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Self-imaging and Discrete Paraxial Optics

  • Chapter
Linear Canonical Transforms

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 198))

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Abstract

Coherent self-imaging, also known as the Talbot effect, describes Fresnel diffraction of strictly periodic wavefronts. Based on a phase-space interpretation of optical signals and systems we review a number of self-imaging phenomena, including the fractional Talbot effect. Recognizing Fresnel diffraction as merely one particular instance of the wider class of linear canonical transforms allows us to discuss various generalizations of self-imaging. Recognizing the discrete Fresnel transformation as a special case of the fractional Talbot effect leads to a definition of discrete linear canonical transformations, which preserve important properties of the continuous transformation for a subset of paraxial signals and systems. This subset can be used as a framework for practical implementations of discrete LCTs discrete linear canonical transform.

To the memory of Adolf Lohmann (1926–2013)

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Authors and Affiliations

  1. Thayer School of Engineering, Dartmouth College, 14 Engineering Drive, Hanover, NH, 03755, USA

    Markus Testorf

  2. Department of Computer Science, National University of Ireland, Maynooth, Co. Kildare, Ireland

    Bryan Hennelly

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  1. Markus Testorf
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Editors and Affiliations

  1. School of Electrical and Electronic Engineering, University College Dublin, Dublin, Ireland

    John J. Healy

  2. The Scientific and Technological Research Council of Turkey, Ankara, Ankara, Turkey

    M. Alper Kutay

  3. Department of Electrical Engineering, Bilkent University, Ankara, Ankara, Turkey

    Haldun M. Ozaktas

  4. School of Electrical and Electronic Engineering, University College Dublin, Dublin, Dublin, Ireland

    John T. Sheridan

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Testorf, M., Hennelly, B. (2016). Self-imaging and Discrete Paraxial Optics. In: Healy, J., Alper Kutay, M., Ozaktas, H., Sheridan, J. (eds) Linear Canonical Transforms. Springer Series in Optical Sciences, vol 198. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3028-9_9

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