OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 24 — Dec. 2, 2013
  • pp: 29505–29515

A three-step least-squares iterative method for tilt phase-shift interferometry

Qian Liu, Yang Wang, Fang Ji, and Jianguo He  »View Author Affiliations

Optics Express, Vol. 21, Issue 24, pp. 29505-29515 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (2344 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An iterative method based on least-squares fittings is proposed to retrieve wavefront phase from tilt phase-shift interferograms. In each iteration cycle, proposed method calculates wavefront phase and tilt phase shifts in x- and y-directions in three individual least-squares fitting steps. In tilt phase shifts extracting steps, phase shifts of interferograms columns or rows are calculated with least-squares method, and then tilt phase shifts of interferograms in x- or y-direction are determined by linear regressions. At least three interferograms of three by three pixels are required with proposed method. The performance of proposed method is demonstrated by simulations and experiments. Tilt gradients and translational phase shifts could be extracted with high accuracy and large wavefront tilts could be well handled with proposed method. The method could be applied to temporal phase-shift interferometers with uncalibrated transducers or that in vibrating environment.

© 2013 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: September 30, 2013
Revised Manuscript: November 14, 2013
Manuscript Accepted: November 14, 2013
Published: November 21, 2013

Qian Liu, Yang Wang, Fang Ji, and Jianguo He, "A three-step least-squares iterative method for tilt phase-shift interferometry," Opt. Express 21, 29505-29515 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Dobroiu, D. Apostol, V. Nascov, and V. Damian, “Tilt-compensating algorithm for phase-shift interferometry,” Appl. Opt.41(13), 2435–2439 (2002). [CrossRef] [PubMed]
  2. O. Soloviev and G. Vdovin, “Phase extraction from three and more interferograms registered with different unknown wavefront tilts,” Opt. Express13(10), 3743–3753 (2005). [CrossRef] [PubMed]
  3. K. Patorski, A. Styk, L. Bruno, and P. Szwaykowski, “Tilt-shift error detection in phase-shifting interferometry,” Opt. Express14(12), 5232–5249 (2006). [CrossRef] [PubMed]
  4. J. Xu, Q. Xu, and L. Chai, “Tilt-shift determination and compensation in phase-shifting interferometry,” J. Opt. A, Pure Appl. Opt.10(7), 075011 (2008). [CrossRef]
  5. L. A. Selberg, “Interferometer accuracy and precision,” Proc. SPIE1400, 24–32 (1991). [CrossRef]
  6. S. Han and E. Novak, “Retrace error for the measurement of a long-radius optic,” Proc. SPIE3749, 597–598 (1999). [CrossRef]
  7. 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]
  8. J. Xu, Q. Xu, L. Chai, Y. Li, and H. Wang, “Direct phase extraction from interferograms with random phase shifts,” Opt. Express18(20), 20620–20627 (2010). [CrossRef] [PubMed]
  9. 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]
  10. G. S. Han and S. W. Kim, “Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting,” Appl. Opt.33(31), 7321–7325 (1994). [CrossRef] [PubMed]
  11. 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]
  12. M. Chen, H. Guo, and C. Wei, “Algorithm immune to tilt phase-shifting error for phase-shifting interferometers,” Appl. Opt.39(22), 3894–3898 (2000). [CrossRef] [PubMed]
  13. J. Xu, Q. Xu, and L. Chai, “Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts,” Appl. Opt.47(3), 480–485 (2008). [CrossRef] [PubMed]
  14. Y. C. Chen, P. C. Lin, C. M. Lee, and C. W. Liang, “Iterative phase-shifting algorithm immune to random phase shifts and tilts,” Appl. Opt.52(14), 3381–3386 (2013). [CrossRef] [PubMed]

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