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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 23 — Nov. 10, 2008
  • pp: 19330–19341

Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry

Noel-Ivan Toto-Arellano, Gustavo Rodriguez-Zurita, Cruz Meneses-Fabian, and Jose F. Vazquez-Castillo  »View Author Affiliations

Optics Express, Vol. 16, Issue 23, pp. 19330-19341 (2008)

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Among several techniques, phase shifting interferometry can be implemented with a grating used as a beam divider to attain several interference patterns around each diffraction order. Because each pattern has to show a different phase-shift, a suitable shifting technique must be employed. Phase gratings are attractive to perform the former task due to their higher diffraction efficiencies. But as is very well known, the Fourier coefficients of only-phase gratings are integer order Bessel functions of the first kind. The values of these real-valued functions oscillate around zero, so they can adopt negative values, thereby introducing phase shifts of π at certain diffraction orders. Because this almost trivial fact seems to have been overlooked in the literature regarding its practical implications, in this communication such phase shifts are stressed in the description of interference patterns obtained with grating interferometers. These patterns are obtained by placing two windows in the object plane of a 4f system with a sinusoidal grating/grid in the Fourier plane. It is shown that the corresponding experimental observations of the fringe modulation, as well as the corresponding phase measurements, are all in agreement with the proposed description. A one-shot phase shifting interferometer is finally proposed taking into account these properties after proper incorporation of modulation of polarization.

© 2008 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(050.5080) Diffraction and gratings : Phase shift
(070.6110) Fourier optics and signal processing : Spatial filtering
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(260.5430) Physical optics : Polarization

ToC Category:
Diffraction and Gratings

Original Manuscript: August 4, 2008
Revised Manuscript: October 6, 2008
Manuscript Accepted: October 6, 2008
Published: November 7, 2008

Noel-Ivan Toto-Arellano, Gustavo Rodriguez-Zurita, Cruz Meneses-Fabian, and Jose F. Vazquez-Castillo, "Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry," Opt. Express 16, 19330-19341 (2008)

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