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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 20 — Sep. 27, 2010
  • pp: 20620–20627

Direct phase extraction from interferograms with random phase shifts

Jiancheng Xu, Qiao Xu, Liqun Chai, Yong Li, and Hui Wang  »View Author Affiliations

Optics Express, Vol. 18, Issue 20, pp. 20620-20627 (2010)

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A new method that extracts phase directly from randomly phase-shifted interferograms is proposed. In this method, the background intensity and the modulation amplitude are determined by a temporal method and used as the system parameters and then the phase is extracted from one single interferogram by arc cosine function with range of (0, π). By partitioning the extracted phase distribution into watershed regions and determining the sign of phase in each region, the extracted phase is recovered to its principle phase with range of (–π, π). Numerical simulation and experiment are implemented to verify the effectiveness of this method. The method has applications in both static and dynamic phase measurement.

© 2010 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

Original Manuscript: July 28, 2010
Revised Manuscript: August 26, 2010
Manuscript Accepted: August 27, 2010
Published: September 14, 2010

Jiancheng Xu, Qiao Xu, Liqun Chai, Yong Li, and Hui Wang, "Direct phase extraction from interferograms with random phase shifts," Opt. Express 18, 20620-20627 (2010)

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  1. J. E. Greivenkamp and J. H. Bruning, “Phase shifting interferometers, ” in Optical Shop Testing, D. Malacara, ed., John Wiley and Sons, 1992, pp. 501–598.
  2. 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.
  3. C. J. Stolz, “The National Ignition Facility: The world’s largest optical system,” Proc. SPIE 6834, 683402 (2007). [CrossRef]
  4. R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361–364 (1984).
  5. M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44(32), 6861–6868 (2005). [CrossRef] [PubMed]
  6. G. Rodriguez-Zurita, C. Meneses-Fabian, N.-I. Toto-Arellano, J. F. Vázquez-Castillo, and C. Robledo-Sánchez, “One-shot phase-shifting phase-grating interferometry with modulation of polarization: case of four interferograms,” Opt. Express 16(11), 7806–7817 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-7806 . [CrossRef] [PubMed]
  7. K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84(3-4), 118–124 (1991). [CrossRef]
  8. 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]
  9. 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]
  10. 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]
  11. Q. Hao, Q. Zhu, and Y. Hu, “Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts,” Opt. Lett. 34(8), 1288–1290 (2009). [CrossRef] [PubMed]
  12. J. Park and S.-W. Kim, “Vibration-desensitized interferometer by continuous phase shifting with high-speed fringe capturing,” Opt. Lett. 35(1), 19–21 (2010). [CrossRef] [PubMed]
  13. Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-8-3110 . [CrossRef] [PubMed]
  14. S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-9-9684 . [CrossRef] [PubMed]
  15. L. Vincent and P. Soille, “Watersheds in digital spaces: an efficient algorithm based on immersion simulations,” IEEE Trans. Pattern Anal. Mach. Intell. 13(6), 583–598 (1991). [CrossRef]

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