Statistical properties of the Mueller matrix of distributed targets

Attention is given to the statistical properties of the Mueller matrix of distributed targets, with emphasis on the copolarized phase angle phi sub c. The latter is shown to exhibit a pdf that is characterized completely by two parameters alpha and zeta, both of which are related to the elements of the Mueller matrix of the target. The parameter alpha governs the width of the pdf, and zeta governs the mean value of phi sub c. It is shown that the magnitudes S sub vv, S sub hh, and S sub hv, and the parameters alpha and zeta completely specify the Mueller matrix, and therefore contain all the statistical information available from the polarimetric backscatter response of the target. These results are verified with experimental observations that show that alpha and zeta are related to the physical and dielectric properties of soil and vegetation targets.