ABSTRACT Title of Dissertation: EXPERIMENTAL CHARACTERIZATION OF ATMOSPHERIC TURBULENCE SUPPORTED BY ADVANCED PHASE SCREEN SIMULATIONS Daniel A. Paulson, Doctor of Philosophy, 2020 Dissertation directed by: Professor Christopher C. Davis Department of Electrical and Computer Engineering Characterization of optical propagation through the low turbulent atmosphere has been a topic of scientific investigation for decades, and has important engineering applications in the fields of free space optical communications, remote sensing, and directed energy. Traditional theories, starting with early radio science, have flowed down from the assumption of three dimensional statistical symmetry of so-called fully developed, isotropic turbulence. More recent experimental results have demonstrated that anisotropy and irregular frequency domain characteristics are regularly observed near boundaries of the atmosphere, and similar findings have been reported in computational fluid dynamics literature. We have used a multi-aperture transmissometer in field testing to characterize atmospheric transparency, refractive index structure functions, and turbulence anisotropy near atmospheric boundaries. Additionally, we have fielded arrays of resistive temperature detector probes alongside optical propagation paths to provide direct measurements of temperature and refractive index statistics supporting optical turbulence observations. We are backing up these experimental observations with a modified algorithm for modeling optical propagation through atmospheric turbulence. Our new phase screen approach utilizes a randomized spectral sampling algorithm to emulate the turbulence energy spectrum and improve modeling of low frequency fluctuations and improve convergence with theory. We have used the new algorithm to investigate open theoretical topics, such as the behavior of beam statistics in the strong fluctuation regime as functions of anisotropy parameters, and energy spectrum power law behavior. These results have to be leveraged in order to develop new approaches for characterization of atmospheric optical turbulence. EXPERIMENTAL CHARACTERIZATION OF ATMOSPHERIC TURBULENCE SUPPORTED BY ADVANCED PHASE SCREEN SIMULATIONS by Daniel A. Paulson Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2020 Advisory Committee: Professor Christopher C. Davis, Chair Professor Thomas M. Antonsen, Jr. Professor Douglas G. Currie Professor Julius Goldhar Professor Phillip A. Sprangle © Copyright by Daniel A. Paulson 2020 Acknowledgements The work contained within this dissertation is the result of collaborative work among many people. First, I thank my adviser Professor Christopher C. Davis for his support during this process, kind words of encouragement, and for providing the academic freedom to investigate areas which I found particularly interesting and seek creative solutions to problems. Secondly, I would like to thank all the current and former members of the Maryland Optics Group I had the pleasure of working with during my graduate research: Dr. Quirino Balzano, Nathaniel Ferlic, Dr. Jonathan Ko, Dr. William Nelson, Dr. John Rzasa, Dr. Igor I. Smolyaninov, Dr. Miranda van Iersel, and Dr. Chensheng Wu. Dr. Rzasa and Dr. Wu were particularly instrumental in conceptualizing the experimental optical equipment used in this dissertation, and Dr. van Iersel dedicated many hours of assistance in field testing. I also thank the staff of Townes Institute Science and Technology Experimentation Facility who were key collaborators during this effort. Additionally, I would like to thank the committee members: Professor Phillip Sprangle, Professor Thomas Antonsen, Professor Julius Goldhar, and Professor Douglas Currie for taking the time to review my dissertation and defense. During my graduate education I also had the pleasure of attending classes instructed by Professor Antonsen and Professor Sprangle which helped to spur my interest in electrophysics research. I’d also like to thank Sarwat Chappell of the Office of ii Naval Research for supporting the bulk of these efforts. Finally, my parents deserve a great deal of gratitude for encouraging my pursuit of higher education. This work was supported by the Office of Naval Research (ONR) under contract number N000141812008. iii Table of Contents Acknowledgements ................................................................................................. ii Table of Contents ................................................................................................... iv List of Figures ........................................................................................................ vi Definitions and abbreviations .............................................................................. xix Chapter 1 : Overview and Theoretical Considerations ............................................1 1.1: Introduction ......................................................................................................1 1.2: Theoretical Background Regarding the Nature of Optical Turbulence ...........2 1.3: Mathematical Background Regarding the Simulation of Optical Propagation ............................................................................................................12 1.4: Theoretical Considerations for Propagation through Anisotropic, Non- Kolmogorov Turbulence ........................................................................................20 1.5: A Note Regarding Alternatives to the Paraxial Approximations ..................33 Chapter 2 : A Revised Method for Simulation of Atmospheric Turbulence .........39 2.1: Background ....................................................................................................39 2.2: Overview of the Split Step Algorithm for Simulation of Optical Propagation through Atmospheric Turbulence ..........................................................................40 2.3: Motivation for a New Method .......................................................................48 2.4: Randomized FFT-based Spectral Sampling, Core Algorithm .......................51 2.5: Core Algorithm Results for Anisotropic, non-Kolmogorov Spectral Models....................................................................................................................56 2.6: Core Algorithm Results for Bounded Spectral Models .................................68 2.7: Hybrid Algorithm Including Subharmonics ..................................................77 2.8: Addition of White Noise to Phase Screens to Support Subresolution Inner Scales .....................................................................................................................81 2.9: Hybrid Algorithm Results for Unbounded Spectral Models .........................88 2.10: Hybrid Algorithm Results for Bounded Spectral Models ...........................93 Chapter 3 : Numerical Verification of the Statistical Theories of Propagation of Optical Beams through Anisotropic, Non-Kolmogorov Turbulence .....................98 3.1: Background ....................................................................................................98 3.2: Spot Size Predictions in the Presence of Non-Kolmogorov Turbulence .......98 3.3: Focused Beams in Non-Kolmogorov Turbulence .......................................103 3.4: Weak Turbulence Regime Predictions of Spot Size ....................................106 3.5: Scintillation Index and Aperture Averaging of Scintillation in the Presence of Optical Turbulence and Refractivity Distortions .............................................109 iv Chapter 4 : Experimental Investigations Atmospheric Distortions Using a Multi- Aperture Transmissometer ...................................................................................134 4.1: Introduction ..................................................................................................134 4.2: MOG MAT Fundamentals ...........................................................................135 4.2: Synchronization of Transmitter and Receiver for Elimination of Background Light .....................................................................................................................139 4.3: Estimates of Extinction Coefficient .............................................................144 4.4: An Iterative Beam Fitting Approach to Capture Refractivity and Turbulence Effects ..................................................................................................................149 4.5: Turbulence Profiling Results in the Weak Fluctuation Regime ..................165 4.6: Simultaneous Extinction Rate and Turbulence Profiling in the Deep Fluctuation Regime ..............................................................................................190 Chapter 5 : Summary and Future Work ...............................................................204 5.1: Summary ......................................................................................................204 5.2: Future Work .................................................................................................208 Appendices ...........................................................................................................212 Appendix A: Tables of RMS Error Statistics over Region of Interest ...............213 Appendix B: Charts of RMS Error Statistics over Entire