Abstract

Elastic light scattering is described by the linear transformation S' = MS, where S and S' are the Stokes vectors before and after scattering and M = (mij) is the Mueller matrix that succinctly describes the light-sample interaction. In this study we examine the degree of polarization of the scattered light r' = f(r, θ, ε; mij) as a function of the degree of polarization r, and the azimuth and ellipticity angles θ and ε of the totally polarized component of the incident light. For a given Mueller matrix mij, the following properties of the function f(r, θ, ε) are considered: (1) Surfaces or loci of input polarizations (r, θ, ε) in the Stokes-Poincaré space that lead to r' = constant. These have been proved to be a family of ellipsoids. Sections of those ellipsoids with the θ = constant equi-azimuth planes are shown. Also, the intersection of those ellipsoids with the Poincaré sphere (r = 1) are represented by a family of contours in the θ–ε plane. (2) Over the surface of a sphere r = constant (0 < r < 1) the values of θ and ε that produce the extrema (maxima and minima) of r‘ are found. (3) Over the surface of a sphere r = constant, <r'>, the average value of r', is determined as a function of r. Several light scattering matrices from the published literature are tested as examples. A Mueller matrix that leads to r' > 1 for any input state is obviously in error and nonphysical.

© 1990 Optical Society of America