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Passive Snapshot Remote Sensing of Orbital Velocity

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Passive Snapshot Remote Sensing of Orbital Velocity ABSTRACT PANTALONE, BRETT ANTHONY. Passive Snapshot Remote Sensing of Orbital Velocity. (Under the direction of Michael Kudenov). Techniques for tracking objects in low Earth orbit include line of sight angle measure- ments and active range measurements using RADAR or laser reflection. Active ranging techniques are less effective for high-altitude orbits because of the relatively large signal loss from distant targets. Passive methods using only optical telescopes require a minimum of three separate observations to solve the orbit equation. This thesis demonstrates how incorporation of passive Doppler shift measurement of solar Fraunhofer lines can improve initial orbit determination, while reducing the number of required observations to two. First, a discussion of the current state of space situational awareness establishes the mo- tivation for this work. Then, a brief review of conventional Doppler velocimetry highlights the strengths and weaknesses of current methods. In Chapter2, passive Doppler velocimetry is discussed, along with the rationale and limitations of Fraunhofer lines as wavelength references. This is followed by a radiometric analysis to estimate the optical power received from sunlight reflected off small orbiting objects. Next, the topic of spatial heterodyning is introduced as a potential technique for im- proving the signal-to-noise ratio of a passive velocimeter. Results of computer simulations are presented to support this idea. The derivation of a new mathematical algorithm for initial orbit determination incor- porating Doppler shift measurement is presented in Chapter3. The new technique is a modification of Gooding’s method, which is also described to provide proper context. Next, the results of orbital simulations using both methods are presented and compared. The results indicate that in some orbital configurations, the new method can successfully solve an initial orbit using only two observations, proving the feasibility of the method. The design and development of optical hardware for measuring the Doppler shift of Fraunhofer lines is described in Chapter4. Trade-space analysis of several alternate designs are considered, before concluding with a walk-through of the final design of a dual-beam, Doppler ratio, polarimetric, direct correlation spectrometer. Chapter5 recounts the assembly, calibration, and preliminary testing of the prototype instrument. Bench tests demonstrate a working spectral resolution of 0.04 nm, while radial velocity measurements of the planet Venus differ from theoretical calculations by only 0.59%. Finally, chapter6 concludes with a summary and discussion of future work. c Copyright 2018 by Brett Anthony Pantalone All Rights Reserved Passive Snapshot Remote Sensing of Orbital Velocity by Brett Anthony Pantalone A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Electrical Engineering Raleigh, North Carolina 2018 APPROVED BY: Robert Kolbas Leda Lunardi Kenan Gundogdu Michael Kudenov Chair of Advisory Committee DEDICATION To my friend and mentor, Herbert Cooper, whose advice and encouragement have been invaluable. ii BIOGRAPHY Brett Pantalone was born in Ravenna, Ohio to parents Paul and Virginia Pantalone. Brett graduated from the University of Akron with a B.S. in electrical engineering in 1992. For the next 20 years, he worked in the consumer electronics industry, writing embedded software for mobile phones and other wireless devices. Brett moved to southern Sweden in 1999, working for the telecommunications giant Ericsson. In 2001 he returned to Raleigh, North Carolina to work in the technology office of the newly formed Sony Ericsson joint venture. In 2006 Brett left Sony Ericsson to become an independent software consultant for technology companies in and around Research Triangle Park. After marrying his wife, Vicki, in 2008, he joined the full-time staff of Device Solutions, a small startup in Morrisville, North Carolina. Cursed with an insatiable curiosity and a desire to solve new types of problems, Brett re- turned to school in 2013 as a graduate student at North Carolina State University. Originally pursuing an M.S. in aerospace engineering, he eventually ended up as a doctoral student in electrical engineering, working in the Optical Sensing Laboratory under the supervision of Dr. Michael Kudenov. Brett’s research interests include remote sensing and astronomical instruments. Now, Brett lives with his wife and two spoiled cats in Pittsboro, North Carolina. He is just waiting for the next adventure. iii ACKNOWLEDGEMENTS Perhaps the most important thing I have learned as a graduate student is that no difficult journey should be undertaken alone. There are many people who deserve my thanks for helping me on this trek. First, I would like to thank Dr. Kudenov for giving me the opportunity and support to do this work. I am also grateful to my current and former peers in the Optical Sensing Laboratory, especially Bryan Maione, Ruonan Yang, David Luo, Ethan Woodard, Yifan Wang, and Brandon Ballance. In addition to their problem-solving assistance, they made a “non-traditional” student feel welcome in their group. I owe a special debt of gratitude to my wife, Dr. Vicki Behrens, for her patience and encouragement. I also thank my parents, Paul and Virginia, for their unflinching belief in my ability. Finally, I thank Misha and Willa for reminding me when to take a break. iv TABLE OF CONTENTS LIST OF TABLES .................................................. vii LIST OF FIGURES ................................................. viii Chapter 1 INTRODUCTION ........................................ 1 1.1 Review of Fraunhofer Lines.................................... 3 1.2 Review of Doppler Velocimetry................................. 5 Chapter 2 PASSIVE DOPPLER VELOCIMETRY .......................... 9 2.1 Radiometric Analysis ........................................ 11 2.1.1 Radiometric Transfer Model.............................. 12 2.1.2 Instrument Noise Model ................................ 13 2.1.3 Signal to Noise Ratio................................... 15 2.2 Spatial Heterodyning........................................ 16 2.3 Heterodyne Simulation....................................... 19 2.4 Velocity-Fitting Simulation.................................... 21 2.4.1 Single-Band Results.................................... 22 2.4.2 Two-Band Results..................................... 28 2.4.3 Three-Band Results.................................... 29 2.4.4 Manual Results....................................... 31 Chapter 3 ORBITAL SIMULATION ................................... 34 3.1 Background............................................... 35 3.2 Mathematical development ................................... 38 3.3 Simulation................................................ 40 3.3.1 Orbit generation...................................... 41 3.3.2 Orbit prediction ...................................... 41 3.4 Testing and results.......................................... 48 3.4.1 Geostationary orbits................................... 50 3.4.2 Mid-altitude orbits .................................... 52 3.4.3 Eccentric and inclined orbits............................. 55 3.4.4 Coplanar observer..................................... 58 3.5 Discussion................................................ 58 Chapter 4 INSTRUMENT DESIGN ................................... 66 4.1 Full Spectral Imaging........................................ 67 4.1.1 Heterodyned Birefringent Interferometer.................... 68 4.1.2 Heterodyned Sagnac Interferometer ....................... 71 4.2 Dual-Band Doppler Ratio..................................... 74 v 4.2.1 Atomic Line Filters .................................... 75 4.2.2 Birefringent Filters .................................... 85 4.2.3 Fiber Bragg Grating.................................... 89 4.2.4 Optical Correlator..................................... 94 4.3 Trade-Space Summary....................................... 103 4.4 Direct Correlation Spectrometer................................ 105 4.4.1 Spatial Light Modulators................................ 106 4.4.2 Design of the Optical Correlator........................... 108 Chapter 5 ASSEMBLY AND CALIBRATION ............................. 113 5.1 Frequency Stability.......................................... 117 5.2 Alignment and Calibration.................................... 119 5.3 Test Results ............................................... 124 Chapter 6 CONCLUSION .......................................... 130 REFERENCES .................................................... 133 vi LIST OF TABLES Table 1.1 Major Fraunhofer line designations, sources, and wavelengths...... 5 Table 2.1 Values used for calculation of system SNR..................... 16 Table 4.1 Filter parameters for the Voigt optical filter.................... 84 Table 4.2 Simulation parameters for the fiber Bragg grating filter. .......... 92 Table 4.3 Optimized grating parameters for the fiber Bragg grating filter. 93 Table 4.4 First order parameters at the Bragg condition for the VPH grating from Wasatch Photonics...................................... 100 Table 4.5 Design trade-space. .................................... 105 Table 5.1 Key specifications of the direct correlation spectrometer. 114 Table 5.2 Imaging sensor Apogee A694 specifications.................... 127 Table 5.3 Santec spatial light modulator SLM-100
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