Light dosimetry in optical phantoms and in tissues: I. Multiple flux and transport theory

This is the first of two papers on the quantitative measurement of light energy fluence rates in optical phantoms and in tissues, in vitro and in vivo. The theory discussed in the present paper will be used in a forthcoming experimental paper to quantitatively check measurements of light energy fluence rates. A simple multiple flux model, which is equivalent to the diffusion approximation, is derived from the equation of transfer in a plane as well as in a spherical geometry. The equations obtained are similar to those of the Kubelka-Munk and related heuristic models. This permits conclusions regarding the limitations of these models and the values of their constants. The heuristic models are equivalent to diffusion theory for diffuse incident light, but not for collimated incident light. We also present a simple calculation of the radiance as a function of direction in the diffusion domain. This, together with the effective attenuation coefficient, permits indirect experimental determination of both the albedo and the anisotropy factor (g) of the scattering function. Similarity relations are discussed, as they result from the so called delta-Eddington approximation, leading to the conclusion that far from boundaries and sources light propagation characteristics do not change very much when g and omega s are varied, provided omega s (1-g) is kept constant (omega s = scattering coefficient). Therefore, only two optical constants are required to approximately describe light propagation in homogeneous and isotropic media in the diffusion approximation.