Optical Review

, Volume 12, Issue 1, pp 29–36

Interferometric Phase-Measurement Using a One-Dimensional Discrete Hilbert Transform



A phase demodulation scheme using a discrete Hilbert transform that can change the interferometric phase by π/2 has been investigated. In-quadrature components of a fringe pattern are obtained from one captured interferogram using a one-dimensional (1-D) discrete Hilbert transform and a 1-D discrete high-pass filtering that are based on a digital signal processing technique. The phase distribution in the range of 15π (rad) can be demodulated with the proposed method. The 1-D discrete Hilbert transform can be extended to two-dimensional calculation with a raster scanning procedure. © 2005 The Optical Society of Japan

Key words

phase measurement optical interferometry 


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  1. 1.
    N. A. Massie, R. D. Nelson and S. Holly: Appl. Opt. 18 (1979) 1797.ADSGoogle Scholar
  2. 2.
    F. M. Mottier: Opt. Eng. 18 (1979) 464.Google Scholar
  3. 3.
    G. E. Sommargren: Appl. Opt. 20 (1981) 610.ADSGoogle Scholar
  4. 4.
    K. Creath: Progress in Optics, ed. E. Wolf (Elsevier, Amsterdam, 1988) Vol. 26, p. 349.Google Scholar
  5. 5.
    J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White and D. J. Brangaccio: Appl. Opt. 13 (1974) 2693.ADSCrossRefGoogle Scholar
  6. 6.
    Y. Ishii: Progress in Optics, ed. E. Wolf (Elsevier, Amsterdam, 2004) Vol. 46, p. 243.Google Scholar
  7. 7.
    M. Takeda, H. Ina and S. Kobayashi: J. Opt. Soc. Am. 72 (1982) 156.CrossRefADSGoogle Scholar
  8. 8.
    M. Sticker, C. K. Hitzenberger, R. Leitgeb and A. F. Fercher: Opt. Lett. 26 (2001) 518.ADSGoogle Scholar
  9. 9.
    K. G. Larkin, D. J. Bone and M. A. Oldfield: J. Opt. Soc. Am. A 18 (2001) 1862.ADSGoogle Scholar
  10. 10.
    Y. Watanabe and I. Yamaguchi: Appl. Opt. 41 (2002) 4497.ADSGoogle Scholar
  11. 11.
    Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. F. de Boer and J. S. Nelson: Opt. Lett. 25 (2000) 114.ADSGoogle Scholar
  12. 12.
    C. K. Hitzenberger, M. Sticker, R. Leitgeb and A. F. Fercher: Opt. Lett. 26 (2001) 1864.ADSGoogle Scholar
  13. 13.
    S. S. C. Chim and G. S. Kino: Appl. Opt. 31 (1992) 2550.ADSCrossRefGoogle Scholar
  14. 14.
    R. N. Bracewell: The Fourier Transform and Its Applications (Mcgraw-hill, New York, 1986) p. 267.Google Scholar
  15. 15.
    S. D. Stearns and R. A. David: Signal Processing Algorithms (Prentice hall, New Jersey, 1988) p. 297.MATHGoogle Scholar
  16. 16.
    N. Mikami: Introduction to Digital Signal Processing by C Language (CQ Publishing Company, Tokyo, 2002) p. 185 [in Japanese].Google Scholar
  17. 17.
    J. E. Greivenkamp and J. H. Bruning: Optical Shop Testing, ed. D. Malacara (Wiley-Interscience, New York, 1992) p. 514.Google Scholar

Copyright information

© The Optical Society of Japan 2005

Authors and Affiliations

  • Ribun Onodera
    • 1
  • Hiroto Watanabe
    • 1
    • 2
  • Yukihiro Ishii
    • 1
  1. 1.Department of ElectronicsUniversity of Industrial TechnologySagamihara, KanagawaJapan
  2. 2.Imaging Laboratory R & D CenterTOPCON CorporationItabashi-kuJapan

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