Approximate solutions of the vector radiative transfer equation for linearly polarized light in discrete random media

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Abstract
A method is presented for obtaining the specific intensity of linearly polarized optical waves propagated in discrete random media. This method is an extension of our previous analysis of circular polarization, applied to linear polarization. Using a combination of small-angle and diffusion solutions in vector form, solutions for the specific intensity are obtained for large particles over a wide range of optical depths. Linearly polarized waves for normal incidence require an analysis of azimuth-dependent terms, and those components contributing to the major scattering process are retained. Copolarized and cross-polarized incoherent intensities are obtained within the framework of a 4 × 4 matrix. A comparison with numerical solutions obtained by the method of extended spherical harmonics is made to demonstrate the validity of the present theory. The ratio of small-angle scattering intensity to total scattering intensity in the forward direction is also represented as a function of optical depths.