abstract: Scattering from random rough surface has been of interest for decades. Several methods were proposed to solve this problem, and Kirchho approximation (KA) and small perturbation method (SMP) are among the most popular. Both methods provide accurate results on rst order scattering, and the range of validity is limited and cross-polarization scattering coecient is zero for these two methods unless these two methods are carried out for higher orders. Furthermore, it is complicated for higher order formulation and multiple scattering and shadowing are neglected in these classic methods. Extension of these two methods has been made in order to x these problems. However, it is usually complicated and problem specic. While small slope approximation is one of the most widely used methods to bridge KA and SMP, it is not easy to implement in a general form. Two scale model can be employed to solve scattering problems for a tilted perturbation plane, the range of validity is limited. A new model is proposed in this thesis to deal with cross-polarization scattering phenomenon on perfect electric conducting random surfaces. Integral equation is adopted in this model. While integral equation method is often combined with numerical method to solve the scattering coecient, the proposed model solves the integral equation iteratively by analytic approximation. We utilize some approximations on the randomness of the surface, and obtain an explicit expression. It is shown that this expression achieves agreement with SMP method in second order. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2017

abstract: We present fast and robust numerical algorithms for 3-D scattering from perfectly electrical conducting (PEC) and dielectric random rough surfaces in microwave remote sensing. The Coifman wavelets or Coiflets are employed to implement Galerkin’s procedure in the method of moments (MoM). Due to the high-precision one-point quadrature, the Coiflets yield fast evaluations of the most off-diagonal entries, reducing the matrix fill effort from O(N^2) to O(N). The orthogonality and Riesz basis of the Coiflets generate well conditioned impedance matrix, with rapid convergence for the conjugate gradient solver. The resulting impedance matrix is further sparsified by the matrix-formed standard fast wavelet transform (SFWT). By properly selecting multiresolution levels of the total transformation matrix, the solution precision can be enhanced while matrix sparsity and memory consumption have not been noticeably sacrificed. The unified fast scattering algorithm for dielectric random rough surfaces can asymptotically reduce to the PEC case when the loss tangent grows extremely large. Numerical results demonstrate that the reduced PEC model does not suffer from ill-posed problems. Compared with previous publications and laboratory measurements, good agreement is observed. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2016

Electromagnetic wave propagation over random sea surfaces is a classical problem of interest for the Navy, and significant research has been done over the years. Here we make use of numerical and analytical methods to predict the propagation of microwaves over random rough surface. The numerical approach involves utilization of the direct solution (using Volterra integral equation of the second kind) to currents induced on a rough surface due to forward propagating waves to compute the scattered field. The mean scattered field is computed using the Monte-Carlo method. Since the exact solution (consisting of an infinite series) to induced current density is computationally intensive, there exists a need to predict the propagation using the closely accurate zeroth order induced current (first term of the series) for time-varying multiple realizations of a random rough surface in a computationally efficient manner. The wind-speed dependent, fully-developed, Piersen-Moskowitz sea spectrum has been considered in order to model a rough sea surface, although other partially-developed roughness spectra may also be utilized. An analytical solution based on the zeroth order current density obtained by deriving the mean scattered field as a function of the range and vertical height by directly using the Parabolic Equation (PE) approximation method and the resulting Green's function has been utilized for a comparative study. The analytical solution takes into account the diffused component of the scattered field.