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Applied Optics

Applied Optics


  • Vol. 43, Iss. 21 — Jul. 20, 2004
  • pp: 4199–4207

Class of 4 + 1-phase algorithms with error compensation

Hongbo Bi, Ying Zhang, Keck Voon Ling, and Changyun Wen  »View Author Affiliations

Applied Optics, Vol. 43, Issue 21, pp. 4199-4207 (2004)

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It is well known that phase-shifting interferometry suffers from inaccuracy in the presence of phase-shifting errors. We have proved the limitation of using a 4-phase algorithm to reduce the phase-measurement error in the presence of the phase-shifting error. A class of 4 + 1-phase error compensating algorithms is formulated. It is shown that the proposed algorithms can effectively minimize the effects of the constant phase-shifting error and possess a superior performance than existing error-compensating algorithms. The effectiveness of the proposed algorithm is demonstrated by computer simulations and experiments.

© 2004 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.2830) Instrumentation, measurement, and metrology : Height measurements
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: September 5, 2003
Revised Manuscript: March 22, 2004
Published: July 20, 2004

Hongbo Bi, Ying Zhang, Keck Voon Ling, and Changyun Wen, "Class of 4 + 1-phase algorithms with error compensation," Appl. Opt. 43, 4199-4207 (2004)

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  1. P. Hariharan, D. Malacara, Interference, Interferometry, and Interferometric Metrology (SPIE Optical Engineering Press, Bellingham, Wa., 1995).
  2. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983). [CrossRef] [PubMed]
  3. K. G. Larkin, B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740–1748 (1992). [CrossRef]
  4. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 13, 2504–2505 (1987). [CrossRef]
  5. J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, N. Streibl, “New compensating four-phase algorithm for phase-shift interferometry,” Opt. Eng. 32, 1883–1885 (1993). [CrossRef]
  6. D. C. Ghiglia, Mark D. Pritt, Two-dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).
  7. H. Zhao, M. J. Lalor, D. R. Burton, “Error-compensating algorithms in phase-shifting interferometry: a comparison by error analysis,” Opt. Lasers Eng. 31, 381–400 (1999). [CrossRef]

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