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      • Department of Electrical and Electronics Engineering
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      Fractional free space, fractional lenses, and fractional imaging systems

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      Author(s)
      Sümbül, U.
      Özaktaş, Haldun M.
      Date
      2003
      Source Title
      Optical Society of America. Journal A: Optics, Image Science, and Vision
      Print ISSN
      1084-7529
      Publisher
      OSA - The Optical Society
      Volume
      20
      Issue
      11
      Pages
      2033 - 2040
      Language
      English
      Type
      Article
      Item Usage Stats
      179
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      206
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      Abstract
      Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they are interpolations of their conventional counterparts. Optical realizations of these operators are possible with use of common physical components. These three operators can be interpreted as fractional lenses, fractional free space, and fractional imaging systems, respectively. Any optical system consisting of an arbitrary concatenation of sections of free space and thin lenses can be interpreted as a fractional imaging system with spherical reference surfaces. As a special case, a system departing from the classical single-lens imaging condition can be interpreted as a fractional imaging system. © 2003 Optical Society of America.
      Keywords
      Convolution
      Fourier transforms
      Interpolation
      Lenses
      Matrix algebra
      Optical systems
      Fractional imaging systems
      Imaging systems
      Permalink
      http://hdl.handle.net/11693/24548
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      • Department of Electrical and Electronics Engineering 4012
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