High frequency approximations to multiple scatter by rough surfaces that exhibit enhanced backscatter

Integral expressions for the single and double scattered radar cross sections are obtained using the full wave approach. The surface heights and slopes at two points on the random rough surface are characterized by Gaussian joint probability density functions. The surface height autocorrelation function and its Fourier transform (the rough surface spectral density function) are also assumed to be Gaussian. Two and six dimensional integral expressions are obtained for the single and double scattered cross sections. They account for the correlations between the heights and the slopes of the random rough surface. The high frequency approximations reduce the expressions for the double scatter cross sections from six to two dimensional integrals. The results show that the enhanced backscatter is due to multiple scatter from rough surfaces with large mean square slopes and heights