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Fourier’s Optics

  • Giovanni GiusfrediEmail author
Chapter
Part of the UNITEXT for Physics book series (UNITEXTPH)

Abstract

We have seen that, in Fresnel’s approximation the propagation of a wave between two parallel planes can be expressed in terms of a Fourier’s transform. Here, we examine an alternative technique, relying on the fact that the field present on the first plane can be represented by its spectrum in plane waves, for which, in a homogeneous space, one can determine their propagation in a simple way. By recombining these waves, one can therefore easily rebuild the field on the second plane with an inverse transform. This fact has two important applications, the first concerns the mathematical and numerical techniques that can be used to calculate the diffracted field, and the second is, in a certain sense, opposite to the first and concerns the processing of signals by optical means. In particular, we will briefly discuss some topics that make use of the Fourier’s transform, including sampling theorems and the numerical techniques for the calculation of diffraction, the formation of images and analysis of the quality of optical systems, the theory of coherence and some of its applications, spatial filtering and finally diffraction gratings.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.European Laboratory for Non-Linear Spectroscopy (LENS)Istituto Nazionale di Ottica—Consiglio Nazionale delle Ricerche (INO-CNR)Sesto FiorentinoItaly

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