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      Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations

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      Author(s)
      Onural, L.
      Date
      2004
      Source Title
      Optical Engineering
      Print ISSN
      0091-3286
      Publisher
      SPIE - International Society for Optical Engineering
      Volume
      43
      Issue
      11
      Pages
      2557 - 2563
      Language
      English
      Type
      Article
      Item Usage Stats
      213
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      Abstract
      The quadratic phase function is fundamental in describing and computing wave-propagation-related phenomena under the Fresnel approximation; it is also frequently used in many signal processing algorithms. This function has interesting properties and Fourier transform relations. For example, the Fourier transform of the sampled chirp is also a sampled chirp for some sampling rates. These properties are essential in interpreting the aliasing and its effects as a consequence of sampling of the quadratic phase function, and lead to interesting and efficient algorithms to simulate Fresnel diffraction. For example, it is possible to construct discrete Fourier transform (DFT)-based algorithms to compute exact continuous Fresnel diffraction patterns of continuous, not necessarily, periodic masks at some specific distances. © 2004 Society of Photo-Optical Instrumentation Engineers.
      Keywords
      Chirp
      Computer-generated holography
      Digital holography
      Discretization
      Fresnel diffraction
      Quadratic phase function
      Sampling
      Algorithms
      Approximation theory
      Computer generated holography
      Computer simulation
      Discrete Fourier transforms
      Functions
      Light propagation
      Chirp
      Diffraction simulation
      Digital holography
      Fresnel diffraction
      Quadratic phase function
      Diffraction
      Permalink
      http://hdl.handle.net/11693/24196
      Published Version (Please cite this version)
      http://dx.doi.org/10.1117/1.1802232
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      • Department of Electrical and Electronics Engineering 4012
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