Classes of source pairs in interference and diffraction

摘要

A description of interference and diffraction based on the concept of class of source pairs is presented. It is the set of pairs of sources whose contributions to the interference or diffraction patterns exhibit the same phase difference. Each class of source pairs provides a specific cosine-like modulation on the intensity distribution of the pattern, in such a way that the set provides an expansion of this intensity distribution in an orthogonal basis. From this point of view, the classes of source pairs are the effective elementary sources for those intensity distributions. The characteristics of the classes of source pairs can be accurately determined by Fourier transforming the intensity distribution of the patterns. The central value of this Fourier spectrum is related to the number of individual sources. The remain values will provide two crucial descriptors of the classes: their positions on the Fourier transform domain will be corresponding to the separation vector of the class of pairs for wavefront splitting interferometers (WSIs) and diffraction, or the time delay for amplitude splitting interferometers (ASIs), and their heights will be proportional to their populations. The concept was also applied to Fraunhofer and Fresnel diffraction, but now the classes of source pairs constitute a continuous set instead of the discrete sets in interference. However, the set of classes can also be determined by Fourier analysis.