Numerical method to compute TE and TM multiple scatter from rough surfaces exhibiting backscatter enhancement

A numerical method is presented to evaluate the full wave solutions for TE (horizontally polarized) and TM (vertically polarized) double scatter cross sections of one dimensional random rough surfaces. The full wave double scatter cross sections are expressed in terms of six dimensional integrals. The cpu time needed to evaluate the six dimensional integrals using standard techniques is excessive even for supercomputers. A numerical technique is used to reduce the six dimensional integrals into three dimensional integrals (one dimensional integral calling two independent two dimensional integrals). These two dimensional integrals account for the correlations between the heights and slopes at two points on the surface. The results exhibit the observed sharp enhanced backscatter and the polarization dependence of the cross sections. The angular width and the magnitude of the enhanced backscatter depend on the rough surface parameters (mean square height and slope)