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Applied Optics

Applied Optics


  • Vol. 39, Iss. 4 — Feb. 1, 2000
  • pp: 585–591

Phase-shifting interferometry with uncalibrated phase shifts

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

Applied Optics, Vol. 39, Issue 4, pp. 585-591 (2000)

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A computationally efficient algorithm for phase-shifting interferometry with imprecise phase shifts is developed. It permits the use of an uncalibrated phase shifter and is also insensitive to spatial intensity variations. The measurement has both spatial and temporal aspects. Comparisons are made between pixels within the same interferogram, and these comparisons are extended across a set of interferograms by a maximum–minimum procedure. A test experiment is performed and confirms the theoretical results. An additional advantage of the algorithm is that an error measure can be developed. This error measure is used to implement an error correction scheme.

© 2000 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: July 19, 1999
Revised Manuscript: November 2, 1999
Published: February 1, 2000

Xin Chen, Maureen Gramaglia, and John A. Yeazell, "Phase-shifting interferometry with uncalibrated phase shifts," Appl. Opt. 39, 585-591 (2000)

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  15. A more comprehensive description of the use of correlations to find the phase difference between two pixels i and j is given by cos(δi - δj) = 〈IiIj〉 - 〈Ii〉〈Ij〉/[〈Ii2〉 - 〈Ii〉2 〈Ii2〉 - 〈Ii〉2]1/2, where Ii and Ij are the intensities at the pixels i and j, respectively. The angle brackets denote an ensemble average over the randomly varying phase ϕ.

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