Radiative Transfer Equation
The RTE is a differential equation describing radiance . It can be derived via conservation of energy. Briefly, the RTE states that a beam of light loses energy through divergence and extinction (including both absorption and scattering away from the beam) and gains energy from light sources in the medium and scattering directed towards the beam. Coherence, polarization and non-linearity are neglected. Optical properties such as refractive index, absorption coefficient μa, scattering coefficient μs, and scattering anisotropy are taken as time-invariant but may vary spatially. Scattering is assumed to be elastic. The RTE (Boltzmann equation) is thus written as:
where
- is the speed of light in the tissue, as determined by the relative refractive index
- μtμa+μs is the extinction coefficient
- is the phase function, representing the probability of light with propagation direction being scattered into solid angle around . In most cases, the phase function depends only on the angle between the scattered and incident directions, i.e. . The scattering anisotropy can be expressed as
- describes the light source.
Read more about this topic: Radiative Transfer Equation And Diffusion Theory For Photon Transport In Biological Tissue
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