Statistical moments for rough surface scatter from two-way parabolic integral equation at low grazing angles

Abstract

The moments of a plane wave scattered at low grazing angles from a one-dimensional perfectly reflecting rough surface are considered. The mean intensity and autocorrelation of the scattered field and the corresponding angular spectrum are obtained to second order in surface height. The derivations are based on an operator expansion of the extended (two-way) parabolic integral equation solution. The resulting operator series describes successively higher-order surface interactions between forward and backward going components. The expressions derived may be regarded as backscatter corrections to those obtained via the standard (one-way) parabolic integral equation method.