Radiative transfer theory for inhomogeneous media with random extinction and scattering coefficients

Abstract

The small-angle scattering approximation of the scalar radiative transfer equation is examined in the case where the extinction and scattering coefficients have a component that is a deterministic function of position along the propagation path and a component that is a random function of position transverse to the propagation direction. It is found that the resulting stochastic radiative transfer equation can be reduced to a system of two stochastic integrodifferential equations for the average and fluctuating components of the radiant intensity. The system is solved to yield two transfer equations: one that describes the average radiant intensity and one that describes the spatial correlation function of the intensity fluctuations. The integrodifferential equation for the average intensity is then solved and applied to a simple propagation scenario; it is found that the fluctuations in the extinction and scattering coefficients reduce the effects due to the average values of these parameters, and also that the effect of these is greater near the point of observation than near the point of transmission of the radiation. An approximate solution is also derived for the equation giving the correlation function. The equations developed here should find application in problems involving short wavelength electromagnetic wave propagation through media possessing variable characteristics of turbulence and turbidity, such as in plasmas, the atmosphere, and the ocean.