Complex degree of spatial coherence over a plane irradiated by quasi-monochromatic light sources

Abstract

We revisit the concept of optical spatial coherence by considering the case of the complex degree of spatial coherence induced over a plane by a quasi-monochromatic irradiating source. We apply the Van Cittert–Zernike theorem and exploit a Lloyd’s two-beam interferometer setup with its two small coherent light sources, as a way to illustrate the calculation of such complex spatial coherence, and because such setup offers a simple way to vary the separation d between its two irradiating sources, which then allows one to analytically obtain the functional dependence of the complex spatial coherence upon that separation d. We then consider the more general case in which the two small light sources of the experimental setup are spatially incoherent and again obtain the complex degree of coherence over a plane. This provides a simple, yet rigorous way, to present the subject of spatial coherences and field correlations to undergraduate physics students. An interesting link with astronomical interferometry, when images of, say, binary stellar objects are acquired, is established.