Diffuse reflectance from turbid media: an analytical model of photon migration

To calculate the diffuse reflectance from a semi-infinite slab of tissue, we introduce a probability distribution function, f(n)(g), that a photon will escape from the tissue after n scattering events. This approach permits the separation of the phase dependence of scattering, described by the anisotropy coefficient, g, from the absorption, micro(alpha), and scattering, micro(s), coefficients in the calculation of diffuse reflectance. We demonstrate that f(n)(g) and g are related to each other through a universal probability function. The analytical form of this probability function is explored and used to obtain the diffuse reflectance from tissue. The diffuse reflectance calculated with this method is in excellent agreement with Monte Carlo simulations over the parameter range typically found in human tissue, even for the values in which diffusion theory is a poor approximation.