Continued fraction solution for the radiative transfer equation in three dimensions

Area of Science:

• Physics
• Optics
• Radiative Transfer Theory

Background:

• The radiative transfer equation (RTE) is fundamental for modeling light propagation.
• Diffusion approximation (DA) is a common simplification but has limitations.
• Accurate modeling is crucial for applications in diverse fields.

Purpose of the Study:

• To derive analytical solutions for the RTE in the Fourier-Laplace domain.
• To determine an accurate effective absorption parameter.
• To develop and validate a differential equation for radiative transport.

Main Methods:

• Analytical solution of the radiative transfer equation.
• Derivation in the Fourier-Laplace domain.
• Development of an analytical approximation procedure.
• Numerical simulations using the Henyey-Greenstein phase function.

Main Results:

• An analytical solution for the free propagator and arbitrary phase function was obtained.
• The effective absorption parameter derived differs significantly from the diffusion approximation.
• A differential equation accurately reproducing the transport process was established.
• Simulations confirmed the validity of the approximations.

Conclusions:

• The derived analytical solutions provide a more accurate description of radiative transfer.
• The proposed method offers a superior alternative to diffusion approximation for certain parameters.
• The validated differential equation can be used for precise modeling of light transport.