Retrieval of the optical properties of a layered medium based on an exact analytical solution of the time-dependent diffusion equation

Abstract

An exact solution of the time dependent diffusion equation for a layered diffusive medium has been obtained by using a method based on the decomposition of the fluence rate in a series of eigenfunctions. Making use of this exact analytical solution inversion procedures have been implemented to retrieve the optical properties of the medium. Time resolved measurements of diffuse reflectance have been generated with Monte Carlo simulations. Inversion procedures have been carried out both for a single time resolved measurement and for multi-distance time resolved measurements. The characteristics of both procedures have been investigated. For the case of a two-layered medium the fitting procedure carried out on a single measurement showed that it is impossible to retrieve correctly all the optical parameters of the layered medium. The inversion procedure correctly retrieves the absorption coefficient of the second layer and the reduced scattering coefficient of the first layer. A significant improvement is obtained by using multi-distance measurements. A particular attention has been devoted to determine the optical properties of muscle with the subcutaneous fat layer.