......................................................... 54 3.6 Conclusion ............................................................................................................... 61 CHAPTER 4 RANGE COMPRESSION FOR HAL ....................................................... 63 4.1 Background ............................................................................................................. 65 4.2 Low Contrast Range Compressed HAL .................................................................. 67 4.3 Point Targets with Range Compressed HAL .......................................................... 76 4.3.1 Experimental design ...................................................................................... 77 4.3.2 Experimental results ...................................................................................... 84 CHAPTER 5 CONCLUSION........................................................................................... 93 5.1 3D Holographic Ladar ............................................................................................. 93 5.2 Original Contributions ............................................................................................. 95 5.3 Publications and Presentations ................................................................................ 96 REFERENCES ................................................................................................................. 97 vii APPENDIX A Digital Holography ................................................................................. 103 APPENDIX B Experimental Equipment ........................................................................ 105 APPENDIX C The Cramer-Rao Lower Bound .............................................................. 106 APPENDIX D Some Details of the Eigenvector Method for 3D Holography ............... 108 viii LIST OF FIGURES Figure 2.1. Circular HAL mode. The sensor platform follows a circular path around the target, deviating from the (xa,ya) plane (red dashed line). ....................................10 Figure 2.2. The inverse circular HAL (IC-HAL) geometry. Notice that the rotation angle θ is positive in the clockwise (CW) direction. This is in keeping with the effective rotation direction that would be observed if the target was non-rotating and the TX instead translated in the positive xa direction.
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