OCEAN WAVE SLOPE AND HEIGHT RETRIEVAL USING AIRBORNE POLARIMETRIC REMOTE SENSING A Dissertation submitted to the Faculty of the Graduate School of Arts and Sciences of Georgetown University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics By Rebecca Baxter, M.S. Washington, DC April 17, 2012 Copyright 2012 by Rebecca Baxter All Rights Reserved ii OCEAN WAVE SLOPE AND HEIGHT RETRIEVAL USING AIRBORNE POLARIMETRIC REMOTE SENSING Rebecca Baxter, M.S. Thesis advisors: Edward Van Keuren, Ph.D. Brett Hooper, Ph.D. ABSTRACT Ocean wave heights are typically measured at select geographic locations using in situ ocean buoys. This dissertation has developed a technique to remotely measure wave heights using imagery collected from a polarimetric camera system mounted on an airborne platform, enabling measurements over large areas and in regions devoid of wave buoys. The technique exploits the polarization properties of Fresnel reflectivity at the ocean surface to calculate wave slopes. Integrating the slope field produces a measurement of significant wave height. In this dissertation, I present experimental data collection and analysis of airborne remotely sensed polarimetric imagery collected over the ocean using Areté Associates’ Airborne Remote Optical Spotlight System-MultiSpectral Polarimeter, as well as modeled results of the expected radiance and polarization at the sensor. The modeling incorporates two sources of radiance/polarization: surface reflected sky radiance and scattered path radiance. The latter accounts for a significant portion of the total radiance and strongly affects the polarization state measured at the sensor. After laying the groundwork, I describe my significant wave height retrieval algorithm, apply it to the polarimetric data, and present the results. While further development and refinement of the significant wave height retrieval algorithm and testing with a more extensive data set are required, the initial results are promising for the practical application of this technique. iii TABLE OF CONTENTS Chapter 1 – Introduction............................................................................................................. 1 Chapter 2 – Prior art, research objectives, and approach............................................................ 3 2.1 Stereo imaging........................................................................................................... 3 2.2 Reflection of sunglint................................................................................................ 5 2.3 Polarimetric slope sensing......................................................................................... 6 2.4 Research objectives and approach............................................................................. 10 Chapter 3 – Theory...................................................................................................................... 13 3.1 Polarization................................................................................................................ 13 3.2 Measuring polarization.............................................................................................. 18 3.3 Natural sources of polarization.................................................................................. 20 3.4 Polarimetric remote sensing...................................................................................... 30 3.5 Ocean waves.............................................................................................................. 32 Chapter 4 – Experimental data collection.................................................................................... 37 4.1 Polarimetric system and data collection..................................................................... 37 4.2 In situ measurements.................................................................................................. 44 Chapter 5 – Polarimetric data analysis......................................................................................... 49 5.1 Comparisons of frequency-direction spectra.............................................................. 49 5.2 Polarimetric imagery.................................................................................................. 51 5.3 Mean value trends over orbital and stripmap runs..................................................... 54 Chapter 6 – Polarimetric modeling.............................................................................................. 60 6.1 Sensor polarization model description....................................................................... 60 6.2 Polarimetric model validation.................................................................................... 68 6.3 Application of polarimetric model to Taylor Bay and open ocean data.................... 75 6.4 Study of variations in Ψ............................................................................................. 81 6.5 Atmospheric correction.............................................................................................. 84 Chapter 7 – Wave slope and height retrieval................................................................................ 91 7.1 Polarization reaching the sensor................................................................................. 91 7.2 Significant wave height retrieval algorithm................................................................ 94 iv 7.3 Example significant wave height retrieval................................................................. 97 7.4 Significant wave height results.................................................................................. 103 7.5 Results with downsampled resolution....................................................................... 112 7.6 Potential improvements to the wave height retrieval algorithm................................ 119 Chapter 8 – Conclusion................................................................................................................ 125 Appendix A – AROSS-MSP calibrations.................................................................................... 129 A.1 Optimal focus............................................................................................................ 131 A.2 Flat field and radiometric calibration........................................................................ 135 A.3 Geometric distortion calibration............................................................................... 144 A.4 Polarization filter orientation calibration.................................................................. 149 A.5 Inter-camera alignment............................................................................................. 154 A.6 Boresight alignment.................................................................................................. 159 Appendix B – Permissions to use copyrighted material.............................................................. 161 Bibliography................................................................................................................................ 168 v LIST OF FIGURES 2.1 – Reflection geometry for polarimetric slope sensing technique, reproduced from [17] ......... 7 2.2 – Three components of radiance contributing to total radiance at the sensor ........................... 8 3.1 – Representations of linearly, circularly, and elliptically polarized light. .............................. 14 3.2 – Setup to measure Stokes parameters with a retarder and a linear polarizer ......................... 18 3.3 – Fresnel reflection and transmission at an interface .............................................................. 21 3.4 – Fresnel coefficients for air-water interface .......................................................................... 23 3.5 – Reflected degree of linear polarization as a function of incident angle ............................... 24 3.6 – Visualization of Rayleigh scattering for vertical and horizontal source polarization .......... 25 3.7 – Plots of the intensity (left) and degree of linear polarization (right) for Rayleigh scattering ....................................................................................................................................................... 26 3.8 – Skydome plots of the degree and angle of linear polarization. The radial distance represents the angle from zenith, while the clockwise angle from vertical represents the azimuth E of N ............................................................................................................................................ 28 3.9 – Plot of maximum P and zenith P normalized by the value at 809 nm with 4th order polynomial fit ................................................................................................................................ 30 3.10 – Schematic (and fanciful) representation of the energy contained in the surface waves of the oceans – in fact, a guess at the power spectrum, reproduced from [53] ................................. 33 3.11 – 2-D f-d spectrum calculated from airborne imagery collected over Torrey Pines Outer buoy............................................................................................................................................... 36 3.12 – Marginal 1-D direction and frequency spectra .................................................................. 36 4.1 – AROSS-MSP system mounted