Full wave multiple scattering from one dimensional random rough surfaces and high frequency stationary phase approximation

Using the full wave approach, integral expressions for the double scattered radar cross sections are given. The rough surface is assumed to be characterized by a Gaussian joint probability density function for the surface heights and slopes at two points. The surface height autocorrelation function and its Fourier transform are also assumed to be Gaussian. The expressions for the double scattered cross section are expressed as six-dimensional integrals which account for the correlations between the heights and the slopes of the random rough surface. The stationary phase approximation is used to reduce the expressions for the double scattered cross section from six to two dimensional integrals. For the stationary phase approximations to the full wave solutions it is not necessary to assume Gaussian joint probability density functions or Gaussian surface height autocorrelation functions. It is shown that enhanced backscatter is due to double scatter when the rough surface mean square slopes and heights are large.<>