Abstract

Electronic speckle pattern interferometry has been used to study resonant in-plane vibrations of a thin square metal plate. An in-plane sensitive arrangement is used with dual-beam illumination from a pulsed laser. Fringe patterns are formed which show a cosinusoidal intensity profile. These fringe patterns inherently carry phase information, which is extracted using the single phase step technique and analyzed to determine the amplitude and phase for the horizontal and vertical components of in-plane vibration. These are automatically combined to yield the total in-plane vibration mode. The final result is displayed as vectors drawn over an image of the object.

© 1991 Optical Society of America

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References

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  1. O. J. Løkberg, “ESPI—the Ultimate Holographic Tool for Vibration Analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
    [CrossRef]
  2. O. J. Løkberg, “Mapping of In-Plane Vibration Modes by Electronic Speckle Pattern Interferometry,” Opt. Eng. 24, 356–359 (1985).
    [CrossRef]
  3. H. J. Tiziani, “Application of Speckling for In-Plane Vibration Analysis,” Opt. Acta 18, 891–902 (1971).
    [CrossRef]
  4. E. Archbold, A. E. Ennos, “Two-Dimensional Vibrations Analysed by Speckle Photography,” Opt. Laser Techol. 7, 17–21 (1975).
    [CrossRef]
  5. J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Phys. E 3, 214–218 (1970).
    [CrossRef]
  6. Y. Y. Hung, J. D. Hovanesian, “Full-Field Surface-Strain and Displacement Analysis of Three-Dimensional Objects by Speckle Interferometry,” Exp. Mech. 12, 454–460 (1972).
    [CrossRef]
  7. R. Jones, “The Design and Application of a Speckle Pattern Interferometer for Total Plane Strain Field Measurement,” Opt. Laser Techol. 8, 215–219 (1976).
    [CrossRef]
  8. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. P., London, 1989), Chap. 4.
    [CrossRef]
  9. M. C. Shellabear, J. R. Tyrer, “Application of ESPI to Three-Dimensional Vibration Measurements,” Opt. Laser Eng., in press.
  10. D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Extraction of Phase Data from Electronic Speckle Pattern Interferometric Fringes Using a Single-Phase-Step Method: A Novel Approach,” J. Opt. Soc. Am. A 7, 820–826 (1990).
    [CrossRef]
  11. D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier Components of Speckle Fringe Patterns as Part of an Interferometric Analysis Process,” J. Mod. Opt. 36, 195–203 (1989).
    [CrossRef]
  12. H. Ekstein, “Free Vibrations of Anisotropic Bodies,” Phys. Rev. 66, 108–118 (1944).
    [CrossRef]
  13. H. A. Vrooman, A. A. M. Maas, “Image Processing in Digital Speckle Interferometry,” in Proceedings, Fringe Analysis ’89 Conference (FASIG), Ioughborough, U.K. (1989).
  14. C. Joenathan, B. Pfister, H. J. Tiziani, “Contouring by Electronic Speckle Pattern Interferometry Employing Dual Beam Illumination,” Appl. Opt. 29, 1905–1911 (1990).
    [CrossRef] [PubMed]

1990

1989

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier Components of Speckle Fringe Patterns as Part of an Interferometric Analysis Process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

1985

O. J. Løkberg, “Mapping of In-Plane Vibration Modes by Electronic Speckle Pattern Interferometry,” Opt. Eng. 24, 356–359 (1985).
[CrossRef]

1984

O. J. Løkberg, “ESPI—the Ultimate Holographic Tool for Vibration Analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
[CrossRef]

1976

R. Jones, “The Design and Application of a Speckle Pattern Interferometer for Total Plane Strain Field Measurement,” Opt. Laser Techol. 8, 215–219 (1976).
[CrossRef]

1975

E. Archbold, A. E. Ennos, “Two-Dimensional Vibrations Analysed by Speckle Photography,” Opt. Laser Techol. 7, 17–21 (1975).
[CrossRef]

1972

Y. Y. Hung, J. D. Hovanesian, “Full-Field Surface-Strain and Displacement Analysis of Three-Dimensional Objects by Speckle Interferometry,” Exp. Mech. 12, 454–460 (1972).
[CrossRef]

1971

H. J. Tiziani, “Application of Speckling for In-Plane Vibration Analysis,” Opt. Acta 18, 891–902 (1971).
[CrossRef]

1970

J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

1944

H. Ekstein, “Free Vibrations of Anisotropic Bodies,” Phys. Rev. 66, 108–118 (1944).
[CrossRef]

Archbold, E.

E. Archbold, A. E. Ennos, “Two-Dimensional Vibrations Analysed by Speckle Photography,” Opt. Laser Techol. 7, 17–21 (1975).
[CrossRef]

Ekstein, H.

H. Ekstein, “Free Vibrations of Anisotropic Bodies,” Phys. Rev. 66, 108–118 (1944).
[CrossRef]

Ennos, A. E.

E. Archbold, A. E. Ennos, “Two-Dimensional Vibrations Analysed by Speckle Photography,” Opt. Laser Techol. 7, 17–21 (1975).
[CrossRef]

Hovanesian, J. D.

Y. Y. Hung, J. D. Hovanesian, “Full-Field Surface-Strain and Displacement Analysis of Three-Dimensional Objects by Speckle Interferometry,” Exp. Mech. 12, 454–460 (1972).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, J. D. Hovanesian, “Full-Field Surface-Strain and Displacement Analysis of Three-Dimensional Objects by Speckle Interferometry,” Exp. Mech. 12, 454–460 (1972).
[CrossRef]

Joenathan, C.

Jones, R.

R. Jones, “The Design and Application of a Speckle Pattern Interferometer for Total Plane Strain Field Measurement,” Opt. Laser Techol. 8, 215–219 (1976).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. P., London, 1989), Chap. 4.
[CrossRef]

Kerr, D.

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Extraction of Phase Data from Electronic Speckle Pattern Interferometric Fringes Using a Single-Phase-Step Method: A Novel Approach,” J. Opt. Soc. Am. A 7, 820–826 (1990).
[CrossRef]

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier Components of Speckle Fringe Patterns as Part of an Interferometric Analysis Process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Leendertz, J. A.

J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

Løkberg, O. J.

O. J. Løkberg, “Mapping of In-Plane Vibration Modes by Electronic Speckle Pattern Interferometry,” Opt. Eng. 24, 356–359 (1985).
[CrossRef]

O. J. Løkberg, “ESPI—the Ultimate Holographic Tool for Vibration Analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
[CrossRef]

Maas, A. A. M.

H. A. Vrooman, A. A. M. Maas, “Image Processing in Digital Speckle Interferometry,” in Proceedings, Fringe Analysis ’89 Conference (FASIG), Ioughborough, U.K. (1989).

Mendoza Santoyo, F.

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Extraction of Phase Data from Electronic Speckle Pattern Interferometric Fringes Using a Single-Phase-Step Method: A Novel Approach,” J. Opt. Soc. Am. A 7, 820–826 (1990).
[CrossRef]

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier Components of Speckle Fringe Patterns as Part of an Interferometric Analysis Process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Pfister, B.

Shellabear, M. C.

M. C. Shellabear, J. R. Tyrer, “Application of ESPI to Three-Dimensional Vibration Measurements,” Opt. Laser Eng., in press.

Tiziani, H. J.

Tyrer, J. R.

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Extraction of Phase Data from Electronic Speckle Pattern Interferometric Fringes Using a Single-Phase-Step Method: A Novel Approach,” J. Opt. Soc. Am. A 7, 820–826 (1990).
[CrossRef]

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier Components of Speckle Fringe Patterns as Part of an Interferometric Analysis Process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

M. C. Shellabear, J. R. Tyrer, “Application of ESPI to Three-Dimensional Vibration Measurements,” Opt. Laser Eng., in press.

Vrooman, H. A.

H. A. Vrooman, A. A. M. Maas, “Image Processing in Digital Speckle Interferometry,” in Proceedings, Fringe Analysis ’89 Conference (FASIG), Ioughborough, U.K. (1989).

Wykes, C.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. P., London, 1989), Chap. 4.
[CrossRef]

Appl. Opt.

Exp. Mech.

Y. Y. Hung, J. D. Hovanesian, “Full-Field Surface-Strain and Displacement Analysis of Three-Dimensional Objects by Speckle Interferometry,” Exp. Mech. 12, 454–460 (1972).
[CrossRef]

J. Acoust. Soc. Am.

O. J. Løkberg, “ESPI—the Ultimate Holographic Tool for Vibration Analysis?” J. Acoust. Soc. Am. 75, 1783–1791 (1984).
[CrossRef]

J. Mod. Opt.

D. Kerr, F. Mendoza Santoyo, J. R. Tyrer, “Manipulation of the Fourier Components of Speckle Fringe Patterns as Part of an Interferometric Analysis Process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. E

J. A. Leendertz, “Interferometric Displacement Measurement on Scattering Surfaces Utilizing Speckle Effect,” J. Phys. E 3, 214–218 (1970).
[CrossRef]

Opt. Acta

H. J. Tiziani, “Application of Speckling for In-Plane Vibration Analysis,” Opt. Acta 18, 891–902 (1971).
[CrossRef]

Opt. Eng.

O. J. Løkberg, “Mapping of In-Plane Vibration Modes by Electronic Speckle Pattern Interferometry,” Opt. Eng. 24, 356–359 (1985).
[CrossRef]

Opt. Laser Techol.

E. Archbold, A. E. Ennos, “Two-Dimensional Vibrations Analysed by Speckle Photography,” Opt. Laser Techol. 7, 17–21 (1975).
[CrossRef]

R. Jones, “The Design and Application of a Speckle Pattern Interferometer for Total Plane Strain Field Measurement,” Opt. Laser Techol. 8, 215–219 (1976).
[CrossRef]

Phys. Rev.

H. Ekstein, “Free Vibrations of Anisotropic Bodies,” Phys. Rev. 66, 108–118 (1944).
[CrossRef]

Other

H. A. Vrooman, A. A. M. Maas, “Image Processing in Digital Speckle Interferometry,” in Proceedings, Fringe Analysis ’89 Conference (FASIG), Ioughborough, U.K. (1989).

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. P., London, 1989), Chap. 4.
[CrossRef]

M. C. Shellabear, J. R. Tyrer, “Application of ESPI to Three-Dimensional Vibration Measurements,” Opt. Laser Eng., in press.

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Figures (3)

Fig. 1
Fig. 1

Experimental layout for pulsed in-plane phase-stepped ESPI.

Fig. 2
Fig. 2

Square center-pinned plate vibrating at 25.8 kHz: (a) horizontal in-plane fringe pattern, 0° phase; (b) horizontal in-plane fringe pattern, 90° phase; (c) horizontal in-plane phase map from (a) and (b); (d) horizontal in-plane phase map with component vectors; (e) vertical in-plane phase map with component vectors; and (f) target showing 2-D in-plane vibration vectors.

Fig. 3
Fig. 3

Square center-pinned plate vibrating at 31.5 kHz: (a) vertical in-plane fringe pattern, 0° phase; (b) vertical in-plane fringe pattern, 90° phase; (c) vertical in-plane phase map from (a) and (b); (d) vertical in-plane phase map with component vectors; (e) horizontal in-plane phase map with component vectors; and (f) target showing 2-D in-plane vibration vectors.

Equations (1)

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d = λ 2 sin θ ,

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