Spatial Coherence in Periodic Systems*

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Abstract
The van Cittert-Zernike theorem states that quasimonochromatic light from a spatially incoherent source, propagating in free space, will increase in spatial coherence. Wolf has shown that quasimonochromatic light, which is initially only partially space coherent or even incoherent, may become coherent upon propagating through a periodic system of apertures. In this paper we employ the mode theory of optical resonators and transmission systems to obtain the results of the van Cittert-Zernike theorem and to study the rapidity with which coherence builds up in periodic systems of apertures and confocal lenses. A perturbation calculation for modes in circular geometries with small Fresnel numbers is included.