Statistical properties of the Mueller matrix of distributed targets

The scattering matrix measured in the backscattering direction by a polarimetric radar system consists of five quantities: |S_vv|, |S_hh|, and |S _hv|, which are the magnitudes of the linearly polarised scattering amplitudes, and φ_c and φ_x, which are the co-polarised and crosspolarised phase angles. The co-polarised phase angle φ_c is shown to exhibit a probability density function (PDF) that is characterised completely by two parameters α and ζ, both of which are related to the elements of the Mueller matrix of the target. The parameter α governs the width of the PDF and ζ governs the mean value of φ _c. It is further shown that the three magnitudes |S _vv|, |S_hh|, and |S_hv| and the two parameters α and ζ 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 α and ζ are related to the physical and dielectric properties of soil and vegetation targets