Effects of linear non-image-forming devices on spectra and on coherence and polarization properties of stochastic electromagnetic beams: Part I: General theory

The classic theoretical techniques of polarization optics are the Jones calculus and the Stokes-Mueller calculus. Both deal with transmission of certain 'one-point quantities, which are associated with a light beam. Recently 'two-point quantities were introduced, which are the elements of a 2×2 cross-spectral density matrix that characterizes the correlations at two points in a beam or which are expressible in terms of them. Unlike the quantities with which the Jones and the Stokes calculus deal, these generalized quantities contain information not only about the polarization properties of the beam but also about its coherence properties. In this paper we present a generalization of the Jones calculus and of the Stokes-Mueller calculus for transformations of the new two-point quantities by linear non-image-forming devices. They may act on the beam in a deterministic or in a random manner.