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      Fundamental structure of Fresnel diffraction: Longitudinal uniformity with respect to fractional Fourier order

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      Author
      Haldun M. Özaktaş
      Arik, S. O.
      Coşkun, T.
      Date
      2011-12-24
      Source Title
      Optics Letters
      Print ISSN
      0146-9592
      Publisher
      Optical Society of America
      Volume
      37
      Issue
      1
      Pages
      103 - 105
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.
      Keywords
      Fractional fourier
      Fractional Fourier transformations
      Fractional Fourier transforms
      Fresnel diffraction
      Fresnel integrals
      Fundamental structures
      Longitudinal direction
      Optical axis
      Propagation distances
      Space-bandwidth product
      Bandwidth
      Diffraction
      Fourier analysis
      Fourier transforms
      Permalink
      http://hdl.handle.net/11693/21642
      Published Version (Please cite this version)
      http://dx.doi.org/10.1364/OL.37.000103
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      • Department of Electrical and Electronics Engineering 3614
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