Modeling subdiffusive light scattering by incorporating the tissue phase function and detector numerical aperture

To detect small-scale changes in tissue with optical techniques, small sampling volumes and, therefore, short source-detector separations are required. In this case, reflectance measurements are not adequately described by the diffusion approximation. Previous studies related subdiffusive reflectance to γ or σ which parameterize the phase function. Recently, it was demonstrated that σ predicts subdiffusive reflectance better than γ, and that σ becomes less predictive for lower numerical apertures (NAs). We derive and evaluate the parameter RpNA, which incorporates the NA of the detector and the integral of the phase function over the NA in the backward and forward directions. Monte Carlo simulations are performed for overlapping source/detector geometries for a range of phase functions, reduced scattering coefficients, NAs, and source/detector diameters. RpNA improves prediction of the measured reflectance compared to γ and σ. It is, therefore, expected that RpNA will improve derivation of optical properties from subdiffusive measurements.