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Analysis of Joint Effects of Refraction and Turbulence On ANALYSIS OF JOINT EFFECTS OF REFRACTION AND TURBULENCE ON LASER BEAM PROPAGATION IN THE ATMOSPHERE Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree Master of Science in Electro-Optics By David Bricker UNIVERSITY OF DAYTON Dayton, Ohio December, 2013 i ANALYSIS OF JOINT EFFECTS OF REFRACTION AND TURBULENCE ON LASER BEAM PROPAGATION IN THE ATMOSPHERE Name: Bricker, David A. APPROVED BY: ______________________________ ______________________________ Mikhail Vorontsov, Ph.D. Partha Banerjee, Ph.D. Advisory Committee Chairman Committee Member Professor, Electro-Optics Program Professor & Director, Electro-Optics Program ______________________________ Paul McManamon, Ph.D. Committee Member Technical Director, LOCI ______________________________ ______________________________ John G. Weber, Ph.D. Tony E. Saliba, Ph.D. Associate Dean Dean, School of Engineering School of Engineering & Wilke Distinguished Professor ii ABSTRACT ANALYSIS OF JOINT EFFECTS OF REFRACTION AND TURBULENCE ON LASER BEAM PROPAGATION IN THE ATMOSPHERE Name: Bricker, David A. University of Dayton Advisor: Dr. Mikhail Vorontsov Experimental data obtained from recently conducted long-range laser beam propagation experiments has revealed inconsistencies with analytic and numeric simulations results based on classical Kolmogorov turbulence theory. This inconsistency may be related with not accounting for refraction effects caused by refractive index variation with elevation and presence of large- scale atmospheric structures which introduce refractive index gradients and can alter the trajectory of optical wave energy flux. In this thesis, atmospheric refraction effects are studied using a ray tracing technique. Due to refraction a ray propagating in the atmosphere doesn‟t follow a straight line and may not arrive to a desired location. In this thesis the ray tracing technique was applied for analysis of optical propagation over a 150 km propagation path. It was shown that due to refraction the ray trajectory may deviate from the geometric straight line by 60m in the middle of the path. We also considered the impact of refraction on atmospheric propagation of laser beams with different wavelengths (λ=0.532µm, λ=1.064µm, and λ=1.550µm) which were launched at the same angle. Due to the difference in refractive index of iii air for different wavelengths, the ray‟s paths follow different trajectories. It was shown that at the end of the propagation path, the distance between ray trajectories can be as long as ~4.1m for the 0.532µm and the 1.064µm rays, and ~4.3m for 0.532µm and 1.550µm rays. Besides traditional ray tracing technique we also introduced a new computational method that allows analysis of combined refraction and turbulence effects on laser beam propagation. In this method, traditional beam propagation using the well-known split step operator method is combined with ray tracing. In this technique the atmospheric volume is represented as a set of thin phase screens that obey Kolmogorov turbulence statistics. The ray tracing technique is applied to describe optical wave propagation between phase screens. At each screen, the turbulence-induced random tip and tilt wave-front phase component is added to the ray angle. In this way, the ray trajectory is no longer deterministic, but it has a turbulence induced uncertainty. It was shown that at the end of a 150km propagation path, the turbulence induced deviation on ray trajectory can be on the order of 5m. These results show that for correct analysis of laser beam propagation over long distances in the atmosphere, refraction and turbulence effects should be considered jointly. The proposed numerical simulation technique allows this joint analysis. iv ACKNOWLEDGEMENTS I would like to express my gratitude to my advisor Dr. Mikhail Vorontsov for his guidance and support of my thesis. I would also like to thank my other committee members; Dr. Partha Banerjee and Dr. Paul McManamon for their input and direction. I received important support for this research from both University of Dayton and Optonicus employees whom I would like to acknowledge: Dr. Jean Minet, Dr. Grigory Filimonov, Dr. Sara John, Morris Maynard, Dr. Thomas Weyruch, and Dr. Ernst Polnau. I would also like to thank the other students who I worked with; Jeff Kraczek, Ramyaa Ramesh ,Ben Dapore, Ujitha Abeywickrema and Diego Garcia. Finally, I would like to thank my wife Hayley and the rest of my family for all their support. My sincerest thanks to everyone who helped me along the way. v TABLE OF CONTENTS ABSTRACT .................................................................................................................................... iii ACKNOWLEDGEMENTS ............................................................................................................. v LIST OF FIGURES ...................................................................................................................... viii CHAPTER 1 .................................................................................................................................... 1 INTRODUCTION ........................................................................................................................... 1 CHAPTER 2 .................................................................................................................................... 3 ATMOSPHERIC OPTICAL REFRACTION EFFECTS AND RAY PROPAGATION ................ 3 2.1 Atmospheric Refractive Index Profile ................................................................................... 3 2.1.1 Index of Refraction: Basic Equations ............................................................................. 3 2.1.2 The US 1976 Standard Atmosphere Temperature Profile .............................................. 5 2.2 Ray Tracing Technique .......................................................................................................... 7 2.2.1 Ray Tracing Equation ..................................................................................................... 9 2.2.2 Numerical Integration of the Ray Tracing Equations ................................................... 11 2.2.3 Implementation in C++ ................................................................................................. 12 2.3 Ray Tracing Atmospheric Optics: Examples ....................................................................... 14 2.3.1 Optical Ray Propagation through Stratified Layers ...................................................... 16 2.3.2 Mirage Formation ......................................................................................................... 18 2.3.3 Analysis of the Coherent Optical Multi-Beam Atmospheric Transmission (COMBAT) Experiment Using Ray Tracing Technique ............................................................................ 20 2.4 Limitations of Ray Tracing Approach ................................................................................. 27 CHAPTER 3 .................................................................................................................................. 29 ATMOSPHERIC TURBULENCE EFFECT ON OPTICAL WAVE PROPAGATION .............. 29 3.1 Atmospheric Turbulence ...................................................................................................... 29 3.2 Optical Wave Propagation. .................................................................................................. 32 3.2.1 Helmholtz Equation ...................................................................................................... 32 3.2.2 Parabolic Equation ........................................................................................................ 33 3.2.3 Split Step Method: Free-Space Propagation ................................................................. 34 3.2.4 Split Step Method: Refraction....................................................................................... 34 vi CHAPTER 4. ................................................................................................................................. 36 MERGING RAY TRACING AND WAVE OPTICS APPROACHES ........................................ 36 4.1 Basic Ideas of Merging Ray Tracing and Wave Optics Approaches ................................... 36 CHAPTER 5 .................................................................................................................................. 42 LASER BEACON ANALYSIS USING WORT TECHNIQUE ................................................... 42 5.1 Simulation Parameters ......................................................................................................... 42 5.2 WORT Simulation Results .................................................................................................. 42 Conclusions .................................................................................................................................... 45 REFERENCES ............................................................................................................................. 47 vii LIST OF FIGURES Figure 2. 1 Reduced refractivity AD vs. wavelength for dry air ...................................................... 4 Figure 2. 2 US 1976 standard atmospheric temperature, density and pressure altitude profiles ..... 5 Figure 2. 3 Refractivity of Troposphere for US 1976 Standard Atmosphere .................................. 7
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