Penetration depth of light re-emitted by a diffusive medium: theoretical and experimental investigation

The depth at which photons penetrate into a diffusive medium before being re-emitted has been investigated with reference to a semi-infinite homogeneous medium illuminated by a pencil beam. By using the diffusion equation analytical expressions have been obtained for the probability that photons penetrate at a certain depth before being detected, and for the mean path length they travel inside each layer of the medium. Expressions have been obtained both for the cw and the time domain, and simple approximate scaling relationships describing the dependence on the scattering properties of the medium have been found. For time-resolved measurements both the probability and the mean path length are expected to be independent of the distance from the light beam at which the detector is placed and of the absorption coefficient of the medium. The penetration depth increases as the time of flight increases. In contrast, for cw measurements both the probability and the mean path length strongly depend on the distance and absorption. The penetration depth increases as the distance increases or absorption decreases. The accuracy of the analytical expressions has been demonstrated by comparisons with cw experimental results. The penetration depth and the mean path length provide useful information, for instance, for measurements of tissue oxygenation and for functional imaging of muscle and brain. In particular, the depth reached by received photons provides overall information on the volume of the tissue actually investigated, while the mean path is strictly related to the sensitivity to local variations of absorption.