Field transformational approach to three-dimensional scattering from two-dimensional rough surfaces

In 1985, Tappert and Nghiem-Phu introduced a field-transformation technique for computing rough surface scattering from a parabolic equation model utilizing a split-step Fourier marching algorithm. The approach was based on a two-dimensional parabolic equation with a standard operator approximation that was capable of computing scattering from a one-dimensional rough surface. Although this approach has been used extensively and effectively, extensions of this approach to higher order approximations or three-dimensional propagation have only recently been investigated. In this work, the expressions that incorporate higher-order approximations and three-dimensional scattering from two-dimensional rough surfaces are presented. The implications of some computationally necessary approximations are also provided.