Transmission, backscattering, and depolarization of waves in randomly distributed spherical particles

General formulations are given for the multiple scattering of a polarized wave incident upon a slab of randomly distributed spherical particles. The radiative transfer equation with Stokes vectors is decomposed into Fourier components, and they are shown for linearly and circularly polarized incident wave. For linear polarization, the copolarized and cross-polarized incoherent intensities show sinusoidal variations with the azimuthal angle. The degree of polarization is also calculated for various directions and optical thickness. The calculations are made for optical waves at 5, 10, and 15 micron in fog and compared with the first-order scattering calculations.