The van Cittert-Zernike Theorem

Abstract

The beam of light emanating from a quasi-monochromatic point source (or a sufficiently distant extended source) is said to be spatially coherent: the reason is that, at any two points on a given cross-section of the beam, the oscillating electromagnetic fields maintain their relative phase at all times. If an opaque screen with two pinholes is placed at such a cross-section, Young's interference fringes will form, and the observed fringe contrast will be 100% (at and around the center of the fringe pattern). This is the sense in which the fields at two points are said to be spatially coherent relative to each other. If the relative phase of the fields at the two points varies randomly with time, the pair of point sources will fail to produce Young's fringes and, therefore, the fields are considered to be incoherent. In practice there is a continuum of possibilities between the aforementioned extremes, and the resulting fringe contrast may fall anywhere between zero and 100%. The fields at the two points are then said to be partially coherent with respect to one another, and the properly defined fringe contrast in Young's experiment is used as the measure of their degree of coherence. Optical systems involving partially coherent illumination are explored in several other chapters of this book; see, for example, “Coherent and incoherent imaging” (Chapter 5), “Michelson's stellar interferometer” (Chapter 35), “Zernike's method of phase contrast” (Chapter 38), and “polarization microscopy” (Chapter 39).