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Proceedings Paper

Fourier optics through the looking glass of digital computers
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Paper 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.

Paper Details

Date Published: 20 September 2011
PDF: 9 pages
Proc. SPIE 8122, Tribute to Joseph W. Goodman, 81220E (20 September 2011); doi: 10.1117/12.894955
Show Author Affiliations
Leonid P. Yaroslavsky, Tel Aviv Univ. (Israel)

Published in SPIE Proceedings Vol. 8122:
Tribute to Joseph W. Goodman
H. John Caulfield; Henri H. Arsenault, Editor(s)

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