Abstract

Double-pulsed (image-plane) TV holograms of transient bending waves in plates are recorded on separate frames in a CCD camera. A small angular offset between the reference and object beams, giving a spatial-frequency bias to the recorded pattern, permits quantitative evaluation of the phase of the interference. The Fourier spectrum of the image exhibits distinct parts that can be filtered out and inverse transformed to yield the phase information. Three different apertures of the imaging system are tested: a single slit, a double slit, and a three-hole aperture. Spatial speckle averaging is possible in the cases of the double-slit and three-hole apertures.

© 1997 Optical Society of America

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References

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  1. K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
    [CrossRef]
  2. S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
    [CrossRef]
  3. B. H. Timmerman, D. W. Watt, “Tomographic high-speed digital holographic interferometry measurements in free-jet flows,” in Proceedings of the Seventh International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.
  4. R. Dändliker, R. Thalmann, J.-F. Willemin, “Fringe interpolation by two-reference beam holographic interferometry: reducing sensitivity to hologram misalignment,” Opt. Commun. 42, 301–306 (1982).
    [CrossRef]
  5. J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus65–71 (May1982).
  6. H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV-holography for vibration analysis,” Opt. Eng. 34, 486–492 (1996).
  7. O. J. Løkberg, “Recording of sound emission and propagation in air using TV holography,” J. Acoust. Soc. Am. 96, 2244–2250 (1994).
    [CrossRef]
  8. R. Spooren, A. Aksnes Dyrseth, M. Vaz, “Electronic shear interferometry: application of a (double-) pulsed laser,” Appl. Opt. 32, 4719–4727 (1993).
    [CrossRef] [PubMed]
  9. G. Pedrini, H. Tiziani, “Double-pulsed electronic speckle interferometry for vibration analysis,” Appl. Opt. 33, 7857–7863 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. D. E. Duffy, “Moiré gauging of in-plane displacement using double aperture imaging,” Appl. Opt. 11, 1778–1781 (1972).
    [CrossRef] [PubMed]
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  14. R. Cusak, J. M. Huntley, H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995).
    [CrossRef]
  15. K.-E. Fällström, N.-E. Molin, K. Olofsson, S. Schedin, A. Wåhlin, “Mechanical and thermal effects in a steel plate impacted by a focused laser pulse,” Nondestruct. Test. Eval. (to be published).
  16. G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
    [CrossRef]

1997 (1)

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

1996 (3)

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV-holography for vibration analysis,” Opt. Eng. 34, 486–492 (1996).

H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (3)

1993 (1)

1989 (1)

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

1982 (2)

R. Dändliker, R. Thalmann, J.-F. Willemin, “Fringe interpolation by two-reference beam holographic interferometry: reducing sensitivity to hologram misalignment,” Opt. Commun. 42, 301–306 (1982).
[CrossRef]

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus65–71 (May1982).

1972 (1)

Cusak, R.

Dändliker, R.

R. Dändliker, R. Thalmann, J.-F. Willemin, “Fringe interpolation by two-reference beam holographic interferometry: reducing sensitivity to hologram misalignment,” Opt. Commun. 42, 301–306 (1982).
[CrossRef]

Duffy, D. E.

Dyrseth, A. Aksnes

Fällström, K.-E.

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

K.-E. Fällström, N.-E. Molin, K. Olofsson, S. Schedin, A. Wåhlin, “Mechanical and thermal effects in a steel plate impacted by a focused laser pulse,” Nondestruct. Test. Eval. (to be published).

Goldrein, H. T.

Gren, P. O.

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

Gustavsson, H.

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

Huntley, J. M.

R. Cusak, J. M. Huntley, H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995).
[CrossRef]

J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 246–257 (1995).

Løkberg, O. J.

O. J. Løkberg, “Recording of sound emission and propagation in air using TV holography,” J. Acoust. Soc. Am. 96, 2244–2250 (1994).
[CrossRef]

Mohan, N. Krishna

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV-holography for vibration analysis,” Opt. Eng. 34, 486–492 (1996).

Molin, N.-E.

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV-holography for vibration analysis,” Opt. Eng. 34, 486–492 (1996).

H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

K.-E. Fällström, N.-E. Molin, K. Olofsson, S. Schedin, A. Wåhlin, “Mechanical and thermal effects in a steel plate impacted by a focused laser pulse,” Nondestruct. Test. Eval. (to be published).

Olofsson, K.

K.-E. Fällström, N.-E. Molin, K. Olofsson, S. Schedin, A. Wåhlin, “Mechanical and thermal effects in a steel plate impacted by a focused laser pulse,” Nondestruct. Test. Eval. (to be published).

Pedrini, G.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

G. Pedrini, H. Tiziani, “Double-pulsed electronic speckle interferometry for vibration analysis,” Appl. Opt. 33, 7857–7863 (1994).
[CrossRef] [PubMed]

Saldner, H. O.

H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV-holography for vibration analysis,” Opt. Eng. 34, 486–492 (1996).

Schedin, S.

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

K.-E. Fällström, N.-E. Molin, K. Olofsson, S. Schedin, A. Wåhlin, “Mechanical and thermal effects in a steel plate impacted by a focused laser pulse,” Nondestruct. Test. Eval. (to be published).

Schnars, U.

Spooren, R.

Stetson, K. A.

Thalmann, R.

R. Dändliker, R. Thalmann, J.-F. Willemin, “Fringe interpolation by two-reference beam holographic interferometry: reducing sensitivity to hologram misalignment,” Opt. Commun. 42, 301–306 (1982).
[CrossRef]

Timmerman, B. H.

B. H. Timmerman, D. W. Watt, “Tomographic high-speed digital holographic interferometry measurements in free-jet flows,” in Proceedings of the Seventh International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Tiziani, H.

Tiziani, H. J.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

Vaz, M.

Wåhlin, A.

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

K.-E. Fällström, N.-E. Molin, K. Olofsson, S. Schedin, A. Wåhlin, “Mechanical and thermal effects in a steel plate impacted by a focused laser pulse,” Nondestruct. Test. Eval. (to be published).

Wåhlin, A. O.

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

Watt, D. W.

B. H. Timmerman, D. W. Watt, “Tomographic high-speed digital holographic interferometry measurements in free-jet flows,” in Proceedings of the Seventh International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Willemin, J.-F.

R. Dändliker, R. Thalmann, J.-F. Willemin, “Fringe interpolation by two-reference beam holographic interferometry: reducing sensitivity to hologram misalignment,” Opt. Commun. 42, 301–306 (1982).
[CrossRef]

Wyant, J. C.

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus65–71 (May1982).

Zou, Y.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

Appl. Opt. (5)

Exp. Mech. (1)

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

J. Acoust. Soc. Am. (2)

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

O. J. Løkberg, “Recording of sound emission and propagation in air using TV holography,” J. Acoust. Soc. Am. 96, 2244–2250 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

Laser Focus (1)

J. C. Wyant, “Interferometric optical metrology: basic principles and new systems,” Laser Focus65–71 (May1982).

Opt. Commun. (1)

R. Dändliker, R. Thalmann, J.-F. Willemin, “Fringe interpolation by two-reference beam holographic interferometry: reducing sensitivity to hologram misalignment,” Opt. Commun. 42, 301–306 (1982).
[CrossRef]

Opt. Eng. (1)

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV-holography for vibration analysis,” Opt. Eng. 34, 486–492 (1996).

Opt. Lasers Eng. (1)

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

Other (3)

K.-E. Fällström, N.-E. Molin, K. Olofsson, S. Schedin, A. Wåhlin, “Mechanical and thermal effects in a steel plate impacted by a focused laser pulse,” Nondestruct. Test. Eval. (to be published).

J. M. Huntley, “Random phase measurement errors in digital speckle pattern interferometry,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 246–257 (1995).

B. H. Timmerman, D. W. Watt, “Tomographic high-speed digital holographic interferometry measurements in free-jet flows,” in Proceedings of the Seventh International Symposium on Application of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

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Figures (6)

Fig. 1
Fig. 1

Double-slit aperture. Focusing of the object light field.

Fig. 2
Fig. 2

(a) Symmetric three-hole aperture and (b) the Fourier spectrum obtained for the case in which the reference beam is positioned in the center.

Fig. 3
Fig. 3

(a) Experimental setup: BS, beam splitter; EB, excitation beam; NL, negative lens; M, mirrors; O, object; OL, object light; OU, optical unit; R, reference light; RL, ruby laser. (b) Optical unit: A, aperture; AR, aperture for the reference light; BS, beam splitter; FL, field lens; M, mirror, NL, negative lens; OL, object light; R, Reference light; REL, relay lens; VL, video lens.

Fig. 4
Fig. 4

Phase maps showing propagating bending waves in the aluminium plate at 30 µs after impact: (a) from a single-slit aperture and (b) from a double-slit aperture with speckle averaging.

Fig. 5
Fig. 5

Bending waves at 60 µs after impact on the aluminium plate. The three-hole aperture is used with speckle averaging. (a) Wrapped phase map. (b) Three-dimensional plot showing the unwrapped phase map.

Fig. 6
Fig. 6

Bending waves at 300 µs after impact on the cymbal. The three-hole aperture is used with speckle averaging. (a) Wrapped phase map. (b) Three-dimensional plot showing the unwrapped phase map.

Equations (7)

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U=R+S1 expikd1 sin θ+ΔΦ+S2 expi -kd2 sin θ+ΔΦ,
I=UU*=RS1 expikd1θ+ΔΦ+RS2* expikd2θ-ΔΦ+RS1* expi-kd1θ-ΔΦ+RS2 expi-kd2θ+ΔΦ+S1S2*×expikd1+d2θ+S1*S2 exp-ikd1+d2θ+R2+S1S1*+S2S2*,
s=RS1 expikd1θ+RS2* expikd2θ,
s=RS1 expi kd1θ+ΔΦ+RS2* expikd2θ-ΔΦ,
s=2RScoskdθ+isinkdθ,
s=RScoskdθ+ΔΦ+isinkdθ+ΔΦ+RScoskdθ-ΔΦ+isinkdθ-ΔΦ.
ΔΦ=arctanResIms-ImsResImsIms+ResRes.

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