Characteristic properties of the conical Mueller matrix

We present results of mathematical relations existing between the Mueller matrix obtained for an in-plane of incidence scattering geometry (plane Mueller matrix, PMM) and the Mueller matrix obtained for an out-the-plane of incidence scattering geometry (conical Mueller matrix, CMM), for light scattered from a rough surface. We obtain a similarity relation between the CMM and the PMM for one- (1-D) and for two-dimensional (2-D) surfaces. This similarity relation implies that the PMM and the CMM have the same determinant, trace and eigenvalues for 1-D and 2-D surfaces, respectively. We can say that measurements made in the conical geometry are “Similarity Equivalent” to those in the in-plane geometry for both kind of surfaces, respectively.