The paradox of steady-state light diffusion

Area of Science:

• * Physics
• * Optics
• * Applied Mathematics

Background:

• * The definition of the diffusion coefficient in light transport has been debated for over 30 years.
• * The canonical expression includes absorption dependence, violating the radiative transfer equation's (RTE) scaling properties.
• * Absorption-dependent formulations are common in practical data analysis despite evidence favoring absorption-independent definitions in the time domain.

Purpose of the Study:

• * To resolve the controversy surrounding the diffusion coefficient's definition in light transport.
• * To establish a rigorous consistency test based on diffusion converging to the RTE in the limit of infinite propagation.
• * To determine the correct formulation for both time-domain and continuous-wave regimes.

Main Methods:

• * An exact consistency test was developed, requiring diffusion to converge to the RTE in the limit of infinite propagation.
• * Analytical methods were used to prove convergence properties in both time-domain and continuous-wave regimes.
• * The intrinsic error introduced by incorrect parameterizations was quantified in idealized scenarios.

Main Results:

• * In the time domain, the absorption-independent diffusion coefficient is proven to be necessary and sufficient for exact long-time convergence to the RTE.
• * In the continuous-wave regime, no scalar diffusion coefficient can make diffusion asymptotically equivalent to the RTE when absorption is non-zero.
• * Mismatches in attenuation length and residue highlight the asymptotic failure of diffusion models with absorption.

Conclusions:

• * The time-domain, absorption-independent formulation is the only self-consistent reference for light transport diffusion.
• * Continuous-wave diffusion models with non-zero absorption are fundamentally inconsistent with the RTE.
• * A re-examination of diffusion's application in optical transport studies is warranted, particularly regarding parameterization choices.