Diffusion of light in turbid media with internal reflections

Abstract

We relate the the Kubelka-Munk equations for the description of the intensity transfer of light in turbid media to a one-dimensional diffusion equation, which is obtained by averaging the three-dimensional diffusion equation over the lateral directions. This enables us to identify uniquely the Kubelka-Munk parameters and derive expressions for diffuse reflection and transmission coefficients including the effect of internal reflections. Without internal reflections we recover the Kubelka-Munk formulae for these coefficients. We show that the Kubelka-Munk equations are the proper radiative-transfer equations for the one-dimensional diffusion problem.