The method of the local parabolic approximation for rough surface scattering

A method for evaluation of scattering from rough surfaces which is similar to the Kirchhoff approximation is considered. However, it is based on a local parabolic approximation of the surface irregularities rather than a tangent plane approximation and two iterations of the surface field integral equation. The method, first proposed by Belobrov and Fuks [Izv. VUZ Radiofiz. 29, 1083-1089 (1986); Soy. Phys. Acoust. 31, 442-445 (1985)], accounts for local diffraction effects. Important modifications to the original method are introduced and extensive numerical results for Gaussian, one-dimensional randomly rough surfaces for both the Dirichlet and Neumann problems are provided. The validity of the local parabolic approximation is assessed by comparison with results from Monte Carlo simulations. It is demonstrated that the local parabolic approximation improves the Kirchhoff approximation for large and intermediate values of the surface correlation length especially in the backscattering region.