Abstract

Vibration analysis in quasi-real time is studied by recording the time-averaged speckle pattern in a bismuth silicon oxide crystal (Bi12SiO20). When the crystal is illuminated with a spherical wave, the spatially structured information from the time-averaged speckle pattern leads to fringes in the Fraunhofer plane. No storage device is required when the appropriate wavelength is chosen for writing and reading out the information. Experimental results will be presented together with a comparison of measurements obtained with a Doppler shift vibrometer.

© 1981 Optical Society of America

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References

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  1. J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
    [CrossRef]
  2. J. P. Huignard, J. P. Herriau, Appl. Opt. 16, 1807 (1977).
    [CrossRef] [PubMed]
  3. J. P. Huignard, J. P. Herriau, G. Rivet, P. Günter, Opt. Lett. 5, 102 (1980).
    [CrossRef] [PubMed]
  4. H. J. Tiziani, K. Leonhardt, J. Klenk, Opt. Commun. 34, 327 (1980).
    [CrossRef]
  5. T. Takemori, S. Ueha, J. Tsujiuchi, Opt. Commun. 32, 24 (1980).
    [CrossRef]
  6. H. J. Tiziani, Opt. Acta 18, 891 (1971).
    [CrossRef]
  7. D. A. Gregory, Opt. Laser Technol. 8, 201 (1976).
    [CrossRef]

1980

H. J. Tiziani, K. Leonhardt, J. Klenk, Opt. Commun. 34, 327 (1980).
[CrossRef]

T. Takemori, S. Ueha, J. Tsujiuchi, Opt. Commun. 32, 24 (1980).
[CrossRef]

J. P. Huignard, J. P. Herriau, G. Rivet, P. Günter, Opt. Lett. 5, 102 (1980).
[CrossRef] [PubMed]

1977

1976

D. A. Gregory, Opt. Laser Technol. 8, 201 (1976).
[CrossRef]

J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
[CrossRef]

1971

H. J. Tiziani, Opt. Acta 18, 891 (1971).
[CrossRef]

Gregory, D. A.

D. A. Gregory, Opt. Laser Technol. 8, 201 (1976).
[CrossRef]

Günter, P.

Herriau, J. P.

Huignard, J. P.

Klenk, J.

H. J. Tiziani, K. Leonhardt, J. Klenk, Opt. Commun. 34, 327 (1980).
[CrossRef]

Leonhardt, K.

H. J. Tiziani, K. Leonhardt, J. Klenk, Opt. Commun. 34, 327 (1980).
[CrossRef]

Micheron, F.

J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
[CrossRef]

Rivet, G.

Takemori, T.

T. Takemori, S. Ueha, J. Tsujiuchi, Opt. Commun. 32, 24 (1980).
[CrossRef]

Tiziani, H. J.

H. J. Tiziani, K. Leonhardt, J. Klenk, Opt. Commun. 34, 327 (1980).
[CrossRef]

H. J. Tiziani, Opt. Acta 18, 891 (1971).
[CrossRef]

Tsujiuchi, J.

T. Takemori, S. Ueha, J. Tsujiuchi, Opt. Commun. 32, 24 (1980).
[CrossRef]

Ueha, S.

T. Takemori, S. Ueha, J. Tsujiuchi, Opt. Commun. 32, 24 (1980).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. P. Huignard, F. Micheron, Appl. Phys. Lett. 29, 591 (1976).
[CrossRef]

Opt. Acta

H. J. Tiziani, Opt. Acta 18, 891 (1971).
[CrossRef]

Opt. Commun.

H. J. Tiziani, K. Leonhardt, J. Klenk, Opt. Commun. 34, 327 (1980).
[CrossRef]

T. Takemori, S. Ueha, J. Tsujiuchi, Opt. Commun. 32, 24 (1980).
[CrossRef]

Opt. Laser Technol.

D. A. Gregory, Opt. Laser Technol. 8, 201 (1976).
[CrossRef]

Opt. Lett.

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Figures (7)

Fig. 1
Fig. 1

Experimental arrangement of in-plane deformation and vibration analysis in quasi-real time with an electrooptical BSO crystal.

Fig. 2
Fig. 2

Real-time fringes of deformation measurement (Δξ = 40-μm horizontally).

Fig. 3
Fig. 3

Real-time fringes of tilt measurement with a TV column analyzer (Δγ = 20-sec of arc horizontally).

Fig. 4
Fig. 4

Quasi-real-time fringes of a vibration measurement of an oscillating tuning fork (amplitude ρ = 13.5 μm).

Fig. 5
Fig. 5

Horizontally vibrating tuning fork was also shifted horizontally between two exposures (Δη = ρ = 15 μm).

Fig. 6
Fig. 6

Horizontally vibrating tuning fork shifted vertically between two exposures (Δη = ρ = 15 μm).

Fig. 7
Fig. 7

Comparison of vibration measurements with the speckle technique (solid line, two independent measurements) and a laser Doppler vibrometer (dotted line).

Equations (10)

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I ( u ) = q p ψ ( x p ) ψ * ( x q ) exp [ i 2 π u ( x p x q ) ] ,
I ( u , ρ ) = C 0 1 T T / 2 T / 2 q p ψ ( x p ) ψ * ( x q ) × exp [ i 2 π ( x p x q ) ( u ρ cos ω t ) ] d t ,
I ( u , ρ ) = C 0 T q p ψ ( x p ) ψ * + ( x q ) J 0 [ 2 π ρ ( x p x q ) ] × exp [ i 2 π u ( x p x q ) ] .
A ( u , ρ ) = A 0 ( u ) C 1 exp ( i 2 π λ 1 d Δ n ) ,
Δ n = Δ n s C I ( u , ρ ) I ( u ) , Δ n s = n 3 r E s c 2 ,
A ( u ) = A 0 C 1 { 1 i 2 π λ 1 d Δ n } = A 0 C 1 { 1 i 2 π λ 1 d Δ n s I ( u , ρ ) I ( u ) } ,
a ( x 1 ) = A 0 C 1 crystal [ 1 i 2 π λ 1 d Δ n s I ( u , ρ ) I ( u ) ] × exp ( i 2 π λ 2 f 2 u x 1 ) d u .
a ( x 1 ) = A 0 C 1 [ δ ( x 1 ) i 2 π λ 1 d Δ n s × q ψ ( x 1 + x q ) ψ * ( x q ) I ( u ) J 0 ( 2 π λ 2 f 2 ρ x 1 ) ,
| a ( x 1 ) | 2 = | A 0 | 2 C 1 2 [ δ ( x 1 ) + ( 2 π λ 1 d Δ n s ) 2 × | q ψ ( x 1 + x q ) ψ * ( x q ) I ( u ) | 2 J 0 2 ( 2 π λ 2 f 2 ρ x 1 ) ] .
ρ = 0.76 f 2 λ 2 M x p 1 1 .

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