POLARIZATION SIGNATURES IN VECTOR SPACE 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 Diane Krupp Beamer, B.S., M.S., M.B.A. UNIVERSITY OF DAYTON Dayton, Ohio August, 2018 POLARIZATION SIGNATURES IN VECTOR SPACE Name: Beamer, Diane Krupp APPROVED BY: ____________________________________ ____________________________________ Partha P. Banerjee, Ph.D. Joseph W. Haus, Ph.D. Advisory Committee Chairman Committee Member Department Chair Professor Department of Electro-Optics and Photonics Department of Electro-Optics and Photonics ____________________________________ ____________________________________ Dean R. Evans, Ph.D. Samir Bali, Ph.D. Committee Member Committee Member Air Force Research Laboratory Professor Wright Patterson Air Force Base Physics Department Graduate Faculty Miami University of Ohio Department of Electro-Optics and Photonics ____________________________________ ____________________________________ Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean Professor School of Engineering School of Engineering ii © Copyright by Diane Krupp Beamer All rights reserved 2018 iii ABSTRACT POLARIZATION SIGNATURES IN VECTOR SPACE Name: Beamer, Diane Krupp University of Dayton Advisor: Dr. Partha P. Banerjee The use of polarimetric information to enhance the identification process for unresolved and unknown targets in GEO orbit is quite rare. The majority of observations made of objects at that distance are spectral measurements, without the polarization information that is available in the same stream of photons being captured. It is proposed to use polarimetric signatures to enhance the speed and accuracy of the identification of unknown objects. Three methods of polarization signatures are proposed. First, the standard Stokes signature plotted as a function of solar phase angle is recommended. But beyond that, two other methods are proposed to help qualitative and quantitative assessment of the unknown target. The second method is the use of vector space, a ratio of one Stokes parameter to another in all combinations possible (six spaces), plotted against the solar phase angle in a similar manner to the Stokes signatures. The third method is novel, using a technique borrowed from astronomers who characterize distant stars based on color-color analysis of the intensity ratios of celestial objects. A statistical method of analyzing the resulting iv object characterization is also proposed, which is the Bhattacharyya distance, a non- Euclidean method to characterize the clusters produced by the third method. The experiments were conducted comparing simple geometries with one another to determine if polarization could differentiate simple geometries. Next different materials and surfaces were compared with one another to test polarization as a differentiator of the materials. Third, two complex models made up of three simple geometries that are representative of satellite construction were built and tested by the same three methods, to differentiate them from each other based on polarization signatures. Last, a third composite, different than both previous composites was built, and the method tested to see if it would identify the geometry most dissimilar to the new object so that a selection process could be created. Each of the polarization methods tested was successful in differentiating geometry, material, surface configuration, and complex composite geometries made up of the simpler geometries tested. Polarization signatures are ubiquitous and consistent. It was found that the peaks and valleys observed in the signatures of compound objects were caused by the geometry and material of the simpler parts making up the complex object. A selection procedure was demonstrated based on identifying the most dissimilar object of two choices, and eliminating it. Polarization signatures were capable of differentiating which objects were most like and most dissimilar to the test object. In conclusion, using polarimetry as an analytical tool to help identify unresolved objects in space is potentially an excellent process that would complement current methods of spectral analysis. v DEDICATION This work is dedicated first to the Lord, Jesus Christ, King of kings and Lord of all lords, at Whose command I undertook this effort. I have set my face as flint and did as instructed. This work is also dedicated to my husband, Denny Beamer, who listened throughout the years and encouraged me, and to my children, Laura Dawson and Christian Dawson, who cheered and encouraged me the whole way. Last but not least, this work is dedicated to my friend Judy Vineyard, for all the prayer support and encouragement she supplied to me. Without all of you, I could not have done it. My deepest thanks and heartfelt appreciation are offered to you. vi ACKNOWLEDGEMENTS First of all I would like to thank my advisor Dr. Partha Banerjee for his guidance, wisdom, insight and understanding applied to this process from start to finish. He supplied a listening ear, good questions, and many good ideas on my research. I appreciate all his support. I would also like to thank Dr. Joseph Haus for his support when I needed someone to listen to new ideas. I thank Dr. Dean Evans for the loan of his AOM for several months during early experimentation. I thank Dr. Samir Bali for his extensive feedback and attention to my proposal and dissertation. My special thanks go to Dr. Ujitha Abeywickrema for reading and editing all my papers, for his endless support in the lab, for his ready smile and the many times when we all laughed out loud. I also thank (soon to be Dr.) Rudra Gnawali for his friendship and encouragement. I thank the UD physics department for the 18 month loan of their halogen lamp as a light source for the polarization experiments. I would especially like to thank the EO staff for continuous support and help overcoming the day to day problems and making the department a great place to work. vii TABLE OF CONTENTS ABSTRACT ....................................................................................................................... iv DEDICATION ................................................................................................................... vi ACKNOWLEDGEMENTS .............................................................................................. vii LIST OF FIGURES .......................................................................................................... xii LIST OF ABBREVIATIONS .......................................................................................... xix LIST OF SYMBOLS ....................................................................................................... xxi CHAPTER 1 INTRODUCTION AND OBJECTIVES ...................................................... 1 CHAPTER 2 THE SCIENCE OF POLARIZATION ........................................................ 5 2.1 Introduction ...................................................................................................... 5 2.2 The Electric Vector .......................................................................................... 8 2.3 Special Cases – Linear and Circular Polarization ............................................. 9 2.4 Polarization by Reflection............................................................................... 12 2.5 What Polarimetry Adds................................................................................... 13 CHAPTER 3 POLARIZATION ALGEBRA AND PROPAGATION ............................ 18 3.1 Jones Calculus ................................................................................................ 18 viii 3.2 Stokes Vectors .............................................................................................. 22 3.3 The Poincaré Sphere: the Basis for Vector Space .......................................... 27 3.4 Propagation of the Polarization Vector ........................................................... 31 3.5 Conclusion ...................................................................................................... 38 CHAPTER 4 ANALYTICAL METHODS ...................................................................... 40 4.1 Introduction and Motivation ......................................................................... 40 4.2 Traditional Polarization Signatures................................................................ 42 4.3 Intensity Analysis Methods from Other Disciplines ...................................... 45 4.4 Application of Color Space Concept to Polarimetry .................................... 48 4.5 A Computational Approach to Identifying Targets ....................................... 54 4.6 Statistical Approach ...................................................................................... 55 4.7 Conclusions ..................................................................................................... 73 CHAPTER 5 RELATED WORK ON POLARIMETRY OF SPACE OBJECTS ........... 74 5.1 Polarization Signatures of Space Objects ...................................................... 74 5.2 Polarization Detection Through Haze and Clouds......................................... 82 CHAPTER 6 EXPERIMENTAL SETUP FOR STOKES VECTOR DETERMINATION ........................................................................................................