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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 8 — Mar. 10, 2012
  • pp: 1137–1148

Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems

Marc Brunel, Huanhuan Shen, Sebastien Coetmellec, and Denis Lebrun  »View Author Affiliations

Applied Optics, Vol. 51, Issue 8, pp. 1137-1148 (2012)

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We present a new model to predict diffraction patterns of femtosecond pulses through complex optical systems. The model is based on the extension of an ABCD matrix formalism combined with generalized Huygens–Fresnel transforms (already used in the CW regime) to the femtosecond regime. The model is tested to describe femtosecond digital in-line holography experiments realized in situ through a cylindrical Plexiglas pipe. The model allows us to establish analytical relations that link the holographic reconstruction process to the experimental parameters of the pipe and of the incident beam itself. Simulations and experimental results are in good concordance. Femtosecond digital in-line holography is shown to allow significant coherent noise reduction, and this model will be particularly efficient to describe a wide range of optical geometries. More generally, the model developed can be easily used in any experiment where the knowledge of the precise evolution of femtosecond transverse patterns is required.

© 2012 Optical Society of America

OCIS Codes
(010.3310) Atmospheric and oceanic optics : Laser beam transmission
(050.1970) Diffraction and gratings : Diffractive optics
(100.0118) Image processing : Imaging ultrafast phenomena
(090.1995) Holography : Digital holography

ToC Category:
Diffraction and Gratings

Original Manuscript: October 17, 2011
Revised Manuscript: January 13, 2012
Manuscript Accepted: January 13, 2012
Published: March 8, 2012

Marc Brunel, Huanhuan Shen, Sebastien Coetmellec, and Denis Lebrun, "Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems," Appl. Opt. 51, 1137-1148 (2012)

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