Abstract
The like and cross polarized single and double scattered fields are derived using a full wave approach. This approach is based on the complete expansion of the electromagnetic fields, the imposition of exact boundary conditions and the conversion of Maxwell's equations into generalized telegraphists equations for the scattered wave amplitudes. Thus, the zero order iterative solutions for the generalized telegraphists equations yield the primary electromagnetic (source) fields impressed upon the rough surface. The first and second order iterative solutions to the generalized telegropherts' equations yield the single and double scattered fields. This can be clearly demonstrated by taking the geometric optics limit of the full wave solutions. To obtain the corresponding like and cross polarized scatter cross sections, as in the case of scattering from one dimensional rough surfaces, it is necessary to account for contributions from the quasi parallel double scatter paths as well as the quasi antiparallel double scatter paths. However, for scattering from two dimensional rough surfaces, these paths are not restricted to the plane of incidence. The full wave solutions for the double scattered fields are expressed as six dimensional integrals, that account for the complete wave spectra of scattered fields and the coordinate variables at a pair of points on the rough surface. These expressions are used to obtain the multidimensional integrals for the like and cross polarized cross sections. To make these solutions tractable for computational purposes, a high frequency approximation of the full wave double scatter cross sections are expressed as four dimensional integrals involving scatter wave vector variables. These results can be evaluated in significantly less time than standard numerical solutions of the integral equations. Moreover, the physical interpretation of the results shed light on the impact, of different statistical parameters of the random rough surfaces, upon the backscatter enhancement.
