Characteristics of the light transmitted through diffusing media: angular distribution and photon flux at the external boundary

The characteristics of the light transmitted through diffusing media have been studied by using the diffusion approximation of the radiative transfer equation. Making use of the partial-current-boundary condition an analytical expression for the angular dependence of the specific intensity emerging from a diffusing medium has been obtained. The analytical expression gives results in excellent agreement with Monte Carlo simulations for the slab geometry. The limits of validity of the theory have been investigated. Making use of the diffusion equation and of the extrapolated boundary condition, an heuristic analytical expression for the time-resolved reflectance has also been obtained assuming the photon flux as being simply proportional to the fluence rate. The proposed expression is simpler with respect to other commonly used expressions and seems to give better results when used to retrieve the optical properties from time-resolved measurements.