A new path integral approximation to photon propagation in turbid media

Abstract

The path integral approach is applied to describe the propagation of photons in bounded homogeneous turbid media. Introducing a new controlled perturbative expansion centred on the diffusion limit, new analytic solutions for continuous wave reflectance and transmittance are determined, as relevant for non-invasive measurements of tissue optical properties based on continuous wave photon migration instruments. A comparative analysis with the diffusion approximation of radiative transfer theory is made to show that non-diffusive effects are enhanced in turbid regions with increasing absorption coefficients and decreasing reduced scattering coefficients as well as when the distance between interface boundaries increases. The relation between the transport equation (which is the starting point for the path integral approach) and multiple scattering theory is also discussed.