Light transmittance in turbid media slabs used to model biological tissues; scaling laws

Near infrared (NIR) light propagation through turbid media, such as some polymers or milky solutions, is dominated by multiple scattering. Common equations for light transmittance in slabs of these turbid media include summations of infinite order. These preclude to obtain simple expressions from which information such as scale laws, absorption and scattering coefficient, etc. can be retrieved.In the present work we show, starting from the transmittances for semi-infinite media, that the cumbersome expressions from the theory can be written in a much more compact way, thus allowing, for example, to relate some magnitudes which are, in principle, not easily compared. Moreover, it is shown that it is simple to find out the mentioned scale laws, to fit the shape of the distribution of time of flight of photons and to obtain the momenta, 〈tk〉〈tk〉 or, eventually 〈lk〉〈lk〉, being l=(c/n)tl=(c/n)t, which can be useful for recovering the optical properties of the medium. This is of great interest for the case of biological media because it allows to retrieve simultaneously both, the absorption and scattering coefficient.