Researchers have shown that the widely used diffusion model for light in strongly scattering, absorbing materials cannot be an exact description of light transport over long distances when illumination is continuous. The finding, reported by André Liemert and colleagues in the journal Reports on Progress in Physics, addresses a disagreement among physicists that has persisted for more than 30 years.
Diffuse optics studies how light moves through materials such as biological tissue, powders and disordered solids. In these materials light is scattered so many times that tracking each photon is impractical. After many scattering events, the more exact but more complicated radiative transfer equation is usually replaced by the simpler diffusion equation, which is expected to grow more accurate as light travels farther. The diffusion equation depends on a coefficient describing how quickly light spreads, known as the diffusion coefficient.
The problem lies in how that coefficient is defined. The version most commonly used includes an explicit dependence on the absorption of the material. That dependence conflicts with a basic scaling property of the radiative transfer equation, which the diffusion model is meant to approximate. Researchers have been aware of this inconsistency for decades, and several alternative definitions have been proposed, but no consensus has emerged on which is correct.
Settling the question has proved difficult because the competing expressions can differ by very small amounts, which makes them hard to distinguish through experiments or numerical simulations. Liemert and colleagues therefore approached the problem analytically, using solutions of the radiative transfer equation to examine both pulsed and continuous illumination.
For a short pulse of light, the team found that the long-time behaviour converges exactly to the diffusion description only if the diffusion coefficient is independent of absorption, as the radiative transfer equation requires. For continuous illumination the picture is different, and the researchers describe a paradox. Even at arbitrarily large distances, where diffusion would be expected to become increasingly accurate, no single diffusion coefficient can reproduce both the rate at which the light signal decays and its amplitude.
The result means that steady-state diffusion remains a useful approximation, but it can never be the exact long-distance limit of light transport in an absorbing material. The implications extend to fields that rely on these models. Future studies in biomedical optics or materials physics that use diffusion models to extract absorption and scattering properties will need to account for the findings, according to the research.
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