Rough surface Green's function based on the first-order modified perturbation and smoothed diagram methods

This paper presents an analytical theory of rough surface Green's functions based on the extension of the diagram method of Bass, Fuks, and Ito with t he smoothing approximation used by Watson and Keller. The method is a modif ication of the perturbation method and is applicable to rough surfaces with small RMS height. But the range of validity is considerably greater than f or the conventional perturbation solutions. We consider one-dimensional rou gh surfaces with a Dirichlet boundary condition. The coherent Green's funct ion is obtained from the smoothed Dyson's equation using a spatial Fourier transform. The mutual coherence function for the Green's function is obtain ed by first-order iteration of the smoothing approximation applied to the B ethe-Salpeter equation in terms of a quadruple Fourier transform. These int egrals are evaluated by the saddle-point technique. The equivalent bistatic cross section per unit length of the surface is compared with that for the conventional perturbation method and the Watson-Keller result. With respec t to the Watson-Keller result, it should be noted that our result is recipr ocal while the Watson-Keller result is non-reciprocal. Included in this pap er is a discussion of the specific intensity at a given observation point. The theory developed will be useful for RCS signature related problems and low grazing angle scattering when both the transmitter and the object are c lose to the surface.