Quantifying phase function influence in subdiffusively backscattered light

Abstract

Light backscattering at short source-detector separations is considerably influenced by the scattering phase function of a turbid medium. We seek to more precisely relate a medium's subdiffusive backscattering to the angular scattering characteristics of its microstructure. First, we demonstrate the inability of the scattering asymmetry g1 = < cos θ > to predict phase function influence on backscattering and reveal ambiguities related to the established phase function parameter γ. Through the use of high-order similarity relations, we introduce a new parameter that more accurately relates a scattering phase function to its subdiffusive backscattering intensity. Using extensive analytical forward calculations based on solutions to the radiative transfer equation in the spatial domain and spatial frequency domain, we demonstrate the superiority of our empirically derived quantifier σ over the established parameter γ.

Lookup table-based sampling of the phase function for Monte Carlo simulations of light propagation in turbid media

“…Due to the characteristic shape of the CDF for forward peaked phase functions, the uniformly distributed random numbers evaluate to unevenly spaced cos θ values, where the density of points increases towards the smaller scattering angles. However, according to Bodenschatz et al [7], at short SDS, photons that scatter at larger angles significantly contribute to the reflectance signal, thus making the corresponding part of the phase function important. Consequently, the FLT sampling method is observed to perform better for shorter SDS.…”

“…3 and 4, the RRE significantly depends on the numerical sampling method and underlying lookup table size. This suggests that special care should be taken when implementing the phase functions in the MC simulations, and moreover, include the information in research articles as this was not a common practice to date [4][5][6][7]10,11].…”

“…From our experience, we have noticed that the number of the tabulated CDF values as well as the sampling method applied to the phase function can significantly influence the accuracy of the MC simulated reflectance. Most of the studies that have used numerical phase function sampling as described above, lack the information on the details of the employed sampling method [4][5][6][7]10,11]. Consequently, it is very difficult to properly repeat the experiments conducted in those studies.…”

“…The diameter of optical fibers was set to 200 μm and SDS values of 220, 440, 660, 880, and 1100 μm were considered. The selected range of the SDS should encompass the transition of the reflectance from the sub-diffusive to the diffusion regime [7]. The photon packets were launched uniformly over the source fiber opening and uniformly over the solid angle defined by the numerical aperture of the fiber (NA = 0.22).…”

“…In terms of Monte Carlo (MC) simulations, which are often used for modeling the light propagation [1,2], scattering is described by the scattering coefficient and scattering angle typically drawn from the inverse cumulative distribution of the phase function. In recent studies, phase functions have become increasingly important in modeling of the reflectance obtained by spatially-resolved reflectance spectroscopy [3][4][5] or spatial-frequency domain reflectance spectroscopy [6][7][8], in particular for small source-detector separations or high spatial frequencies. The Henyey-Greenstein (HG) phase function [9] is most commonly used in the biomedical community since it offers an analytical inverse of the cumulative distribution function (CDF), which is convenient for sampling the scattering angles by a random number drawn from a uniform distribution.…”