OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 18 — Sep. 5, 2005
  • pp: 7160–7173

Super-resolution Fourier transform method in phase shifting interferometry

Rajesh Langoju, Abhijit Patil, and Pramod Rastogi  »View Author Affiliations

Optics Express, Vol. 13, Issue 18, pp. 7160-7173 (2005)

View Full Text Article

Acrobat PDF (598 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The paper proposes a super-resolution Fourier transform method for phase estimation in phase shifting interferometry. Incorporation of a super-resolution technique before the application of Fourier transform significantly enhances the resolution capability of the proposed method. The other salient features of the method lie in its ability to handle multiple harmonics, PZT miscalibration, and arbitrary phase steps in the optical configuration. The method does not need addition of any carrier fringes to separate the spectral contents in the intensity fringes. The proposed concept thus overcomes the limitations of other methods based on Fourier transform techniques. The robustness of the proposed method is studied in the presence of noise.

© 2005 Optical Society of America

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Research Papers

Original Manuscript: August 1, 2005
Revised Manuscript: August 28, 2005
Published: September 5, 2005

Rajesh Langoju, Abhijit Patil, and Pramod Rastogi, "Super-resolution Fourier transform method in phase shifting interferometry," Opt. Express 13, 7160-7173 (2005)

Sort:  Journal  |  Reset


  1. T. Kreis, �??Holographic interferometry Principles and Methods,�?? Akademie Verlag, 1996, pp. 101-170.
  2. J. E. Greivenkamp and J. H. Bruning, Phase shifting interferometry, Optical Shop Testing, ed D. Malacara (New York: Wiley ) 501-598 (1992).
  3. 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, 3421-3432 (1983).
  4. Y. Zhu and T. Gemma, �??Method for designing error-compensating phase-calculation algorithms for phase-shifting interferometry,�?? Appl. Opt. 40, 4540-4546 (2001).
  5. P. Hariharan, B. F. Oreb, and T. Eiju, �??Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,�?? Appl. Opt. 26, 2504-2506 (1987).
  6. J. Schwider, O. Falkenstorfer, H. Schreiber, and A. Zoller, �??New compensating four-phase algorithm for phase-shift interferometry,�?? Opt. Eng. 32, 1883-1885 (1993). [CrossRef]
  7. Y. Surrel, �??Phase stepping: a new self-calibrating algorithm,�?? Appl. Opt. 32, 3598-3600 (1993).
  8. Y. Surrel, �??Design of algorithms for phase measurements by the use of phase stepping,�?? Appl. Opt. 35, 51-60 (1996).
  9. Y. �??Y. Cheng and J. C. Wyant, �??Phase-shifter calibration in phase-shifting interferometry,�?? Appl. Opt. 24, 3049-3052 (1985).
  10. K. G. Larkin and B. F. Oreb, �??Design and assessment of symmetrical phase-shifting algorithms,�?? J. Opt. Soc. Am. A 9, 1740-1748 (1992).
  11. K. G. Larkin, �??A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,�?? Opt. Exp. 9, 236-253 (2001).
  12. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, �??Phase shifting for nonsinusoidal waveforms with phase-shift errors,�?? J. Opt. Soc. Am. A 12, 761-768 (1995).
  13. C. J. Morgan, �??Least squares estimation in phase-measurement interferometry,�?? Opt. Lett. 7, 368-370 (1982).
  14. J. E. Grievenkamp, �??Generalized data reduction for heterodyne interferometry,�?? Opt. Eng. 23, 350-352 (1984).
  15. G. Lai and T. Yatagai, �??Generalized phase-shifting interferometry,�?? J. Opt. Soc. Am. A 8, 822-827 (1991).
  16. 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).
  17. K. A. Goldberg and J. Bokor, �??Fourier-transform method of phase-shift determination,�?? Appl. Opt. 40, 2886-2894 (2001).
  18. C. S. Guo, Z. Y. Rong, J. L. He, H. T. Wang, L. Z. Cai, and Y. R. Wang, �??Determination of global phase shifts between interferograms by use of an energy-minimum algorithm,�?? Appl. Opt. 42, 6514-6519 (2003).
  19. L. R. Watkins, S. M. Tan, and T. H. Barnes, �??Determination of interferometer phase distributions by use of wavelets,�?? Opt. Lett. 24, 905-907 (1999).
  20. P. Stoica and R. Moses, Introduction to Spectral Analysis (Prentice Hall, New Jersey, 1997).
  21. T. Söderström and P. Stoica, �??Accuracy of high-order Yule-Walker methods for frequency estimation of complex sine waves,�?? IEEE Proceedings-F 140, 71-80 (1993).
  22. J. J. Fuchs, �??Estimating the number of sinusoids in additive white noise,�?? IEEE Transactions on Acoustics, Speech, and Signal Processing 36, 1846-1853 (1988).
  23. P. K. Rastogi, �??Phase-shifting holographic moiré: phase-shifter error-insensitive algorithms for the extraction of the difference and sum of phases in holographic moiré,�?? Appl. Opt. 32, 3669-3675 (1993).
  24. R. Roy and T. Kailath, �??ESPRIT-Estimation of signal parameters via rotational invariance techniques,�?? IEEE Transactions on Acoustics, Speech, and Signal Processing 37, 984-995 (1989).

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