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
Famous quotes containing the words transfer and/or equation:
“I have proceeded ... to prevent the lapse from ... the point of blending between wakefulness and sleep.... Not ... that I can render the point more than a point—but that I can startle myself ... into wakefulness—and thus transfer the point ... into the realm of Memory—convey its impressions,... to a situation where ... I can survey them with the eye of analysis.”
—Edgar Allan Poe (1809–1849)
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)