OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 26 — Sep. 10, 2013
  • pp: 6572–6578

Phase shift estimation from variances of fringe pattern differences

Hongwei Guo and Zhihui Zhang  »View Author Affiliations


Applied Optics, Vol. 52, Issue 26, pp. 6572-6578 (2013)
http://dx.doi.org/10.1364/AO.52.006572


View Full Text Article

Enhanced HTML    Acrobat PDF (769 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

This paper presents a simple algorithm for estimating phase shifts from only three interferograms. In it, the fringe pattern differences are computed first in order to remove the background component, and then the variances and further the standard deviations (SDs) of fringe pattern differences are calculated. The phase shifts are estimated, by using the law of cosines, from a triangle whose lengths of sides are the SDs just calculated. This algorithm offers several advantages over others, e.g., being efficient, easy to implement, accurate, and less sensitive to noise. Numerical simulations and an experiment are performed to demonstrate its validity.

© 2013 Optical Society of America

OCIS Codes
(100.2650) Image processing : 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: June 26, 2013
Revised Manuscript: August 14, 2013
Manuscript Accepted: August 17, 2013
Published: September 9, 2013

Citation
Hongwei Guo and Zhihui Zhang, "Phase shift estimation from variances of fringe pattern differences," Appl. Opt. 52, 6572-6578 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-26-6572


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shifting interferometry,” Opt. Commun. 84, 118–124 (1991). [CrossRef]
  2. I.-B. Kong and S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–188 (1995). [CrossRef]
  3. 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]
  4. H. Guo, Z. Zhao, and M. Chen, “Efficient iterative algorithm for phase-shifting interferometry,” Opt. Lasers Eng. 45, 281–292 (2007). [CrossRef]
  5. Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004). [CrossRef]
  6. C. T. Farrell and M. A. Player, “Phase step measurement and variable step algorithms in phase-shifting interferometry,” Meas. Sci. Technol. 3, 953–958 (1992). [CrossRef]
  7. J. Vargas, J. A. Quiroga, and T. Belenguer, “Phase-shifting interferometry based on principal component analysis,” Opt. Lett. 36, 1326–1328 (2011). [CrossRef]
  8. L. Z. Cai, Q. Liu, and X. L. Yang, “Simultaneous digital correction of amplitude and phase errors of retrieved wave-front in phase-shifting interferometry with arbitrary phase shift errors,” Opt. Commun. 233, 21–26 (2004). [CrossRef]
  9. 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, 1966–1968 (2006). [CrossRef]
  10. P. Gao, B. Yao, N. Lindlein, K. Mantel, I. Harder, and E. Geist, “Phase-shift extraction for generalized phase-shifting interferometry,” Opt. Lett. 34, 3553–3555 (2009). [CrossRef]
  11. X. Chen, M. Gramaglia, and J. A. Yeazell, “Phase-shifting interferometry with uncalibrated phase shifts,” Appl. Opt. 39, 585–591 (2000). [CrossRef]
  12. Q. Hao, Q. Zhu, and Y. Hu, “Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts,” Opt. Lett. 34, 1288–1290 (2009). [CrossRef]
  13. J. Xu, Q. Xu, L. Chai, Y. Li, and H. Wang, “Direct phase extraction from interferograms with random phase shifts,” Opt. Express 18, 20620–20627 (2010). [CrossRef]
  14. K. A. Goldberg and J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001). [CrossRef]
  15. K. G. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236–253 (2001). [CrossRef]
  16. K. Qian, S. H. Soon, and A. Asundi, “Calibration of phase shift from two fringe patterns,” Meas. Sci. Technol. 15, 2142–2144 (2004). [CrossRef]
  17. H. Guo, Y. Yu, and M. Chen, “Blind phase shift estimation in phase-shifting interferometry,” J. Opt. Soc. Am. A 24, 25–33 (2007). [CrossRef]
  18. H. Guo, “Blind self-calibrating algorithm for phase-shifting interferometry by use of cross-bispectrum,” Opt. Express 19, 7807–7815 (2011). [CrossRef]
  19. J. Deng, H. Wang, D. Zhang, L. Zhong, J. Fan, and X. Lu, “Phase shift extraction algorithm based on Euclidean matrix norm,” Opt. Lett. 38, 1509–1561 (2013). [CrossRef]
  20. H. Guo, “A simple algorithm for fitting a Gaussian function,” IEEE Signal Process. Mag. 28(5), 134–137 (2011). [CrossRef]
  21. M. Tur, K. C. Chin, and J. W. Goodman, “When is speckle noise multiplicative?,” Appl. Opt. 21, 1157–1159 (1982). [CrossRef]
  22. E. Hack and J. Burke, “Measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82, 061101 (2011). [CrossRef]
  23. K. A. Stetson and W. R. Brohinsky, “Electro-optic holography and its application to hologram interferometry,” Appl. Opt. 24, 3631–3637 (1985). [CrossRef]
  24. H. Guo and M. Chen, “Fourier analysis of the sampling characteristics of the phase-shifting algorithm,” Proc. SPIE 5180, 437–444 (2003). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited