AUTHOR=Koklu Halide 

TITLE=Calculation of radiative thickness using spherical harmonic methods for the radiative transfer equation

JOURNAL=Frontiers in Physics

VOLUME=Volume 13 - 2025

YEAR=2025

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1570080

DOI=10.3389/fphy.2025.1570080

ISSN=2296-424X

ABSTRACT=The radiative transfer equation (RTE) plays a fundamental role in modeling photon transport in various media such as biological tissues and atmospheric systems, where scattering phenomena are critical. In this study, the RTE is solved using two spherical harmonic-based numerical techniques: the Chebyshev and Legendre polynomial methods. Both the Henyey–Greenstein (HG) and Anlı–Güngör (AG) scattering phase functions are employed to analyze their effectiveness in radiative thickness computations. The Marshak boundary condition is applied, and the eigenvalue problems are solved using Mathematica software across various single scattering albedo values (ω) and anisotropy coefficients (g). The results indicate that the AG phase function produces outcomes highly consistent with the HG function, demonstrating numerical robustness and stability for both methods. These findings suggest that the AG phase function, commonly used in neutron transport, can be effectively applied in radiative transfer modeling as a computationally efficient and accurate alternative in biomedical and atmospheric applications.