OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 1 — Jan. 1, 2000
  • pp: 21–27

Interferometric data analysis based on Markov nonlinear filtering methodology

Igor P. Gurov and Denis V. Sheynihovich  »View Author Affiliations

JOSA A, Vol. 17, Issue 1, pp. 21-27 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (194 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



For data processing in conventional phase shifting interferometry, Fourier transform, and least-squares-fitting techniques, a whole interferometric data series is required. We propose a new interferometric data processing methodology based on a recurrent nonlinear procedure. The signal value is predicted from the previous step to the next step, and the prediction error is used for nonlinear correction of an a priori estimate of the parameters phase, visibility, or frequency of interference fringes. Such a recurrent procedure is correct on the condition that the noise component be a Markov stochastic process realization. The accuracy and stability of the recurrent Markov nonlinear filtering algorithm were verified by computer simulations. It was discovered that the main advantages of the proposed methodology are dynamic data processing, phase error minimization, and high noise immunity against the influence of non-Gaussian noise correlated with the signal and the automatic solution of the phase unwrapping problem.

© 2000 Optical Society of America

OCIS Codes
(030.4280) Coherence and statistical optics : Noise in imaging systems
(050.5080) Diffraction and gratings : Phase shift
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(100.5070) Image processing : Phase retrieval

Original Manuscript: March 15, 1999
Revised Manuscript: July 15, 1999
Manuscript Accepted: August 2, 1999
Published: January 1, 2000

Igor P. Gurov and Denis V. Sheynihovich, "Interferometric data analysis based on Markov nonlinear filtering methodology," J. Opt. Soc. Am. A 17, 21-27 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wave-front measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  2. J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus 18, 65–71 (1982).
  3. K. Creath, “Phase measurement interferometry technique,” Prog. Opt. 26, 349–383 (1988). [CrossRef]
  4. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  5. D. W. Robinson, “Automatic fringe analysis with a computer image-processing system,” Appl. Opt. 22, 2169–2176 (1983). [CrossRef] [PubMed]
  6. C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1683 (1987). [CrossRef] [PubMed]
  7. R. Jozwicki, M. Kujawinska, L. Salbut, “New contra old wavefront measurement concepts for interferometric optical testing,” Opt. Eng. 31, 422–433 (1992). [CrossRef]
  8. S. M. Pandit, N. Jordache, G. A. Joshi, “Data-dependent system methodology for noise-insensitive phase unwrapping in laser interferometric surface characterization,” J. Opt. Soc. Am. A 11, 2584–2592 (1994). [CrossRef]
  9. I. P. Gurov, I. M. Nagibina, “The structure of multichannel interference measuring systems for precision control of the objects geometric characterization,” Izv. Vyssh. Uchebn. Zaved. Priborostr. 34, 59–66 (1991) (in Russian).
  10. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  11. H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer-Verlag, Berlin, 1982).
  12. J. E. Grevenkamp, J. H. Bruning, “Phase-shifting interferometry,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992).
  13. D. K. Bowen, D. G. Chetwynd, D. R. Schwarzenberger, “Sub-nanometre displacements calibration using x-ray interferometry,” Meas. Sci. Technol. 1, 107–119 (1990). [CrossRef]
  14. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). [CrossRef] [PubMed]
  15. G. Lai, T. Yatagai, “Generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 8, 822–827 (1991). [CrossRef]
  16. C. T. Farrell, M. A. Player, “Phase step measurement and variable step algorithms in phase shifting interferometry,” Meas. Sci. Technol. 3, 953–958 (1992). [CrossRef]
  17. Y. Sarrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993). [CrossRef]
  18. G. S. Han, S. W. Kim, “Numerical correction of reference phases in phase-shifting interferometry by iterative least-squares fitting,” Appl. Opt. 33, 7321–7325 (1994). [CrossRef] [PubMed]
  19. K. Hibino, B. F. Oreb, D. I. Farrant, K. G. Larkin, “Phase shifting for nonsinusoidal waveform with phase-shift errors,” J. Opt. Soc. Am. A 12, 761–767 (1995). [CrossRef]
  20. E. Lloyd, ed. Statistics, Vol.6 of Handbook of Applicable Mathematics, Walter Ledermann, ed. (Wiley, Chichester, UK, 1984).
  21. P. J. de Groot, “Vibration in phase-shifting interferometry,” J. Opt. Soc. Am. A 12, 354–365 (1995). [CrossRef]
  22. J. Schwider, R. Burow, K. E. Ellsner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983). [CrossRef] [PubMed]
  23. M. S. Yarlykov, M. A. Mironov, Markov Theory of Stochastic Processes Estimation (Radio I svyaz, Moscow, 1993) (in Russian).
  24. R. E. Kalman, R. S. Bucy, “New results in linear filtering and prediction theory,” Basic Eng. 82, 35–40 (1960). [CrossRef]
  25. V. I. Tikhonov, M. A. Mironov, Markov Processes (Soviet Radio, Moscow, 1977) (in Russian).
  26. I. P. Gurov, D. V. Sheynikhovich, “Noise-immune phase-shifting interferometric system based on Markov non-linear filtering method,” in Statistical and Stochastic Methods for Image Processing, E. R. Dougherty, F. Preteux, J. L. Davidson, eds., Proc. SPIE2823, 121–125 (1996). [CrossRef]
  27. I. P. Gurov, D. V. Sheynihovich, “Non-linear phase estimation by computer-aided Markov filtering method: accuracy investigations,” in Proceedings of the IEEE TENCON ’96 Conference, Perth, Australia (Institute of Electrical and Electronics Engineers, New York, 1996), Vol. 2, pp. 758–762.
  28. I. P. Gurov, D. V. Sheynikhovich, “Determination of phase characteristics of an interference pattern by the method of nonlinear Markov filtering,” Opt. Spectrosc. (USSR) 83, 137–142 (1997).

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