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We show that the Kubelka-Munk equations for the description of the intensitytransfer of light in turbid media are equivalent to a one-dimensional diffusionequation, which is obtained by averaging the three-dimensional diffusionequation over the lateral directions. This enables us to identify uniquely theKubelka-Munk parameters and derive expressions for diffuse reflection andtransmission coefficients including the effect of internal reflections. Withoutinternal reflections we recover the Kubelka-Munk formulas for thesecoefficients. We show that the Kubelka-Munk equations are the properradiative-transfer equations for the one-dimensional diffusion problem andcomment on previous attempts to derive the Kubelka-Munk equations.

Diffusion of light in turbid media and Kubelka-Munk theory