Chandrasekhar, S. (1947) On the radiative equilibrium of a stellar atmosphere. XV. Astrophysical Journal, 105 . pp. 424434. ISSN 0004637X

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Official URL: http://adsabs.harvard.edu//abs/1947ApJ...105..424C
Related URL: http://dx.doi.org/10.1086/144917
Abstract
In this paper the general equations of transfer for an atmosphere scattering radiation in accordance with Rayleigh's law and allowing for a partial elliptic polarization of the radiation field are formulated. It is shown that, under these conditions, we must consider, in addition to the intensities I_{l} and I_{r} in two directions at right angles to each other in the plane of the electric and the magnetic vectors, the two further quantities U=(I_{l}I_{r})tan 2χ and V=(I_{l}I_{r}) tan 2β9 sec 2χ, where χ denotes the inclination of the plane of polarization to the direction to which l refers and π/2≤β≤π/2 is an angle, the tangent of which is equal to the ratio of axes of the ellipse characterizing the state of polarization. (The sign of β depends on whether the polarization is right handed or left handed.) It is found that the equations of transfer for I_{l}, I_{r}, and U are of exactly the same forms as in cases in which only partial planepolarization is contemplated and that the equation for V is independent of others. On Rayleigh's law, V is scattered in accordance with a phase function,3/2cosθ. The solution of the equation for V appropriate for the problem of diffuse reflection by a semiinfinite atmosphere is also given.
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