Hybrid scattering method of finite multiplicity and diffusion approximation in optical visualization of biological tissues

Abstract

We consider the problem of distribution of the intensity of diffusely reflected radiation along the surface of semibounded random inhomogeneous medium under the condition that a narrow monodirected light beam impinges upon the surface. Here, the starting point is the transfer equation for the light intensity in diffusing medium. Using a reciprocity to the canonical form of the integral equation for the Green function, the light intensity can be rewritten as the sum of two summands, namely, the contributions made by scatterings of multiplicities from 0 to N (N = 0, 1, 2, …), and the radiation of the efficient generator, in construction of which the radiation with scattering multiplicity N + 1 takes part. Practical realization of the proposed method consists in combining the usage of the diffusive asymptotic for the Green function in the term with the efficient source of radiation and the Monte Carlo method for computing the aforementioned contributions of scattering multiplicities. It is shown that, starting from some critical value of the scattering multiplicity, we have the asymptotic coincidence of computational results obtained by the hybrid method and by the standard Monte Carlo method for solving the problem formulated in its entirety. Moreover, this critical value of the scattering multiplicity depending on the elongation of the indicatrix and the albedo of the elementary act of radiation scattering is estimated.