Statistical testing of the form of the Mueller matrix of terrain at millimeter wavelengths

A number of target symmetries, such as azimuthal symmetry for natural terrain, have a consequence on the form of the Mueller matrix. If these symmetries are found to be plausible, it can greatly assist in the modeling of the polarimetric response from the class of targets that exhibit such symmetry. By applying the test to large numbers of measured covariance matrices organized by terrain class (i.e. tree canopies, dry snow near grazing, etc.), the plausibility of various forms of the covariance matrix is explored. An example of symmetry which gives rise to a form of the covariance matrix is the hypothesis that co-polarized backscatter can be dominated by single scattering, while cross-polarized backscatter is multiple scattering. This results in the coherence between co- and cross-polarized radar backscatter being zero. This hypothesis is put to the complex R² test for W-band backscattering from snow