Photon diffusion equation

{{Duplication|dupe=Radiative transfer equation and diffusion theory for photon transport in biological tissue#The diffusion equation}}

{{Short description|Second order partial differential 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.

$$\backslash nabla(D(r)\backslash cdot\backslash nabla)\backslash Phi(\backslash vec\{r\},t)-v\backslash mu\_a(\backslash vec\{r\})\backslash Phi(\backslash vec\{r\},t)+vS(\backslash vec\{r\},t)=\backslash frac\{\backslash partial\backslash Phi(\backslash vec\{r\},t)\}\{\backslash partial\; t\}$$

where $\backslash Phi$ is photon fluence rate (W/cm²), $\backslash nabla$ is del operator, $\backslash mu\_a$ is absorption coefficient (cm⁻¹), $D$ is diffusion constant, $v$ is the speed of light in the medium (m/s), and $S$ 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.