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Applied Optics

Applied Optics


  • Editor: Jospeh N. Mait
  • Vol. 48, Iss. 3 — Jan. 20, 2009
  • pp: 579–583

Digital phase contrast with the fractional Fourier transform

Marc Brunel, Sebastien Coëtmellec, Denis Lebrun, and Kamel Aït Ameur  »View Author Affiliations

Applied Optics, Vol. 48, Issue 3, pp. 579-583 (2009)

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A new method of digital phase contrast based on fractional-order Fourier reconstruction is proposed. We show that the diffraction patterns produced by pure phase objects exhibit linear chirp functions that can be advantageously processed using the fractional Fourier transform. The optimal fractional orders lead to the longitudinal location of the phase object, while the analysis of the reconstructed pattern leads to its diameter and to the value of the phase shift. Simulations and experimental results are given. The configuration tested in this paper is a very general Gaussian illumination.

© 2009 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(090.1995) Holography : Digital holography
(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

ToC Category:
Fourier Optics and Signal Processing

Original Manuscript: September 29, 2008
Manuscript Accepted: November 28, 2008
Published: January 16, 2009

Marc Brunel, Sebastien Coëtmellec, Denis Lebrun, and Kamel Aït Ameur, "Digital phase contrast with the fractional Fourier transform," Appl. Opt. 48, 579-583 (2009)

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