Van Cittert–Zernike Theorem, Spatial Coherence, and Scattering

Abstract

This chapter is concerned with the van Cittert–Zernike theorem, including an examination of the assumptions involved in its derivation, the requirement of spatial incoherence of a source, and the interferometer response to a coherent source. Some optical terminology is used, for example, mutual coherence, which includes complex visibility. There is also a brief discussion of some aspects of scattering by irregularities in the propagation medium. Much of the development of the theory of coherence and similar concepts of electromagnetic radiation is to be found in the literature of optics. The terminology is sometimes different from that which has evolved in radio interferometry, but many of the physical situations are similar or identical. However, in spite of the similarity, the literature shows that in the early development of radio astronomy, the optical experience was hardly ever mentioned, an exception being the reference by Bracewell (1958) to Zernike (1938) for the concept of the complex degree of coherence. The van Cittert–Zernike theorem contains a simple formalism that includes the basic principles of correlation in electromagnetic fields.