Integral equation formulation for object scattering above a rough surface

In this thesis, we consider the scattering from an object buried within a rough surface environment. The presence of the rough surface produces random fluctuations in the field, which are modeled by a rough surface Green's function. The rough surface Green's function is applicable to rough surfaces of small rms height and is based upon the modified diagram method and the second-order perturbation method. The coherent (average) Green's function G is obtained by solving Dyson's equation, which is the re-normalized perturbation expansion of Green's theorem. The second moment of the Green's function ⟨ GG*⟩, also called the Mutual Coherence function (MCF), is obtained by solving Bethe-Salpeter's equation under the first order, second-order ladder and second-order cyclic theory. It should be noted that in order to construct a Green's function for a surface using the diagram process, one must be able to write the boundary condition as a perturbation process. In this thesis, we construct rough surface Green's function for these surfaces. (1) Dirichlet's boundary condition. (2) Neumann's boundary condition. (3) TE and TM Impedance boundary condition. (4) Dyadic boundary condition for perfectly electric conducting rough surface.; The interaction of the Green's function with the object is determined by the modified electric field integral equations (“S”-EFIE) for statistical Green's functions. The “S”-EFIE is obtained by averaging the deterministic EFIE and assuming that the Green's function and the induced currents on the object are complex, circular Gaussian random variables. These integral equations are solved using method of moments (MOM) to provide solutions for the coherent and fluctuating current distributions induced on the object near a rough surface. Once these currents are known, the coherent and incoherent intensity radiating from the object may also be obtained.