An international collaboration involving INRiM has clarified a theoretical controversy surrounding light diffusion that remained unresolved for more than thirty years.
Published in Reports on Progress in Physics, the study establishes how to define a key parameter used to describe light propagation in scattering materials and identifies a limitation of diffusion theory under continuous illumination.
The research was coordinated by Fabrizio Martelli, from the Department of Physics and Astronomy at the University of Florence, and involved Lorenzo Pattelli, Senior Researcher at INRiM, alongside researchers from the Institut für Lasertechnologien in der Medizin und Meßtechnik (ILM) at Ulm University.
When light travels through a scattering material, such as biological tissue, it is repeatedly redirected by the inhomogeneities it encounters. After many scattering events, this complex behaviour can be described using a diffusion law, similar to the one governing heat propagation.
This simplified description has been used for decades in the optics of disordered materials and in biomedical techniques. However, different, non-equivalent expressions have been used for the diffusion coefficient, the quantity that describes how rapidly light spreads through space. The debate centres on whether this coefficient should depend on light absorption by the material.
To address this question, the researchers examined the conditions under which diffusion theory reproduces the predictions of the more general radiative transfer theory as propagation times or distances become sufficiently large.
The analysis shows that, when light propagation is observed over time, the correct diffusion coefficient depends on the material’s scattering properties, but not on absorption. Absorption reduces the amount of light surviving during propagation without changing the random process through which it spreads in space.
The picture changes in the steady-state regime, when a source emits continuously and the light distribution no longer varies with time. In the presence of absorption, no single value of the diffusion coefficient can reproduce both the spatial decay rate of the light signal and its amplitude as predicted by radiative transfer theory, even at arbitrarily large distances. This reveals an intrinsic limitation of the diffusion description under these conditions.
The study also quantifies errors that can arise when incorrect definitions of the coefficient are used to estimate the optical properties of materials. This is relevant to biomedical applications, where light measurements are used to retrieve information about absorption and scattering in biological tissues.
These findings clarify the theoretical foundations of light diffusion and provide guidance for a more informed use of models when interpreting optical measurements.