Approximate P3 solution for the semi-infinite medium: steady state and time domain

Area of Science:

• Physics
• Biomedical Optics
• Computational Modeling

Background:

• Accurate modeling of light transport is crucial in various scientific fields.
• The diffusion equation is a common model but has limitations in certain scenarios.
• Developing improved models for light propagation is an ongoing research area.

Purpose of the Study:

• To present the steady-state solution of the Green's function using the P3 equation in a semi-infinite medium.
• To establish two time-domain solutions based on the P3 equation: the optical parameter method and the double-diffusion coefficient method.
• To compare the accuracy of the P3 model with the diffusion equation and Monte Carlo simulations.

Main Methods:

• Derivation of the steady-state P3 equation solution.
• Development of two time-domain solutions: optical parameter method and double-diffusion coefficient method.
• Validation using Monte Carlo simulations for both steady-state and time-domain results.

Main Results:

• The P3 steady-state and time-domain solutions show good agreement with Monte Carlo simulations.
• The P3 equation is more accurate than the diffusion equation at short source-detector distances (within several free paths).
• The P3 model demonstrates higher accuracy than the diffusion model for large absorption coefficients.

Conclusions:

• The P3 equation provides a more accurate diffusion-based model for light transport in semi-infinite media.
• The optical parameter method is more accurate for time-domain calculations, while the double-diffusion coefficient method aligns better with the diffusion equation.
• The P3 model offers significant advantages over the diffusion equation in specific optical property regimes.