Examination of large radius of curvature approximation for rough surface scatter cross sections

Examines the impact of the large radius of curvature approximation on the random rough surface scatter cross section. The full wave expressions for the single scatter cross sections for one dimensional random rough surfaces are given. The height and slope correlations are accounted for in this work. The single scatter cross section is expressed in terms of three dimensional integrals over the slopes at two distinct points on the surface and the spatial distance between them. Using the large radius of curvature approximation, the solution reduces to a two dimensional integral. This is because the slope variables at two neighboring points (within few correlation lengths) are assumed to be the same. The joint probability density function of the heights and slopes and the autocorrelation function for the heights are assumed to be Gaussian. When the large radius of curvature approximation is not valid, double humps appear in the plots for the cross section around the quasi specular direction.