Photon diffusion equation

Photon diffusion equation is a second order partial differential equation describing the time behavior of photon fluence rate distribution in a low-absorption high-scattering medium.

Its mathematical form is as follows.

$${\displaystyle \nabla (D(r)\cdot \nabla )\Phi ({\vec {r}},t)-v\mu _{a}({\vec {r}})\Phi ({\vec {r}},t)+vS({\vec {r}},t)={\frac {\partial \Phi ({\vec {r}},t)}{\partial t}}}$$

where ${\displaystyle \Phi }$ is photon fluence rate (W/cm²), ${\displaystyle \nabla }$ is del operator, ${\displaystyle \mu _{a}}$ is absorption coefficient (cm⁻¹), ${\displaystyle D}$ is diffusion constant, ${\displaystyle v}$ is the speed of light in the medium (m/s), and ${\displaystyle S}$ is an isotropic source term (W/cm³).

Its main difference with diffusion equation in physics is that photon diffusion equation has an absorption term in it.