Abstract

A new algorithm for precise determination of the global phase shift between two interferograms is introduced. First we calculate the frame difference between the first and the second interferogram; the difference is multiplied by a properly chosen test phase factor, and then we implement a two-dimensional Fourier transform of the frame difference and calculate the energy of the first positive (or negative) diffraction order. An iterative approach is used for the test phase to ensure that the minimum energy is obtained, and then the correct phase shift value is found. This method is called the energy-minimum Fourier transform method, which is accurate and noise insensitive compared with the single-point Fourier transform method. Both the theoretical analysis and experimental results are given.

© 2003 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Bucholtz, K. P. Koo, G. H. Sigel, A. Dandridge, “Optimization of the fiber/metallic glass bond in fiber-optic magnetic sensors,” J. Lightwave Technol. 3, 814–817 (1985).
    [CrossRef]
  2. R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).
  3. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
    [CrossRef] [PubMed]
  4. J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront corrections systems (for telescopes),” Appl. Opt. 14, 2622–2626 (1975).
    [CrossRef] [PubMed]
  5. J. Schwider, R. Burrow, K. E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wavefront measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
    [CrossRef]
  6. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometer: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]
  7. K. G. Larkin, B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740–1748 (1992).
    [CrossRef]
  8. Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt. 32, 3598–3600 (1993).
    [CrossRef] [PubMed]
  9. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
    [CrossRef] [PubMed]
  10. G. Kieran, A. Larkin, “Self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236–253 (2001).
    [CrossRef]
  11. C. S. Guo, L. Zhang, H. T. Wang, J. Liao, Y. Y. Zhu, “Phase-shifting error and its elimination in phase-shifting digital holography,” Opt. Lett. 27, 1687–1689 (2002).
    [CrossRef]
  12. T. Yamaguchi, K. Hamano, “Inteferometric method of measuring complex piezoelectric constants of crystals in a frequency range up to about 50 kHz,” Jpn. J. Appl. Phys. 18, 927–932 (1979).
    [CrossRef]
  13. A. Nesci, R. Dändliker, H. P. Herzig, “Quantitative amplitude and phase measurement by use of a heterodyne scanning near-field optical microscope,” Opt. Lett. 26, 208–210 (2001).
    [CrossRef]
  14. K. A. Goldberg, J. Bokor, “Fourier-transform method of phase-shift determination,” Appl. Opt. 40, 2886–2894 (2001).
    [CrossRef]
  15. 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]
  16. C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987).
    [CrossRef] [PubMed]
  17. F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1982), pp. 415–424.

2002

2001

1996

1993

1992

1987

1985

F. Bucholtz, K. P. Koo, G. H. Sigel, A. Dandridge, “Optimization of the fiber/metallic glass bond in fiber-optic magnetic sensors,” J. Lightwave Technol. 3, 814–817 (1985).
[CrossRef]

1983

1982

1979

T. Yamaguchi, K. Hamano, “Inteferometric method of measuring complex piezoelectric constants of crystals in a frequency range up to about 50 kHz,” Jpn. J. Appl. Phys. 18, 927–932 (1979).
[CrossRef]

1975

1974

1969

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

Bokor, J.

Brangaccio, D. J.

Bruning, J. H.

Bucholtz, F.

F. Bucholtz, K. P. Koo, G. H. Sigel, A. Dandridge, “Optimization of the fiber/metallic glass bond in fiber-optic magnetic sensors,” J. Lightwave Technol. 3, 814–817 (1985).
[CrossRef]

Burrow, R.

Crane, R.

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

Dändliker, R.

Dandridge, A.

F. Bucholtz, K. P. Koo, G. H. Sigel, A. Dandridge, “Optimization of the fiber/metallic glass bond in fiber-optic magnetic sensors,” J. Lightwave Technol. 3, 814–817 (1985).
[CrossRef]

Eiju, T.

Elssner, K. E.

Gallagher, J. E.

Goldberg, K. A.

Grzanna, J.

Guo, C. S.

Hamano, K.

T. Yamaguchi, K. Hamano, “Inteferometric method of measuring complex piezoelectric constants of crystals in a frequency range up to about 50 kHz,” Jpn. J. Appl. Phys. 18, 927–932 (1979).
[CrossRef]

Hariharan, P.

Herriott, D. R.

Herzig, H. P.

Ina, H.

Kieran, G.

Kobayashi, S.

Koo, K. P.

F. Bucholtz, K. P. Koo, G. H. Sigel, A. Dandridge, “Optimization of the fiber/metallic glass bond in fiber-optic magnetic sensors,” J. Lightwave Technol. 3, 814–817 (1985).
[CrossRef]

Larkin, A.

Larkin, K. G.

Liao, J.

Merkel, K.

Nesci, A.

Oreb, B. F.

Roddier, C.

Roddier, F.

Rosenfeld, D. P.

Schwider, J.

Sigel, G. H.

F. Bucholtz, K. P. Koo, G. H. Sigel, A. Dandridge, “Optimization of the fiber/metallic glass bond in fiber-optic magnetic sensors,” J. Lightwave Technol. 3, 814–817 (1985).
[CrossRef]

Spolaczyk, R.

Surrel, Y.

Takeda, M.

Wang, H. T.

White, A. D.

Wyant, J. C.

Yamaguchi, T.

T. Yamaguchi, K. Hamano, “Inteferometric method of measuring complex piezoelectric constants of crystals in a frequency range up to about 50 kHz,” Jpn. J. Appl. Phys. 18, 927–932 (1979).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1982), pp. 415–424.

Zhang, L.

Zhu, Y. Y.

Appl. Opt.

J. Lightwave Technol.

F. Bucholtz, K. P. Koo, G. H. Sigel, A. Dandridge, “Optimization of the fiber/metallic glass bond in fiber-optic magnetic sensors,” J. Lightwave Technol. 3, 814–817 (1985).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

T. Yamaguchi, K. Hamano, “Inteferometric method of measuring complex piezoelectric constants of crystals in a frequency range up to about 50 kHz,” Jpn. J. Appl. Phys. 18, 927–932 (1979).
[CrossRef]

Opt. Express

Opt. Lett.

Other

F. T. S. Yu, Optical Information Processing (Wiley-Interscience, New York, 1982), pp. 415–424.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics