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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 17, Iss. 11 — Nov. 1, 2000
  • pp: 2061–2066

Phase-shift calibration algorithm for phase-shifting interferometry

Xin Chen, Maureen Gramaglia, and John A. Yeazell  »View Author Affiliations


JOSA A, Vol. 17, Issue 11, pp. 2061-2066 (2000)
http://dx.doi.org/10.1364/JOSAA.17.002061


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Abstract

We propose a novel phase-shift calibration algorithm. With this technique we determine the unknown phase shift between two interferograms by examining the sums and differences of the intensities on each interferogram at the same spatial location, i.e., I1(x, y)±I2(x, y). These intensities are normalized so that they become sinusoidal in form. A uniformly illuminated region of the interferograms that contains at least a 2π variation in phase is examined. The extrema of these sums and differences are found in this region and are used to find the unknown phase shift. An error analysis of the algorithm is provided. In addition, an error-correction algorithm is implemented. The method is tested by numerical simulation and implemented experimentally. The numerical tests, including digitization error, indicate that the phase step has a root-mean-square (RMS) phase error of less than 10-6 deg. Even in the presence of added intensity noise (5% amplitude) the RMS error does not exceed 1 deg. The accuracy of the technique is not sensitive to nonlinearity in the interferogram.

© 2000 Optical Society of America

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry

History
Original Manuscript: October 22, 1999
Revised Manuscript: March 31, 2000
Manuscript Accepted: March 31, 2000
Published: November 1, 2000

Citation
Xin Chen, Maureen Gramaglia, and John A. Yeazell, "Phase-shift calibration algorithm for phase-shifting interferometry," J. Opt. Soc. Am. A 17, 2061-2066 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-11-2061


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References

  1. P. K. Rastogi, Holographic Interferometry (Springer-Verlag, Berlin, 1994).
  2. D. Malacara, M. Servin, Zacarias Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker Inc., New York, 1998).
  3. D. W. Robinson, G. T. Reid, eds., Interferogram Analysis (Institute of Physics, Bristol, UK, 1993).
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  7. N. A. Ochoa, J. M. Huntley, “Convenient method for calibrating nonlinear phase modulators for use in phase-shifting interferometry,” Opt. Eng. (Bellingham) 37, 2501–2505 (1998). [CrossRef]
  8. Hedser van Brug, “Phase-step calibration for phase-stepped interferometry,” Appl. Opt. 38, 3549–3555 (1999). [CrossRef]

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