The transmission of radiation through a spatially stochastic medium

The transport of radiation through a medium which is spatially random is studied using diffusion theory and the method of smoothing. Equations are established for the average flux and current in the medium, together with the variance of these quantities. The theory is applied to a plane slab one side of which is irradiated by a uniform source of radiation. The reflection and transmission factors are calculated and a measure of their fluctuations is obtained. For more generality, the boundary conditions allow internal reflection of the radiation using the Fresnel coefficient, which is particularly useful for applications to optical tomography where we believe this problem to have some relevance. The results are illustrated numerically using stochastic models for weak and strong clumping and applied to transmission through adult brain tissue. Stochastic effects are seen to be significant.