Spatial coherence beams in the far field

Spatial coherence of optical fields can be considered as beam structured if the size of the coherence patch varies slowly through the propagation of the optical field. As a consequence, the correlation of the optical field will be concentrated in a finite region around the direction of propagation. For properly describing it in the Fraunhofer-Fresnel domain, the marginal cross-spectral density is introduced. The superposition of spatial coherence beams in this domain is also analyzed. It produces an interference field and a spatial coherence Moire.