Nonlinear fitting procedure for accurate time-resolved measurements in diffusive media

Abstract

In this work we studied the accuracy of a non-linear fitting procedure, based on the Levenberg-Marquardt algorithm, for time-resolved measurements to retrieve the absorption and the reduced scattering coefficients of an absorbing diffusive medium. This procedure is suitable for retrieving optical properties in a wider range of situations (e.g. solid samples, reflectance geometry), with respect to the linear inversion procedures recently presented for both CW and time domain measurements. By means of both analytical and numerical (Monte Carlo) simulations, we quantified the influence of photon counts, temporal sampling, analytical model, background and instrument response function on the accuracy in the estimation of the optical properties. Furthermore, we validated our results with preliminary measurements on calibrated diffusive solutions. The main source of error that affects the accuracy of the absorption and reduced scattering coefficients retrieved by the non-linear procedure appears to be the analytical model adopted in the inversion procedure.