Single and double like are cross polarized scatter from two dimensional random rough surfaces-high frequency approximations

Single and double scatter bistatic radar cross sections for two dimensional random rough surfaces are obtained. The full wave solutions are given as multi-dimensional integrals. The excitations are assumed to be plane waves. The high frequency approximations are applied to these expressions to reduce the dimensions of the multidimensional integrals. The large radius of curvature approximation is assumed in this work. The high frequency double scatter expressions are given by four dimensional integrals and the single scatter cross sections are given in closed form. This research is an extension to earlier work on double scatter from one dimensional random rough surfaces. The numerical results (using the high frequency approximations) show sharp enhancement in the backscatter direction at normal and oblique incident angles. This sharp enhancement is associated with the quasi anti-parallel double scatter path for both the like and cross polarized waves. The level and width of the peak in the backscatter direction depends on the mean square height and slope of the two dimensional random rough surfaces.