Photon diffusion
= Photon diffusion
{title2=$D_\gamma$}
<Photon diffusion> approximates the spreading of radiation after many <scattering> events have largely randomized propagation directions. Individual <photons> travel along paths; their distribution can obey a <diffusion equation> on scales much larger than a <transport mean free path>. The longer arrival times arise from longer, repeatedly redirected paths.
For homogeneous, conservative isotropic <scattering>, the <photon diffusion coefficient for isotropic scattering> is $D=v\ell/3$, where $v$ is the transport speed and $\ell$ the scattering <mean free path>. Directional persistence replaces that scale by a <transport mean free path> in an appropriate transport model. Crossing a characteristic thickness $L$ then takes a time of order $L^2/D$, with geometry-dependent factors, which can greatly exceed the direct travel time $L/v$.
A <diffuse photon time-of-flight experiment> sends a short pulse into a scattering sample and measures the delayed transmitted or returning light. A pulsed source, a fast <photodetector> and <time-correlated single-photon counting> can build an arrival-time histogram from repeated pulses. The detector's timing response must be accounted for before attributing all measured broadening to the sample.<Time-Correlated Single Photon Counting (technical note v. 2.1) by Michael Wahl>[Scattering-medium response measurement and iterative reconvolution, p.3]{ref}
The 1989 study by <M. S. Patterson>, <Britton Chance> and <B. C. Wilson> used a slab <diffusion> model to relate picosecond-pulse reflectance and transmittance to <absorption> and <scattering>, comparing predictions with preliminary measurements and <Monte Carlo simulations>.<Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties by M. S. Patterson and others>[Abstract: model, optical interaction coefficients and experiment/simulation comparison]{ref} The earliest nearly unscattered light, nearby boundaries and strongly directional transport can require a fuller <radiative transfer> description.