Advanced Monte Carlo methods for deriving optical properties of scattering media using cubic spline-parameterized phase functions

In this study, we conducted optical goniometric measurements of turbid media and utilized a Monte Carlo model to characterize their optical properties. Our methodology employs an inverse fitting approach that combines Monte Carlo simulations with a Levenberg-Marquardt optimization routine. To enhance the accuracy and robustness of the inverse fitting process, we incorporated second-order derivatives into the algorithm. We also investigated the critical role of the single-scattering phase function and assessed the limitations associated with the commonly used Henyey-Greenstein (HG) approximation. To address these limitations, we developed a fitting procedure that determines the single-scattering phase function via cubic splines. This allows for the simultaneous extraction of both the cubic spline phase function and the scattering and absorption coefficients from goniometric measurements. This approach provides a refined and novel model for analyzing turbid media.