The concept of partial coherence in optics

Abstract It is shown that a ‘phase-coherence factor’ may be defined in a manner which leads, without recourse to explicit statistical analysis, to the theorems established by van Cittert (1934) and Zernike (1938) for analogous factors. An invalid approximation made in their calculations of the phase-coherence factor for a plane illuminated directly by a source is corrected. The new treatment is applied to the theory of Young’s experiment, the stellar interferometer, and illumination in the microscope. The phase-coherence factor defined here enables a general theory of the formation of optical images to be formulated. Further, it is shown that the diameter of the area of coherence on a plane illuminated by a source of angular radius α is given by d ═ 0⋅16λ/N sin α, where N is the refractive index of the intervening medium.