Accuracy of the diffusion equation to describe photon migration through aninfinite medium: numerical and experimental investigation

The accuracy of results obtained from the diffusion equation (DE) has been investigated far the case of an isotropic point source in a homogeneous, we akly absorbing, infinite medium. The results from the DE have been compared both with numerical solutions of the radiative transfer equation obtained with Monte Carlo (MC) simulations and with cw experimental results. Compari sons showed that for the cw fluence rate, discrepancies are of the same ord er as statistical fluctuations on MC results (within 1%) when the distance r from the source is >2/mu(s)' (mu(s)' is the reduced scattering coefficien t). For these values of r, discrepancies for the time-resolved fluence rate are of the same order of statistical fluctuations (within 5%) when the tim e of flight is t > 4t(0) with to time of flight for unscattered photons. Fo r shorter times the DE overestimates the fluence; discrepancies are larger for larger Values of the asymmetry factor. As to the specific intensity, fo r small values of r the MC results are more forward peaked than expected fr om the DE, and the forward peak is stronger for photons arriving at shea ti mes. We assumed r > 2/mu(s)' and t > 4t(0) for the domain of validity of th e DE and we determined the requirements for which the simplifying assumptio ns necessary to obtain the DE, expressed by two inequalities, are fulfilled . Comparisons with cw experimental results showed a good agreement with MC re sults both at high and at small values of r mu(s)', while the comparison wi th the DE showed significant discrepancies for small values of r mu(s)'. Using MC results we also investigated the error made on the optical propert ies of the medium when they are retrieved using the solution of the DE. To obtain accuracy better than 1% from fitting procedures on time-resolved flu ence rate data it is necessary to disregard photons with time of flight <4t (0). Also from cw data it is possible to retrieve the optical properties wi th good accuracy by using the added absorber technique discrepancies are <1 %, both on mu(s)' and on mu(a). if the absorption coefficient is small (mu( a)/mu(s)' < 0.005).