Fourier optics through the looking glass of digital computers

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Abstract

Optical transforms are represented in computers by their discrete versions. In particular, Fourier optics is represented through Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT). Being discrete representation of the optical Fourier transform, these transforms feature a number of peculiarities that cast a new light on such fundamental properties of the Fourier Transform as sampling theorem and the uncertainty principle. In this paper, we formulate the Discrete Sampling Theorem and the discrete uncertainty principle, demonstrate that discrete signals can be both bandlimited in DFT or DCT domains and have strictly limited support in signal domain and present examples of such "bandlimited/ space-limited" signals that remain to be so for whatever large of their samples.

Original languageEnglish
Title of host publicationTribute to Joseph W. Goodman
DOIs
StatePublished - 2011
EventTribute to Joseph W. Goodman - San Diego, CA, United States
Duration: 21 Aug 201122 Aug 2011

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8122
ISSN (Print)0277-786X

Conference

ConferenceTribute to Joseph W. Goodman
Country/TerritoryUnited States
CitySan Diego, CA
Period21/08/1122/08/11

Keywords

  • Discrete Cosine transform
  • Discrete Fourier Transform
  • Fourier Optics
  • Sampling Theory
  • Uncertainty Principle

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