Optical Review

, Volume 6, Issue 3, pp 196–203 | Cite as

Phase Retrieval of Phase-Shifting Interferometry with Iterative Least-Squares Fitting Algorithm: Experiments



We report our experimental results of phase-shifting interferometry with an iterative least-squares fitting technique to estimate both the wave front phases and the phase shifts. The method allows phase retrieval from phase-shifting interferograms even though the calibration data of the phase shifter is unknown. The algorithm is used to analyze two sets of experimental interferograms. One records by moving a piezoelectric transducer shifter randomly and therefore has embedded random phase shifter errors, and the other samples the interference movie recorded by a video recorder while driving a stepping motor and therefore has embedded random intensity noises. The results are comparable with that of the conventional M-frame algorithm. Investigation of the effects of the intensity noises and phase shift errors shows the algorithm to perform well in both. Problems such as convergence, unique solution and reliability are also discussed.

Key words

interferometry phase-shifting interferometry fringe analysis phase retrieval iterative least-squares fitting inverse problem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White and D. J. Brangaccio: Appl. Opt. 13 (1974) 2693.Google Scholar
  2. 2.
    P. K. Rastogi: Holographic Interferometry (Springer-Verlag, Berlin, 1995) Chap. 5, p. 109.Google Scholar
  3. 3.
    B. Bhuhan, J. C. Wyant and C. L. Koliopoulos: Appl. Opt. 24 (1985) 1489.Google Scholar
  4. 4.
    K. Creath: Prog. Opt. 26 (1988) 349.Google Scholar
  5. 5.
    E. W. Rogala and H. H. Barrett: Appl. Opt. 36 (1997) 8871.Google Scholar
  6. 6.
    K. Hibino, B. F. Oreb, D. I. Farrant and K. G. Larkin: J. Opt. Soc. Am. A 14 (1997) 918.Google Scholar
  7. 7.
    C. J. Morgan: Opt. Lett. 7 (1982) 368.Google Scholar
  8. 8.
    K. Kinnstaetter, A. W. Lohmann, J. Schwider and N. Streibl: Appl. Opt. 27 (1988) 5080.Google Scholar
  9. 9.
    P. Hariharan, B. F. Oreb and T. Eiju: Appl. Opt. 26 (1987) 2504.Google Scholar
  10. 10.
    J. Schwider: Appl. Opt. 28 (1989) 3889.Google Scholar
  11. 11.
    Y. Y. Cheng and J. C. Wyant: Appl. Opt. 24 (1985) 3049.Google Scholar
  12. 12.
    J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller and N. Streibl: Opt. Eng. 32 (1993) 1883.Google Scholar
  13. 13.
    K. Hibino, B. F. Oreb, D. I. Farrant and K. G. Larkin: J. Opt. Soc. Am. A 12 (1995) 761.Google Scholar
  14. 14.
    K. G. Larkin and B. F. Oreb: J. Opt. Soc. Am. A 9 (1992) 1740.Google Scholar
  15. 15.
    C. T. Farred and M. A. Player: Meas. Sci. Technol. 5 (1994) 648.CrossRefGoogle Scholar
  16. 16.
    G. M. Lai and T. Yatagai: J. Opt. Soc. Am. A 8 (1991) 822.Google Scholar
  17. 17.
    I. P. Gurov and D. V. Sheinikhovich: Opt. Spectrosc. 83 (1997) 137.Google Scholar
  18. 18.
    G. S. Han and S. W. Kim: Appl. Opt. 33 (1994) 7321.Google Scholar
  19. 19.
    L-B. Kong and S.-W. Kim: Opt. Eng. 34 (1995) 183.Google Scholar
  20. 20.
    I. Melao, H. Huang, M. Tsai, M. Itoh and T. Yatagai: Second International Symposium on ‘Optics in Engineering, Tsukuba, 1997, p. 2.Google Scholar

Copyright information

© The Optical Society of Japan 1999

Authors and Affiliations

  • Hongxin Huang
    • 1
  • Masahide Itoh
    • 1
  • Toyohiko Yatagai
    • 1
  1. 1.Institute of Applied Physics, University of TsukubaTsukuba, IbarakiJapan

Personalised recommendations