Properties of the light emerging from a diffusive medium: angular dependence and flux at the external boundary

By using the diffusion approximation of the radiative transfer equation and the partial-current boundary condition, an analytical expression for the angular dependence of the specific intensity emerging from a diffusive medium has been obtained. The analytical expression for the angular distribution has been validated by comparisons with the results of Monte Carlo simulations. By using the diffusion equation and the extrapolated boundary condition, an heuristic analytical expression for the diffuse time-resolved reflectance has also been obtained by assuming that the photon flux is simply proportional to the fluence rate. For the case of the semi-infinite medium, comparisons with Monte Carlo results are presented and time-resolved reflectance data are fitted with the simple fluence rate formula. The results obtained show that the simple expression correctly describes the time-resolved reflectance giving an error in the retrieved optical parameters smaller than that of other commonly used expressions.