This research has resolved a 30-year controversy in light diffusion.
The Backstory For over thirty years, researchers in optical transport, biomedical imaging, and tissue optics have debated whether the diffusion coefficient should depend on the absorption coefficient. While absorption-dependent expressions violate fundamental scaling properties of the Radiative Transfer Equation (RTE), they have remained widely used in practical continuous-wave (CW) and time-domain (TD) data fitting.
Key Findings This study resolves this long-standing controversy through rigorous asymptotic analysis:
- Time domain Proves analytically that an absorption-independent diffusion coefficient is both necessary and sufficient for exact long-time convergence to the Radiative Transfer Equation (RTE).
- Steady-state Demonstrates an inherent paradox: no scalar diffusion coefficient can make steady-state diffusion asymptotically equivalent to the RTE when absorption is present.
- Implications for data fitting Shows that the use of the canonical absorption-dependent diffusion coefficient introduces intrinsic model biases in optical-property retrievals. This study advises against the use of absorption-dependent diffusion coefficients and instead advocates time-domain transport theory as the appropriate reference framework.
These findings provide a fundamental clarification of the theoretical foundations of diffuse optics.
You can read the full open-access article here (Reports on Progress in Physics: “The paradox of steady-state light diffusion”, by André Liemert, Lorenzo Pattelli, Alwin Kienle, Federico Tommasi, and Fabrizio Martelli) and access our open-source RTE solution scripts on GitHub.
The Author Team
Institut für Lasertechnologien in der Medizin und Meßtechnik an der Universität Ulm, Germany
Istituto Nazionale di Ricerca Metrologica (INRiM), Torino, Italy
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Firenze, Italy
ILM Ulm | INRiM Turin | UNIFI Florence