OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 15 — Jul. 16, 2012
  • pp: 16471–16479

Spatial carrier phase-shifting algorithm based on principal component analysis method

Yongzhao Du, Guoying Feng, Hongru Li, J. Vargas, and Shouhuan Zhou  »View Author Affiliations

Optics Express, Vol. 20, Issue 15, pp. 16471-16479 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1109 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A non-iterative spatial phase-shifting algorithm based on principal component analysis (PCA) is proposed to directly extract the phase from only a single spatial carrier interferogram. Firstly, we compose a set of phase-shifted fringe patterns from the original spatial carrier interferogram shifting by one pixel their starting position. Secondly, two uncorrelated quadrature signals that correspond to the first and second principal components are extracted from the phase-shifted interferograms by the PCA algorithm. Then, the modulating phase is calculated from the arctangent function of the two quadrature signals. Meanwhile, the main factors that may influence the performance of the proposed method are analyzed and discussed, such as the level of random noise, the carrier-frequency values and the angle of carrier-frequency of fringe pattern. Numerical simulations and experiments are given to demonstrate the performance of the proposed method and the results show that the proposed method is fast, effectively and accurate. The proposed method can be used to on-line detection fields of dynamic or moving objects.

© 2012 OSA

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: May 11, 2012
Revised Manuscript: June 20, 2012
Manuscript Accepted: June 25, 2012
Published: July 5, 2012

Yongzhao Du, Guoying Feng, Hongru Li, J. Vargas, and Shouhuan Zhou, "Spatial carrier phase-shifting algorithm based on principal component analysis method," Opt. Express 20, 16471-16479 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Marcel Dekker, 1998).
  2. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am.72(1), 156–160 (1982). [CrossRef]
  3. W. W. Macy., “Two-dimensional fringe-pattern analysis,” Appl. Opt.22(23), 3898–3901 (1983). [CrossRef] [PubMed]
  4. K. A. Nugent, “Interferogram analysis using an accurate fully automatic algorithm,” Appl. Opt.24(18), 3101–3105 (1985). [CrossRef] [PubMed]
  5. D. J. Bone, H. A. Bachor, and R. J. Sandeman, “Fringe-pattern analysis using a 2-D Fourier transform,” Appl. Opt.25(10), 1653–1660 (1986). [CrossRef] [PubMed]
  6. C. Roddier and F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt.26(9), 1668–1673 (1987). [CrossRef] [PubMed]
  7. J. B. Liu and P. D. Ronney, “Modified Fourier transform method for interferogram fringe pattern analysis,” Appl. Opt.36(25), 6231–6241 (1997). [CrossRef] [PubMed]
  8. J. H. Massig and J. Heppner, “Fringe-pattern analysis with high accuracy by use of the Fourier-transform method: theory and experimental tests,” Appl. Opt.40(13), 2081–2088 (2001). [CrossRef] [PubMed]
  9. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt.22(24), 3977–3982 (1983). [CrossRef] [PubMed]
  10. M. Kujawinska and J. Wójciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE1508, 61–67 (1991). [CrossRef]
  11. P. H. Chan, P. J. Bryanston-Cross, and S. C. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng.23(5), 343–354 (1995). [CrossRef]
  12. M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt.42(9), 1853–1862 (1995). [CrossRef]
  13. J. A. Ferrari and E. M. Frins, “Multiple phase-shifted interferograms obtained from a single interferogarm with linear carrier,” Opt. Commun.271(1), 59–64 (2007). [CrossRef]
  14. S. K. Debnath and Y. Park, “Real-time quantitative phase imaging with a spatial phase-shifting algorithm,” Opt. Lett.36(23), 4677–4679 (2011). [CrossRef] [PubMed]
  15. H. Guo, Q. Yang, and M. Chen, “Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications,” Appl. Opt.46(7), 1057–1065 (2007). [CrossRef] [PubMed]
  16. A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase shifting applied to interferogram intensity contrast determination,” Appl. Opt.46(21), 4613–4624 (2007). [CrossRef] [PubMed]
  17. J. Xu, Q. Xu, and H. Peng, “Spatial carrier phase-shifting algorithm based on least-squares iteration,” Appl. Opt.47(29), 5446–5453 (2008). [PubMed]
  18. D. Li, P. Wang, X. Li, H. Yang, and H. Chen, “Algorithm for near-field reconstruction based on radial-shearing interferometry,” Opt. Lett.30(5), 492–494 (2005). [CrossRef] [PubMed]
  19. D. Liu, Y. Yang, L. Wang, and Y. Zhuo, “Real time diagnosis of transient pulse laser with high repetition by radial shearing interferometer,” Appl. Opt.46(34), 8305–8314 (2007). [CrossRef] [PubMed]
  20. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt.43(13), 2695–2702 (2004). [CrossRef] [PubMed]
  21. Q. Kemao, H. Wang, and W. Gao, “Windowed Fourier transform for fringe pattern analysis: theoretical analyses,” Appl. Opt.47(29), 5408–5419 (2008). [CrossRef] [PubMed]
  22. W. Gao, N. T. Huyen, H. S. Loi, and Q. Kemao, “Real-time 2D parallel windowed Fourier transform for fringe pattern analysis using Graphics Processing Unit,” Opt. Express17(25), 23147–23152 (2009). [CrossRef] [PubMed]
  23. L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett.24(13), 905–907 (1999). [CrossRef] [PubMed]
  24. J. Zhong and J. Weng, “Phase retrieval of optical fringe patterns from the ridge of a wavelet transform,” Opt. Lett.30(19), 2560–2562 (2005). [CrossRef] [PubMed]
  25. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2007).
  26. 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]
  27. J. Vargas, J. A. Quiroga, and T. Belenguer, “Analysis of the principal component algorithm in phase-shifting interferometry,” Opt. Lett.36(12), 2215–2217 (2011). [CrossRef] [PubMed]
  28. http://en.wikipedia.org/wiki/Principal_component_analysis
  29. J. Xu, L. Sun, Y. Li, and Y. Li, “Principal component analysis of multiple-beam Fizeau interferograms with random phase shifts,” Opt. Express19(15), 14464–14472 (2011). [CrossRef] [PubMed]
  30. J. Xu, W. Jin, L. Chai, and Q. Xu, “Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method,” Opt. Express19(21), 20483–20492 (2011). [CrossRef] [PubMed]
  31. http://en.wikipedia.org/wiki/Principal_component_analysis .
  32. http://en.wikipedia.org/wiki/Singular_value_decomposition .
  33. http://en.wikipedia.org/wiki/Karhunen%E2%80%93Lo%C3%A8ve_theorem .

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited