Derivation of phase statistics from the Mueller matrix
Experimental observations show a strong dependence of phase differences of scattering matrix elements on the physical parameters of random media. Here, the statistical behavior of the phase differences is studied for distributed targets. The pdfs of the phase differences are derived from the Mueller matrix of the target. In deriving the density functions, it is assumed that the real and imaginary parts of the copolarized and cross-polarized terms of the scattering matrix are jointly Gaussian and their covariance matrices are found in terms of the Mueller matrix elements. The functional forms of the copolarized and cross-polarized density functions are similar and are obtained independently. It is shown that the density function of the phase difference is completely determined in terms of only two parameters.