Eigenvalue analysis of Mueller matrices for bead-blasted aluminum surfaces

This paper deals with the depolarization properties of rough surface back-scattering at visible and infra-red wavelengths. It is well known that rough surfaces depolarize incident light. In this paper we analyze the structure of surface depolarization using a coherency matrix approach and show that quantitative estimates of roughness may be obtained from a single Mueller matrix parameter, the scattering anisotropy A. Multi-spectral backscatter Mueller matrix data has been obtained for a set of controlled laboratory measurements on roughened Aluminum surfaces. The surfaces were manufactured using a bead-blasting process and the surface statistics have been carefully measured. We then applied a technique first developed for applications in radar scattering, which involves transformation of the Mueller matrix into a complex hermitian coherency matrix with subsequent eigenanalysis. These eigenvalues are then used to characterize the depolarizing properties of the surface. We show how important surface information is contained in the eigenvalue variation with angle of incidence and conclude as to the possibility for quantitative surface roughness measurements using this technique.