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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 14 — May. 10, 2013
  • pp: 3381–3386

Iterative phase-shifting algorithm immune to random phase shifts and tilts

Yi-Chun Chen, Po-Chih Lin, Chung-Min Lee, and Chao-Wen Liang  »View Author Affiliations

Applied Optics, Vol. 52, Issue 14, pp. 3381-3386 (2013)

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An iterative phase-shifting algorithm based on the least-squares principle is developed to overcome the random piston and tilt wavefront errors generated from the phase shifter. The algorithm iteratively calculates the phase distribution and the phase-shifting map to minimize the sum of squared errors in the interferograms. The performance of the algorithm is evaluated via computer simulations and validated by the Fizeau interferometer measurements. The results show that the proposed algorithm has a fast convergence rate and satisfactory phase-estimation accuracy, improving the measurement precision of the phase-shifting interferometers with significant phase-shifter errors.

© 2013 Optical Society of America

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

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 21, 2012
Revised Manuscript: March 20, 2013
Manuscript Accepted: April 15, 2013
Published: May 9, 2013

Virtual Issues
Vol. 8, Iss. 6 Virtual Journal for Biomedical Optics

Yi-Chun Chen, Po-Chih Lin, Chung-Min Lee, and Chao-Wen Liang, "Iterative phase-shifting algorithm immune to random phase shifts and tilts," Appl. Opt. 52, 3381-3386 (2013)

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  1. H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley-Interscience, 2007).
  2. K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84, 118–124 (1991). [CrossRef]
  3. Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004). [CrossRef]
  4. G.-S. Han and S.-W. Kim, “Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting,” Appl. Opt. 33, 7321–7325 (1994). [CrossRef]
  5. L. Cai, Q. Liu, and X. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 28, 1808–1810 (2003). [CrossRef]
  6. L. Cai, Q. Liu, and X. Yang, “Generalized phase-shifting interferometry with arbitrary unknown phase steps for diffraction objects,” Opt. Lett. 29, 183–185 (2004). [CrossRef]
  7. X. Xu, L. Cai, X. Meng, G. Dong, and X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31, 1966–1968 (2006). [CrossRef]
  8. M. Rivera, R. Bizuet, A. Martinez, and J. A. Rayas, “Out of step phase shifting,” Opt. Express 14, 3204–3213 (2006). [CrossRef]
  9. B. Chen and C. Basaran, “Statistical phase-shifting step estimation algorithm based on the continuous wavelet transform for high-resolution interferometry metrology,” Appl. Opt. 50, 586–593 (2011). [CrossRef]
  10. M. Chen, H. Guo, and C. Wei, “Algorithm immune to tilt phase-shifting error for phase-shifting interferometers,” Appl. Opt. 39, 3894–3898 (2000). [CrossRef]
  11. A. Dobroiu, A. Apostol, V. Nascov, and V. Damian, “Tilt compensating algorithm for phase-shift interferometry,” Appl. Opt. 41, 2435–2439 (2002). [CrossRef]
  12. J. Xu, Q. Xu, and L. Chai, “Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts,” Appl. Opt. 47, 480–485 (2008). [CrossRef]
  13. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing (Cambridge University, 2007).
  14. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). [CrossRef]
  15. H. S. Chang, C. W. Liang, and C. C. Lee, “Using Hariharan algorithm to calibrate the piezoelectric transducers in Fizeau interferometer,” presented at Optics & Photonics Taiwan 2010, Tainan, Taiwan, 3–4 December2010.

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