A high order renormalization method for radar backscatter from a random medium

The problem of radar backscattering from a half-space random medium is formulated in terms of a series solution to Dyson´s equation for the mean field in the random medium. The renormalization method is applied to given an approximate solution through the use of Feynman diagrams. An improved approximation is then obtained by including two additional summations of infinite series of these diagrams. The results from this improved approximation are used to calculate the radar backscattering cross sections and compared with those of a previous paper (1980). For comparison with experimental data, a field of vegetation is modeled as a random medium with an average complex permittivity as well as fluctuations in the real and imaginary parts of the permittivity. The values of the average permittivity and the variance of the fluctuations are estimated by the use of dielectric mixture theory