OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 21 — Jul. 20, 2014
  • pp: 4628–4636

Model-based phase shifting interferometry

Leslie L. Deck  »View Author Affiliations

Applied Optics, Vol. 53, Issue 21, pp. 4628-4636 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1143 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A general method of surface profiling with phase-shifting interferometry techniques uses iterative linear regression to fit the sequence of interferograms to a physical model of the cavity. The physical model incorporates all important cavity influences, including environmentally induced rigid-body motion, phase shifter miscalibrations, multiple interference, geometry-induced spatial phase-shift variations, and their cross-couplings. By incorporating an initial estimate of the surface profile and iteratively solving for space- and time-dependent variables separately, convergence is robust and rapid. The technique has no restriction on surface shape or departure.

© 2014 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(120.7280) Instrumentation, measurement, and metrology : Vibration analysis

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: April 24, 2014
Manuscript Accepted: May 27, 2014
Published: July 11, 2014

Leslie L. Deck, "Model-based phase shifting interferometry," Appl. Opt. 53, 4628-4636 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. Schreiber and J. Bruning, “Optical shop testing,” in Phase Shifting Interferometry, D. Malacara, ed., 3rd ed. (Wiley, 2007), Chap. 14.
  2. P. de Groot, “Vibration in phase shifting interferometry,” J. Opt. Soc. Am. A 12, 354–365 (1995). [CrossRef]
  3. P. de Groot, “Correlated errors in phase shifting laser Fizeau interferometry,” Appl. Opt. 53, 4334–4342 (2014). [CrossRef]
  4. The techniques described in this paper are protected by U.S. patents7,796,273, 7,796,275, 7,948,639, and foreign patents or patents pending.
  5. L. Deck, “Phase shifting interferometry in the presence of vibration,” U.S. patent7,948,639 (24May2011).
  6. The technique described in this paper is marketed by Zygo Corporation under the name QPSI.
  7. I. Kong and S. Kim, “General algorithm for phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–187 (1995). [CrossRef]
  8. K. Okada, A. Sato, and J. Tsujiuchi, “Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry,” Opt. Commun. 84, 118–124 (1991). [CrossRef]
  9. G. S. Han and S. W. Kim, “Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting,” Appl. Opt. 33, 7321–7325 (1994). [CrossRef]
  10. 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]
  11. Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004). [CrossRef]
  12. Q. Liu, Y. Wang, F. Ji, and J. He, “A three-step least-squares iterative method for tilt phase-shift interferometry,” Opt. Express 21, 29505–29515 (2013). [CrossRef]
  13. L. Deck, “Suppressing phase errors from vibration in phase shifting interferometry,” Appl. Opt. 48, 3948–3960 (2009). [CrossRef]
  14. P. de Groot, “Phase shift calibration errors in interferometers with spherical Fizeau cavities,” Appl. Opt. 34, 2856–2863 (1995). [CrossRef]
  15. P. Wizinowich, “Phase shifting interferometry in the presence of vibration: a new algorithm and system,” Appl. Opt. 29, 3271–3279 (1990). [CrossRef]
  16. L. Deck, “Phase shifting interferometry in the presence of vibration,” U.S. patent7,796,273 (14September2010).
  17. L. Deck, “Phase shifting interferometry in the presence of vibration using phase bias,” U.S. patent7,796,275 (14September2010).
  18. P. de Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt. 39, 2658–2663 (2000). [CrossRef]
  19. D. M. Sykora and M. L. Holmes, “Dynamic measurements using a Fizeau interferometer,” Proc. SPIE 8082, 80821R (2011). [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.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited