Anisotropic diffusive transport: connecting microscopic scattering and macroscopic transport properties

Area of Science:

• Physics
• Optical Engineering
• Materials Science

Background:

• Radiative transfer in anisotropic turbid media is challenging to model.
• Existing diffusion theories have limitations in accurately describing anisotropic scattering properties.

Purpose of the Study:

• To develop an accurate anisotropic diffusion theory for radiative transfer in turbid media.
• To establish a robust relationship between microscopic scattering properties and macroscopic diffusion tensors.
• To derive appropriate boundary conditions for anisotropic radiance.

Main Methods:

• Development of a theoretical framework linking differential scattering cross-sections to the diffusion tensor for independent scatterers.
• Implementation of a numerical method for calculating radiative transfer based on the developed theory.
• Derivation of a novel boundary condition suitable for anisotropic radiance modeling.

Main Results:

• The developed anisotropic diffusion theory accurately models radiative transfer in anisotropic turbid media.
• Solutions from the anisotropic diffusion equation show excellent agreement with Monte Carlo simulations.
• The study validates the theory for both steady-state and time-domain radiative transfer.

Conclusions:

• Anisotropic diffusion theory, with the presented developments, can accurately describe radiative transfer in anisotropic turbid media.
• This work corrects previous discrepancies between diffusion theory and simulations by addressing boundary conditions and diffusion tensor relations.
• The findings enable accurate, quantitative, diffusion-based modeling of anisotropic turbid materials.