OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 29 — Oct. 10, 2008
  • pp: 5446–5453

Spatial carrier phase-shifting algorithm based on least-squares iteration

Jiancheng Xu, Qiao Xu, and Hansheng Peng  »View Author Affiliations

Applied Optics, Vol. 47, Issue 29, pp. 5446-5453 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (7811 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An advanced spatial carrier phase-shifting (SCPS) algorithm based on least-squares iteration is proposed to extract the phase distribution from a single spatial carrier interferogram. The proposed algorithm divides the spatial carrier interferogram into four phase-shifted interferograms. By compensating for the effects of the variations of phase shifts between pixels and the variations of background and contrast, the proposed algorithm determines the local phase shifts and phase distribution simultaneously and accurately. Numerical simulations show that the accuracy of the proposed algorithm is obviously improved by compensating for the effects of background and contrast variations. The peak to valley of the residual phase error remains less than 0.002 rad when the magnitude of spatial carrier is in the range from π / 5 to π / 2 and the direction of the spatial carrier is in the range from 25 ° to 65 ° . Numerical simulations and experiments demonstrate that the proposed algorithm exhibits higher precision than the existing SCPS algorithms. The proposed algorithm is sensitive to random noise, but the error can be reduced by N times if N measurements are taken and averaged.

© 2008 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(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: May 9, 2008
Revised Manuscript: September 4, 2008
Manuscript Accepted: September 8, 2008
Published: October 8, 2008

Jiancheng Xu, Qiao Xu, and Hansheng Peng, "Spatial carrier phase-shifting algorithm based on least-squares iteration," Appl. Opt. 47, 5446-5453 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. Robinson and G. Reid, eds. (IOP Publishing, 1993), pp. 95-140.
  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, 156-160 (1982). [CrossRef]
  3. M. Kujawinska and J. Wójciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61-67(1991). [CrossRef]
  4. P. H. Chan and P. J. Bryanston-Cross, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23, 343-354 (1995). [CrossRef]
  5. M. Pirga and M. Kujawinska, “Two directional spatial-carrier phase-shifting method for analysis of crossed and closed fringe patterns,” Opt. Eng. 34, 2459-2466 (1995). [CrossRef]
  6. M. Servin and F. J. Cuevas, “A novel technique for spatial phase-shifting interferometry,” J. Mod. Opt. 42, 1853-1862(1995). [CrossRef]
  7. H. Guo, Q. Yang, and M. Chen, “Local frequency estimation for the fringe pattern with a spatial carrier: principle and applications,” Appl. Opt. 46, 1057-1065 (2007). [CrossRef] [PubMed]
  8. A. Styk and K. Patorski, “Analysis of systematic errors in spatial carrier phase-shifting applied to interferogram intensity contrast determination,” Appl. Opt. 46, 4613-4624 (2007). [CrossRef] [PubMed]
  9. Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671-1673 (2004). [CrossRef] [PubMed]
  10. D. Malacara and S. L. DeVore, “Optical interferogram evaluation and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed. (Wiley Interscience, 1992).
  11. M. Pirga and M. Kujawinska, “Errors in two-dimensional spatial-carrier phase-shifting method for closed fringe pattern analysis,” Proc. SPIE 2860, 72-83 (1996). [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.


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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited