Abstract

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

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2008 (1)

2006 (2)

2005 (1)

2004 (1)

1999 (1)

B. Barrientos-García, A. J. Moore, C. Pérez-López, L. Wang, and T , Tschudi, "Spatial Phase-Stepped Interferometry using a Holographic Optical Element," Opt. Eng. 38, 2069-2074 (1999).
[CrossRef]

1986 (1)

1983 (1)

1982 (1)

R. M. A. Azzam, "Division-of-Amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of all Four Stokes Parameters of Light," Opt. Acta 29, 685-689 (1982).

1976 (1)

D. A. Thomas and J. C. Wyant, "High Efficiency Grating Lateral Shear Interferometer," Opt. Eng. 15, 477 (1976).

1973 (1)

1969 (1)

1964 (1)

Arrizon, V.

Arrizón, V.

Azzam, R. M. A.

R. M. A. Azzam, "Division-of-Amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of all Four Stokes Parameters of Light," Opt. Acta 29, 685-689 (1982).

Barrekette, E. S.

E. S. Barrekette, H. Freitag, "Diffraction by a Finite Sinusoidal Phase Grating," IBM Journal, 345-349 (1963).

Barrientos-García, B.

B. Barrientos-García, A. J. Moore, C. Pérez-López, L. Wang, and T , Tschudi, "Spatial Phase-Stepped Interferometry using a Holographic Optical Element," Opt. Eng. 38, 2069-2074 (1999).
[CrossRef]

Brock, N.

Burow, R.

Elssner, K.-E.

Freitag, H.

E. S. Barrekette, H. Freitag, "Diffraction by a Finite Sinusoidal Phase Grating," IBM Journal, 345-349 (1963).

Grzanna, J.

Hayes, J.

Kneubühl, F.

Kreis, T.

Meneses-Fabian, C.

Merkel, K.

Millerd, J.

Moore, A. J.

B. Barrientos-García, A. J. Moore, C. Pérez-López, L. Wang, and T , Tschudi, "Spatial Phase-Stepped Interferometry using a Holographic Optical Element," Opt. Eng. 38, 2069-2074 (1999).
[CrossRef]

North-Morris, M.

Novak, M.

Pérez-López, C.

B. Barrientos-García, A. J. Moore, C. Pérez-López, L. Wang, and T , Tschudi, "Spatial Phase-Stepped Interferometry using a Holographic Optical Element," Opt. Eng. 38, 2069-2074 (1999).
[CrossRef]

Robledo-Sánchez, C.

Rodriguez-Zurita, G.

Ronchi, V.

Sánchez-De-La-Llave, D.

Schwieder, J.

Spolaczyk, R.

Thomas, D. A.

D. A. Thomas and J. C. Wyant, "High Efficiency Grating Lateral Shear Interferometer," Opt. Eng. 15, 477 (1976).

Toto-Arellano, N.

Tschudi, T

B. Barrientos-García, A. J. Moore, C. Pérez-López, L. Wang, and T , Tschudi, "Spatial Phase-Stepped Interferometry using a Holographic Optical Element," Opt. Eng. 38, 2069-2074 (1999).
[CrossRef]

Vázquez-Castillo, J. F.

Wang, L.

B. Barrientos-García, A. J. Moore, C. Pérez-López, L. Wang, and T , Tschudi, "Spatial Phase-Stepped Interferometry using a Holographic Optical Element," Opt. Eng. 38, 2069-2074 (1999).
[CrossRef]

Wyant, J.

Wyant, J. C.

D. A. Thomas and J. C. Wyant, "High Efficiency Grating Lateral Shear Interferometer," Opt. Eng. 15, 477 (1976).

J. C. Wyant, "Double Frequency Grating Lateral Shear Interferometer," Appl. Opt. 12, 2057-2060 (1973).

Appl. Opt. (5)

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

R. M. A. Azzam, "Division-of-Amplitude Photopolarimeter (DOAP) for the Simultaneous Measurement of all Four Stokes Parameters of Light," Opt. Acta 29, 685-689 (1982).

Opt. Commun. (1)

C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizon, "Common-Path Phase-Shifting Interferometer with Binary Grating," Opt. Commun. 264, 13-17 (2006).
[CrossRef]

Opt. Eng. (2)

D. A. Thomas and J. C. Wyant, "High Efficiency Grating Lateral Shear Interferometer," Opt. Eng. 15, 477 (1976).

B. Barrientos-García, A. J. Moore, C. Pérez-López, L. Wang, and T , Tschudi, "Spatial Phase-Stepped Interferometry using a Holographic Optical Element," Opt. Eng. 38, 2069-2074 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (4)

A. Cornejo-Rodríguez, "Ronchi Test," in Optical Shop Testing, D. Malacara ed., (Wiley, New York, 1992)

E. S. Barrekette, H. Freitag, "Diffraction by a Finite Sinusoidal Phase Grating," IBM Journal, 345-349 (1963).

J. W. Goodman, Introduction to Fourier Optics, 2nd edition, (McGraw-Hill, 1988).

P. W. Ramijan, "Processing Stereo Photographs by Optical Subtraction," Ph. D. Thesis, University of Rochester (1978).

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