Two-frequency radiative transfer equation for scalar waves in a random distribution of discrete scatterers with pair correlations

The Dyson equation and the two-frequency Bethe-Salpeter equation for vector-valued electromagnetic waves in the presence of a random distribution of absorptive discrete scatterers with pair correlations are derived on the basis of the Twersky multiple scattering formalism. These equations are subsequently “scalarized” in the case of a tenuous scatterer distribution and within the framework of the Rayleigh-Debye condition. A systematic transition is then made to a two-frequency radiative transfer equation via a phase-space approach. The main strength of the radiative transfer theory expounded here stems from the fact that it is applicable under conditions of large-angle scattering, statistical inhomogeneities and statistical anisotropies. It accounts, also, for a variable scatterer density, absorption, and frequency offsets.