Simple analytical total diffuse reflectance over a reduced-scattering-pathlength scaled dimension of [10-5, 10-1] from a medium with HG scattering anisotropy.

Abstract

Model approximation is necessary for reflectance assessment of tissue at sub-diffusive to non-diffusive scale. For tissue probing over a sub-diffusive circular area centered on the point of incidence, we demonstrate simple analytical steady-state total diffuse reflectance from a semi-infinite medium with the Henyey-Greenstein (HG) scattering anisotropy (factor $g$g). Two physical constraints are abided to: (1) the total diffuse reflectance is the integration of the radial diffuse reflectance; (2) the radial and total diffuse reflectance at $g \gt {0}$g>0 analytically must resort to their respective forms corresponding to isotropic scattering as $g$g becomes zero. Steady-state radial diffuse reflectance near the point of incidence from a semi-infinite medium of $g \approx 0$g≈0 is developed based on the radiative transfer for isotropic scattering, then integrated to find the total diffuse reflectance for $g \approx 0$g≈0. The radial diffuse reflectance for $g \ge 0.5$g≥0.5 is semi-empirically formulated by comparing to Monte Carlo simulation results and abiding to the second constraint. Its integration leads to a total diffuse reflectance for $g \ge 0.5$g≥0.5 that is also bounded by the second constraint. Over a collection diameter of the reduced-scattering pathlength ($1/\mu _s^{ \prime}$1/μs') scaled size of [${{10}^{ - 5}}$10-5, ${{10}^{ - 1}}$10-1] for $g = [{0.5},{0.95}]$g=[0.5,0.95] and the absorption coefficient as strong as the reduced scattering coefficient, the simple analytical total diffuse reflectance is found to be accurate, with an average error of 16.1%.