Array Theorem

doi:10.1117/3.2303.ch3

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Chapter 3:
Array Theorem

Book: The New Physical Optics Notebook: Tutorials in Fourier Optics

Editor(s): George O. Reynolds; John B. DeVelis; George B. Parrent Jr.; Brian J. Thompson

Published: 1989
https://doi.org/10.1117/3.2303.ch3

Abstract

In this chapter, we continue the study of Fraunhofer or far-field diffraction. We have seen in the first chapter that such diffraction is characterized by the fact that the diffracted amplitude distribution is proportional to the Fourier transform of the amplitude distribution across the diffracting aperture. In Chapter 2, some examples of diffraction calculations were given for simple geometries. In this chapter, we examine the effect of combining apertures of similar geometry. In this class of problems, the diffraction integral assumes an interesting and characteristic form and gives rise to a subclass of diffraction effects that is important enough to receive a special nomenclature and study, namely, interference by division of wavefront. A large class of interference effects can be treated with a single theorem, the array theorem. In the next section, this theorem is derived and discussed in terms of a simple example. Then this class of interference effects is illustrated by means of photographic examples.

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CHAPTER 3
9 PAGES

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