Electromagnetic analysis of bidirectional reflectance from roughened surfaces and applications to surface shape recovery

Scattering from randomly rough surfaces is a well-established sub area of electrodynamics. There remains much to be done since each surface and optical processes that may occur in within the scattering medium, and countless other scenarios, is different. There are also illumination models that describe lighting in a scene on the macroscopic scale where geometrical optics can be considered adequate. Of particular interest for us is the intersection of the physical scattering theories and the illumination models. We present two contributions: 1) A minimum of two independent images are needed since any opaque surface can be uniquely specified in terms of its outward-normal vector field. This required the development of a global, nonlinear, alternating optimization scheme to compute parameter estimates. It is shown that high accuracy estimates can be obtained. 2)The smooth emergence of geometrical optics from physical optics using a full wave electromagnetic solution of the 1D scattering problem. It is shown here that the geometrical optics limit is arrived at in a smooth transition from physical optics starting with the electric field integral equation by varying the size of roughness structures on the surface and calculating the scattering cross length . Starting from roughness features smaller than the incident wavelength and also considering the size of the surface fluctuations relative to the size of the surface, the scattered light patterns show expected wave behavior that gradually transitions to geometrical ray optics as the size of surface roughness features increases well beyond the wavelength

The Photometric Effect of Macroscopic Surface Roughness on Sediment Surfaces

The focus of this work was on explaining the effect of macroscopic surface roughness on the reflected light from a soil surface. These questions extend from deciding how to best describe roughness mathematically, to figuring out how to quantify its effect on the spectral reflectance from a soil’s surface. In this document, I provide a background of the fundamental literature in the fields of remote sensing and computer vision that have been instrumental in my research. I then outline the software and hardware tools that I have developed to quantify roughness. This includes a detailed outline of a custom LiDAR operating mode for the GRIT-T goniometer system that was developed and characterized over the course of this research, as well as proposed methods for using convergent images acquired by our goniometer system’s camera to derive useful structure from motion point clouds. These tools and concepts are then used in two experiments that aim to explain the relationship between soil surface roughness and spectral BRF phenomena. In the first experiment, clay sediment samples were gradually pulverized into a smooth powderized state and in steps of reduced surface roughness. Results show that variance in the continuum spectra as a function of viewing angle increased with the roughness of the sediment surface. This result suggests that inter-facet multiple scattering caused a variance in absorption band centering and depth due to an increased path length traveled through the medium. In the second experiment, we examine the performance of the Hapke photometric roughness correction for sand sediment surfaces of controlled sample density. We find that the correction factor potentially underpredicts the effect of shadowing in the forward scattering direction. The percentage difference between forward-modeled BRF measurements and empirically measured BRF measurements is constant across wavelength, suggesting that a factor can be empirically derived. Future results should also investigate the scale at which the photometric correction factor should be applied. Finally, I also outline a structure from motion processing chain aimed at deriving meaningful metrics of vegetation structure. Results show that correlations between these metrics and observed directional reflectance phenomena of chordgrass are strong for peak growing state plants. We observe good agreement between destructive LAI metrics and contact-based LAI metrics

Lunar surface roughness shadowing and thermal emission

Statistical model of lunar surface roughness for shadow and infrared emission characteristic

A Tale of Two Planet(ary bodie)s: The Origin of Ice on Mercury and the Moon

The low obliquity of Mercury and the Moon causes topographic depressions located near their poles to cast persistent shadows, which may cold-trap volatiles for geologic time periods. Despite their similar thermal environments, telescopic and remote sensing observations have previously detected thick, pure water ice deposits near the poles of Mercury but not the Moon - where ice was found to be superficial or mixed with the regolith. This work attempts to resolve the apparent difference between the two planetary bodies employing physical models and spacecraft observations. We study how topographic roughness affects the temperature distribution and the ensuing prevalence of cold-traps, and constrain the amount, age and origin of polar ice deposits on Mercury and the Moon. Our results suggest that the difference between the amount of cold-trapped volatiles on these planetary bodies may not be as significant as previously thought, and that the presence of heavier carbonaceous volatiles on Mercury may explain the higher purity of its ice deposits relative to the Moon

Numerical Investigation of Radar Scattering from Rough Land Surfaces

Electrical Engineerin