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. ∇ ( D ( r ) ⋅ ∇ ) Φ ( r → , t ) − v μ a ( r → ) Φ ( r → , t ) + v S ( r → , t ) = ∂ Φ ( r → , t ) ∂ t where Φ is photon fluence rate (W/cm²), μ 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.