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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 15 — Jul. 18, 2011
  • pp: 14464–14472

Principal component analysis of multiple-beam Fizeau interferograms with random phase shifts

Jiancheng Xu, Lili Sun, Yanli Li, and Yong Li  »View Author Affiliations


Optics Express, Vol. 19, Issue 15, pp. 14464-14472 (2011)
http://dx.doi.org/10.1364/OE.19.014464


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Abstract

A non-iterative method based on principal component analysis (PCA) is presented to directly extract the phase from multiple-beam Fizeau interferograms with random phase shifts. The PCA method is the approach that decomposes the multiple-beam Fizeau interferograms into many uncorrelated quadrature signals and then applies principal component analysis algorithm to extract the measured phase without any prior guess about the phase shifts. Some factors that affect the performance of the proposed method are analyzed and discussed. Numerical simulations and experiments demonstrate that the proposed method extracts phase fast and exhibits high precision. The method can be applied in high precision interferometry.

© 2011 OSA

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: May 23, 2011
Revised Manuscript: June 23, 2011
Manuscript Accepted: June 24, 2011
Published: July 13, 2011

Citation
Jiancheng Xu, Lili Sun, Yanli Li, and Yong Li, "Principal component analysis of multiple-beam Fizeau interferograms with random phase shifts," Opt. Express 19, 14464-14472 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14464


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References

  1. K. Creath, “Temporal phase measurement method, ” in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.
  2. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, New York, 1998).
  3. B. V. Dorrío and J. L. Fernández, “Phase-evaluation methods in whole-field optical measurement techniques,” Meas. Sci. Technol. 10(3), R33–R55 (1999). [CrossRef]
  4. Y. Surrel, “Fringe analysis,” in Photomechanics, P. K. Rastogi, ed., Vol. 77 of Topics in Applied Physics (Springer, 2000), pp. 55–102.
  5. P. Hariharan, “Digital phase-stepping interferometry: effects of multiply reflected beams,” Appl. Opt. 26(13), 2506–2507 (1987). [CrossRef] [PubMed]
  6. C. Ai and J. C. Wyant, “Effect of retroreflection on a Fizeau phase-shifting interferometer,” Appl. Opt. 32(19), 3470–3478 (1993). [CrossRef] [PubMed]
  7. G. Bonsch and H. Bohme, “Phase-determination of Fizeau interferences by phase-shifting interferometry,” Optik (Stuttg.) 82, 161–164 (1989).
  8. B. V. Dorrío, J. Blanco-García, C. López, A. F. Doval, R. Soto, J. L. Fernández, and M. Pérez-Amor, “Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile,” Appl. Opt. 35(1), 61–64 (1996). [CrossRef] [PubMed]
  9. P. B. Clapham and G. D. Dew, “Surface-coated reference flats for testing fully aluminized surfaces by means of the Fizeau interferometer,” J. Sci. Instrum. 44(11), 899–902 (1967). [CrossRef]
  10. P. Hariharan, “Interferometric measurements of small-scale irregularities: highly reflecting surfaces,” Opt. Eng. 37(10), 2751–2753 (1998). [CrossRef]
  11. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase shifting for nonsinusoidal waveforms with phase-shift errors,” J. Opt. Soc. Am. A 12(4), 761–768 (1995). [CrossRef]
  12. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35(1), 51–60 (1996). [CrossRef] [PubMed]
  13. J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22(21), 3421–3432 (1983). [CrossRef] [PubMed]
  14. P. Picart, R. Mercier, and M. Lamare, “Influence of multiple-beam interferences in a phase-shifting Fizeau interferometer and error-reduced algorithms,” Pure Appl. Opt. 5(2), 167–194 (1996). [CrossRef]
  15. A. Patil and P. Rastogi, “Estimation of multiple phases in holographic moiré in presence of harmonics and noise using minimum-norm algorithm,” Opt. Express 13(11), 4070–4084 (2005). [CrossRef] [PubMed]
  16. R. Langoju, A. Patil, and P. Rastogi, “Resolution-enhanced Fourier transform method for the estimation of multiple phases in interferometry,” Opt. Lett. 30(24), 3326–3328 (2005). [CrossRef] [PubMed]
  17. R. Langoju, A. Patil, and P. Rastogi, “Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise,” Opt. Lett. 31(8), 1058–1060 (2006). [CrossRef] [PubMed]
  18. Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29(14), 1671–1673 (2004). [CrossRef] [PubMed]
  19. H. Guo and M. Chen, “Least-squares algorithm for phase-stepping interferometry with an unknown relative step,” Appl. Opt. 44(23), 4854–4859 (2005). [CrossRef] [PubMed]
  20. X. F. Xu, L. Z. Cai, X. F. Meng, G. Y. Dong, and X. X. Shen, “Fast blind extraction of arbitrary unknown phase shifts by an iterative tangent approach in generalized phase-shifting interferometry,” Opt. Lett. 31(13), 1966–1968 (2006). [CrossRef] [PubMed]
  21. K. A. Goldberg and J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40(17), 2886–2894 (2001). [CrossRef] [PubMed]
  22. X. F. Xu, L. Z. Cai, Y. R. Wang, X. F. Meng, W. J. Sun, H. Zhang, X. C. Cheng, G. Y. Dong, and X. X. Shen, “Simple direct extraction of unknown phase shift and wavefront reconstruction in generalized phase-shifting interferometry: algorithm and experiments,” Opt. Lett. 33(8), 776–778 (2008). [CrossRef] [PubMed]
  23. P. Gao, B. Yao, N. Lindlein, J. Schwider, K. Mantel, I. Harder, and E. Geist, “Phase-shift extraction for generalized phase-shifting interferometry,” Opt. Lett. 34(22), 3553–3555 (2009). [CrossRef] [PubMed]
  24. T. E. Zander, V. Madyastha, A. Patil, P. Rastogi, and L. M. Reindl, “Phase-step estimation in interferometry via an unscented Kalman filter,” Opt. Lett. 34(9), 1396–1398 (2009). [CrossRef] [PubMed]
  25. J. Xu, Y. Li, H. Wang, L. Chai, and Q. Xu, “Phase-shift extraction for phase-shifting interferometry by histogram of phase difference,” Opt. Express 18(23), 24368–24378 (2010). [CrossRef] [PubMed]
  26. J. Xu, Q. Xu, L. Chai, and H. Peng, “Algorithm for multiple-beam Fizeau interferograms with arbitrary phase shifts,” Opt. Express 16(23), 18922–18932 (2008). [CrossRef] [PubMed]
  27. J. Vargas, J. A. Quiroga, and T. Belenguer, “Phase-shifting interferometry based on principal component analysis,” Opt. Lett. 36(8), 1326–1328 (2011). [CrossRef] [PubMed]
  28. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2007).
  29. B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009). [CrossRef] [PubMed]

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