Light is an electromagnetic wave satisfying Maxwell’s equations but treating it as such for propagation in turbid (highly scattering) media quickly reaches the limits of practical computation because of the spatial scales involved. It is more common, therefore, to use particle-based methods from transport theory to model the light distribution. The radiative transfer equation (which is Boltzmann’s transport equation applied to low energy, monochromatic, photons) is an integro-differential equation expressing the conservation of energy in the following form: Display Formula
(8)where is the light radiance, is called the scattering phase function and is the probability that a photon originally traveling in direction ends up traveling in direction if scattered, is a source of photons, and is the speed of light in the medium. The terms on the right-hand side of this equation account for the fact that the rate of change of the number of photons within a small region around the point and traveling in direction could be due to (1) sources ; (2) net outflow of photons due to the radiance gradient, ; (3) photons absorbed, ; (4) photons scattered into another direction, ; or (5) photons scattered into direction from another direction (given by the phase integral). Wave effects, polarization, radiative processes, ionization, inelastic scattering, and reactions are all neglected in this model.