Characterization of the reduced scattering coefficient for optically thin samples: Theory and experiments

Diffusion theory is currently used to characterize highly scattering media from time and/or spatially resolved measurements. However, many of the limits of validity of the diffusion approximation in its standard form have been set through assumptions taken during its derivation, and it is generally believed that the diffusion equation holds only for length scales much larger than the transport mean free path (l_tr). We here present several modifications to the standard diffusion approximation to provide a simple expression for characterizing optically thin scattering slabs. The improvements concern mainly the correct modelling of the temporal and spatial distribution of the source term and the use of a frequency dependent diffusion coefficient and boundary conditions. This novel expression is put to the test against Monte Carlo simulations and experimental data taken from measurements with phantoms of known optical properties. The reduced scattering coefficient can be retrieved accurately for slab widths of the order of the mean free path.