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.

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

${\displaystyle \Phi }$

${\displaystyle \nabla }$

${\displaystyle \mu _{a}}$

${\displaystyle D}$

${\displaystyle v}$

${\displaystyle S}$

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