Diagnosis of the phase function of random media from light reflectance

Light reflectance has been widely used to diagnose random media in both in situ and in vivo applications. The quantification of the phase function of the medium from reflectance measurements, however, remains elusive due to the lack of an explicit connection between the light reflectance profile and the phase function. Here we first present an analytical model for reflectance of scattered light at an arbitrary source-detector separation by forward-peaked scattering media such as biological tissue and cells. The model incorporates the improved small-angle scattering approximation (SAA) to radiative transfer for sub-diffusive light reflectance and expresses the dependence of the light reflectance on the phase function of the scattering medium in a closed form. A spreading length scale, l(Θ), is found to characterise subdiffusive light reflectance at the high spatial frequency (close separation) limit. After validation by Monte Carlo simulations, we then demonstrate the application of the model in accurate determination of the complete set of optical properties and the phase function of a turbid medium from the profile of subdiffusive and diffusive light reflectance.