Generalized rays in first-order optics: Transformation properties of Gaussian Schell-model fields

Propagation characteristics of Gaussian Schell-model fields through first-order optical systems and in free space are analyzed by the method of generalized rays. This allows the development of a simple geometrical description of these processes. The invariance of the degree of global coherence is established in full generality. Asymptotic behavior under free propagation and the emergence of a far-zone universal structure are analyzed. New invariants associated with incoherent superpositions of such fields are found.