Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes through complex ABCD optical systems.

The change of coherence and polarization of an electromagnetic beam modulated by a random anisotropic phase screen passing through any optical system is found within the framework of complex ABCD-matrix theory This means that the formalism can treat imaging and Fourier transform and free-space optical systems, as well as fractional Fourier transform systems, with finite-size limiting apertures of Gaussian transmission shape. Thus, the current paper shall be considered as a continuation, extension, and generalization of a previous work by Shirai and Wolf [J. Opt. Soc. Am. A21, 1907 (2004)]. It will be shown that the inclusion of apertures in the optical system strongly influences not only the propagation of spatial coherence but also the degree of polarization of a propagating field. Analytical expressions of coherence and polarization propagation will be given in terms of the matrix elements for any complex optical system.