Generalized Invariants of Multiple Scattered Polarized Radiation at Arbitrary Non-symmetrical Optical Levels of a Uniform Slab

Abstract

Polarimetric invariants of a uniform slab of a finite optical thickness, which were initially introduced at optical levels symmetrical to its middle in mirror directions, for downgoing and upgoing polarized radiation have been generalized for the case of virtual non-symmetrical optical levels τ₁ and τ₂. In the case of the vertical uniformity of an extended uniform slab, there deterministically exist invariant constructions different from and adequate to standard polarimetric invariants at symmetrical optical levels). These constructions express the properties of the local spatial angular symmetry of intensities of multiple scattered radiation internal fields in a more general analytical form of representation. For such new constructions of polarized radiation, which are called generalized polarimetric invariants, a basic boundary problem of the polarized radiation transfer theory has been formulated and linear Fredholm integral equations of the second kind and linear singular integral equations have been obtained. These generalized polarimetric invariants have proved to be effective for numerical modeling of intensities of multiple scattered polarized radiation in a uniform slab of an arbitrary optical thickness τ₀ ≤ ∞, with and without a reflecting bottom.