Modeling scattering in turbid media using the Gegenbauer phase function

Abstract

The choice of scattering phase function is critically important in the modeling of photon propagation in turbid media, particularly when the scattering path within the material is on the order of several mean free path lengths. For tissue applications, the single parameter Henyey-Greenstein (HG) phase function is known to underestimate the contribution of backscattering, while phase functions based on Mie theory can be more complex than necessary due to the multitude of parameter inputs. In this work, the two term Gegenbauer phase function is highlighted as an effective compromise between HG and Mie, as demonstrated when fitting the various phase function to measured data from phantom materials. Further comparison against the Modified Henyey-Greenstein (MHG) phase function, another two term function, demonstrates that the Gegenbauer function provides better control of the higher order phase function moments, and hence allows for a wider range of values for the similarity parameter, γ. Wavelength dependence of the Gegenbauer parameters is also investigated using a range of theoretical particle distributions. Finally, extraction of the scattering properties of solid turbid samples from angularly resolved transmission measurements is performed using an iterative Monte Carlo optimization technique. Fitting results using Gegenbauer, HG, MHG, and Mie phase functions are compared.