"Exact" solutions for the probability density functions of integrated Stokes parameters of partially polarized thermal light or polarization speckle.

Abstract

As a continuation of a previous investigation on the temporal integration of partially polarized thermal light and/or the spatial integration of polarization speckle, we calculate more accurate probability density functions for integrated Stokes parameters. With the aid of the unitary linear transformation and the Karhunen-Loève expansion of the stochastic electric field, the light of interest has been decomposed into an infinite number of statistically independent modes and the integrated Stokes parameters have been expressed as the sums of infinite numbers of random variables known as the polarization-related mode shape. A mathematical formalism of the exact solutions for the distributions of the integrated Stokes parameters has been derived. Through some approximations to the exact solutions, we also make a comparison of the "exact" and approximate solutions to understand the entire statistics of the integrated stochastic phenomena in optics.