Radiative transfer describes emission, absorption, and scattering of radiation through matter.
The Planck spectral radiance of a blackbody is
Specific intensity is power per projected area, solid angle, and frequency interval. In vacuum it is conserved along a ray.
Optical depth satisfies along a path and measures attenuation through in the absence of emission.
In plane-parallel optical-depth coordinates without scattering,
with source function .
In local thermodynamic equilibrium, matter populations are thermal at the local temperature and the source function is the Planck function, .
For an outward ray through a nonscattering atmosphere,
When the source function varies approximately linearly with optical depth, the emergent intensity obeys .
For plane-parallel intensity, the standard moments are
and the radiative flux is .

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Radiative transfer is the process by which energy, in the form of electromagnetic radiation, is transmitted through a medium. This process is governed by the interaction of radiation with matter, which can absorb, emit, and scatter the radiation. Radiative transfer is fundamental in various fields, including astrophysics, climate science, meteorology, remote sensing, and optical engineering.