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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 4 — Feb. 1, 2013
  • pp: 838–848

Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams

Clément Remacha, Sébastien Coëtmellec, Marc Brunel, and Denis Lebrun  »View Author Affiliations

Applied Optics, Vol. 52, Issue 4, pp. 838-848 (2013)

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Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

© 2013 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(090.0090) Holography : Holography
(100.0100) Image processing : Image processing

ToC Category:

Original Manuscript: October 3, 2012
Revised Manuscript: December 14, 2012
Manuscript Accepted: December 16, 2012
Published: February 1, 2013

Clément Remacha, Sébastien Coëtmellec, Marc Brunel, and Denis Lebrun, "Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams," Appl. Opt. 52, 838-848 (2013)

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