Astronomy and Astrophysics – Astrophysics
Scientific paper
Aug 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...275..318n&link_type=abstract
Astronomy and Astrophysics, Vol. 275, p. 318 (1993)
Astronomy and Astrophysics
Astrophysics
6
Radiative Transfer, Polarization
Scientific paper
Two methods to check the Stokes criterion for matrices linearly transforming the Stokes vectors are proposed. The criterion means that a physical vector of incident polarized radiation must be transformed into another physical vector, i.e., both vectors have to describe beams with degrees of polarization not exceeding unity. The criterion may be applied to matrices describing single or multiple scattering, reflection and transmission of radiation, and absorption in anisotropic media.
Both methods are based on the representation of the Stokes parameters as a vector in Minkowski space. One method reduces the criterion to finding the minimum of a quadratic form of three variables on the unit sphere. According to the other method it is necessary to find the eigenvalues of an auxiliary matrix and to verify that the eigenvalue with the time-like eigenvector is greater than or equal to the remaining three eigenvalues. Some important special cases of scattering matrices are discussed.
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