Fourier optics through the looking glass of digital computers

Leonid P. Yaroslavsky

doi:10.1117/12.894955

20 September 2011 Fourier optics through the looking glass of digital computers

Leonid P. Yaroslavsky

Proceedings Volume 8122, Tribute to Joseph W. Goodman; 81220E (2011) https://doi.org/10.1117/12.894955
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

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.

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Leonid P. Yaroslavsky "Fourier optics through the looking glass of digital computers", Proc. SPIE 8122, Tribute to Joseph W. Goodman, 81220E (20 September 2011); https://doi.org/10.1117/12.894955

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KEYWORDS

Transform theory

Computing systems

Fourier transforms

Fourier optics

Reconstruction algorithms

Matrices

Glasses

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