In this paper we consider the relationship between surface roughness in scattering polarimetry and the eigenvalues of the 4 X 4 scattering coherency matrix. These eigenvalues have already been employed in Mueller matrix filtering and particle scattering studies, but here we show that they have a physical significance in terms of scattering amplitudes and that their ratios represent generalized measures of polarimetric coherence. One such ratio, the entropy H, has been introduced in earlier publications, but here we show that a new measure, the anisotropy A, can also be used for surface roughness studies. This parameter is closely linked to the circular polarization coherence but generalizes the concept to account for any residual correlations that may be present in the surface scattering. Increasing surface roughness causes depolarization and hence increasing scattering entropy. However, the distribution of depolarized energy amongst the smaller eigenvalues contains important information about the structure of the surface. Here we suggest how this information may be interpreted and demonstrate the theory by applying it to experimental data collected for laboratory manufactured rough surfaces with known statistical properties.
Shane R. Cloude, Shane R. Cloude,
"Eigenvalue parameters for surface roughness studies", Proc. SPIE 3754, Polarization: Measurement, Analysis, and Remote Sensing II, (25 October 1999); doi: 10.1117/12.366317; https://doi.org/10.1117/12.366317