First-order sources in first-order systems: second-order correlations

The laws of propagation of the second-order correlation of a generalized Gaussian Schell-model source in first-order systems are deduced from the canonical operator formalism. A far-reaching generalization of Kogelnik's q parameter is derived, valid in n dimensions, for misaligned, lossy, and anisotropic sources and systems. Even in one dimension these results extend previous findings. The degree of global coherence is generalized and shown to be an invariant in n dimensions for anisotropic lossless systems. A new invariant, the degree of ripple, is found for a special class of lossy first-order system, which includes the Gaussian aperture.