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Photon diffusion is a situation wherephotons travel through a material without being absorbed, but rather undergoing repeatedscattering events which change the direction of their path. The path of any given photon is then effectively arandom walk. A largeensemble of such photons can be said to exhibitdiffusion in the material, and can be described with adiffusion equation.

Inastrophysics, photon diffusion occurs inside astellar atmosphere. To describe this phenomenon, one should develop the transfer equation in moments and use the Eddington approximation toradiative transfer (i.e. the diffusion approximation). In 3D the results are two equations for the photon energy flux:

${\displaystyle \overrightarrow{F}=-\frac{c}{12\pi \sigma }\overrightarrow{\mathrm{\nabla }}U,}$

${\displaystyle \overrightarrow{\mathrm{\nabla }}\cdot \overrightarrow{F}=0,}$

where${\displaystyle \sigma }$ is the opacity. By substituting the first equation into the second, one obtains the diffusion equation for the photon energy density:

${\displaystyle {\mathrm{\nabla }}^{2}U-\frac{1}{\sigma }\overrightarrow{\mathrm{\nabla }}U\cdot \overrightarrow{\mathrm{\nabla }}\sigma =0.}$

Inmedicine, the diffusion of photons can be used to create images of the body (mainly brain and breast) and has contributed much to the advance of certain fields of research, such as neuroscience. This technique is known asdiffuse optical imaging.

• Diffuse reflection
• Diffusion damping
• Global dimming
• Medical optical imaging
• Optical tomography
• Radiative transfer equation and diffusion theory for photon transport in biological tissue

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