OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 10 — May. 9, 2011
  • pp: 9529–9534

Phase-shifting interferometry corrupted by white and non-white additive noise

M. Servin, J. A. Quiroga, and J. C. Estrada  »View Author Affiliations

Optics Express, Vol. 19, Issue 10, pp. 9529-9534 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (886 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The standard tool to estimate the phase of a sequence of phase-shifted interferograms is the Phase Shifting Algorithm (PSA). The performance of PSAs to a sequence of interferograms corrupted by non-white additive noise has not been reported before. In this paper we use the Frequency Transfer Function (FTF) of a PSA to generalize previous white additive noise analysis to non-white additive noisy interferograms. That is, we find the ensemble average and the variance of the estimated phase in a general PSA when interferograms corrupted by non-white additive noise are available. Moreover, for the special case of additive white-noise, and using the Parseval’s theorem, we show (for the first time in the PSA literature) a useful relationship of the PSA’s noise robustness; in terms of its FTF spectrum, and in terms of its coefficients. In other words, we find the PSA’s estimated phase variance, in the spectral space as well as in the PSA’s coefficients space.

© 2011 OSA

OCIS Codes
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: February 16, 2011
Revised Manuscript: April 18, 2011
Manuscript Accepted: April 21, 2011
Published: May 2, 2011

M. Servin, J. A. Quiroga, and J. C. Estrada, "Phase-shifting interferometry corrupted by white and non-white additive noise," Opt. Express 19, 9529-9534 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13(11), 2693–2703 (1974). [CrossRef] [PubMed]
  2. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, Taylor & Francis CRC Press, 2th edition (2005).
  3. M. Servin, J. C. Estrada, J. A. Quiroga, J. F. Mosiño, and M. Cywiak, “Noise in phase shifting interferometry,” Opt. Express 17(11), 8789–8794 (2009). [CrossRef] [PubMed]
  4. M. Servin, J. C. Estrada, and J. A. Quiroga, “The general theory of phase shifting algorithms,” Opt. Express 17(24), 21867–21881 (2009). [CrossRef] [PubMed]
  5. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7(4), 537–541 (1990). [CrossRef]
  6. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. 12(9), 1997–2008 (1995). [CrossRef]
  7. Y. Surrel, “Additive noise effect in digital phase detection,” Appl. Opt. 36(1), 271–276 (1997). [CrossRef] [PubMed]
  8. K. Hibino, “Susceptibility of systematic error-compensating algorithms to random noise in phase-shiftinginterferometry,” Appl. Opt. 36, 2064–2093 (1997).
  9. A. Papoulis, Probability Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill Series in Electrical Engineering, 2001).
  10. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7(8), 368–370 (1982). [CrossRef] [PubMed]
  11. J. Schwider, R. Burow, K. E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22(21), 3421–3432 (1983). [CrossRef] [PubMed]
  12. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26(13), 2504–2506 (1987). [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.


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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited