We introduce a new technique derived from the classical Stokes parameters for analysis of polarimetric radar astronomical data. This decomposition is based on m (the degree of polarization) and chi (the Poincaré ellipticity parameter). Analysis of the crater Byrgius A demonstrates how m-chi can more easily differentiate materials within ejecta deposits and their relative thicknesses. We use Goldschmidt crater to demonstrate how m-chi can differentiate coherent deposits of water ice. Goldschmidt crater floor is found to be consistent with single bounce Bragg scattering suggesting the absence of water ice and further corroborating adsorbed H to mineral grains or an H2O frost as plausible explanations for a H2O/OH detection by near-infrared instruments.