Fourier Data Processing in Optics

Zeev Zalevsky, David Mendlovic, Gal Shabtay, Uriel Levy

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

This entry provides an overview of the developments in the field of optical Fourier data processing. The discussion begins with definitions and the properties of the Fourier transform and also its relevancy to optics in “Fourier Optics,” and then, in “The Wigner Representation,” by defining the Wigner representation-its mathematical definition and its properties. The subject of optical correlation and pattern recognition is discussed starting with the conventional match filters and then the circular, the Mellin, and the logarithmic harmonics decomposition, and then, the section presents the joint transform correlator and the Wavelet transform. Various techniques for statistical processing are presented, and common performance measurements, such as signal-to-noise ratio, peak-to-correlation efficiency, and Horner efficiency are discussed. The fractional Fourier transform is mentioned, including its mathematical definitions, its relation to fractional correlation, and its applications in engineering science.

Original languageAmerican English
Title of host publicationEncyclopedia of Optical and Photonic Engineering Second Edition
PublisherCRC Press
Pages784-798
Number of pages15
ISBN (Electronic)9781351247177
ISBN (Print)9781439851012
DOIs
StatePublished - 1 Jan 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 by Taylor & Francis Group, LLC.

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