The methods for the convenient treatment of partial polarization are discussed. In particular, it is shown (1) how to introduce the “Stokes parameters” and the “Poincaré sphere” representation in a direct phenomenological way; (2) how an idealized experimental procedure may illustrate the physical analysis of partial polarization; (3) how the Stokes parameter representation fits naturally into the quantum theory of radiation; (4) how the Stokes method applies to Compton scattering.
U. FANO, "Remarks on the Classical and Quantum-Mechanical Treatment of Partial Polarization," J. Opt. Soc. Am. 39, 859-863 (1949)