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In spectroscopy and radiometry, **vector radiative transfer** (VRT) is a method of modelling the propagation of polarized electromagnetic radiation in low density media. In contrast to scalar radiative transfer (RT), which models only the first Stokes component, the intensity, VRT models all four components through vector methods.

For a single frequency, , the VRT equation for a scattering media can be written as follows:

where *s* is the path, is the propagation vector, * K* is the extinction matrix, is the absorption vector,

All the coefficient matrices, * K*, and

Extinction is caused both by simple absorption as well as from scattering out of the line-of-sight, , therefore we calculate the extinction matrix from the combination of the absorption vector and the scattering phase matrix:

where **I** is the identity matrix.

The four-component radiation vector, where *I*, *Q*, *U* and *V* are the first through fourth elements of the Stokes parameters, respectively, fully describes the polarization state of the electromagnetic radiation.
It is this vector-nature that considerably complicates the equation.
Absorption will be different for each of the four components, moreover, whenever the radiation is scattered, there can be a complex transfer between the different Stokes components—see polarization mixing—thus the scattering phase function has 4*4=16 components. It is, in fact, a rank-two tensor.

- Claudia Emde (2004).
*A polarized discrete ordinate scattering model for radiative transfer simulations in spherical atmospheres with thermal source*(PDF) (Thesis). University of Bremen.