Abstract

A simple method for imaging vibrational motion is proposed. The process consists of capturing two speckled images of a region illuminated by coherent radiation. One of the images is captured before the onset of motion and the other during motion. If the mean speckle intensity is below the threshold for detection or above the saturation intensity of the detector, subtracting the two images produces a high contrast image of the moving region. A theory is shown to agree well with experimental data.

© 2010 Optical Society of America

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References

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  1. N.-E. Molin, “Optical methods for acoustics and vibration measurements,” in Handbook of Acoustics, T.Rossing, ed. (Springer, 2007), pp. 1101–1123.
    [CrossRef]
  2. D. D. Duncan and S. J. Kirkpatrick, “Can laser speckle flowmetry be made a quantitative tool?” J. Opt. Soc. Am. A 25, 2088–2094 (2008).
    [CrossRef]
  3. A. R. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
    [CrossRef]
  4. G. Parry, “Speckle patterns in partially coherent light,” inLaser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1984), pp. 77–122.

2008

1980

A. R. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
[CrossRef]

Duncan, D. D.

Fercher, A. R.

A. R. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
[CrossRef]

Kirkpatrick, S. J.

Molin, N.-E.

N.-E. Molin, “Optical methods for acoustics and vibration measurements,” in Handbook of Acoustics, T.Rossing, ed. (Springer, 2007), pp. 1101–1123.
[CrossRef]

Parry, G.

G. Parry, “Speckle patterns in partially coherent light,” inLaser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1984), pp. 77–122.

J. Opt. Soc. Am. A

Opt. Commun.

A. R. Fercher, “Velocity measurement by first order statistics of time-differentiated laser speckles,” Opt. Commun. 33, 129–135 (1980).
[CrossRef]

Other

G. Parry, “Speckle patterns in partially coherent light,” inLaser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1984), pp. 77–122.

N.-E. Molin, “Optical methods for acoustics and vibration measurements,” in Handbook of Acoustics, T.Rossing, ed. (Springer, 2007), pp. 1101–1123.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Plot of the mean recorded intensity of the speckle as a function of speckle contrast predicted by Eq. (5) for three different values of the detector threshold.

Fig. 2
Fig. 2

Plot of the visibility of SSI as a function of γ 1 for three different values of γ 2 . The threshold for detection is assumed to be twice the mean intensity of the speckle ( I L = 2 I ) .

Fig. 3
Fig. 3

Plot of the normalized intensity of SSI image as a function of contrast for three different threshold values. The curves represent the predictions of Eq. (5).

Fig. 4
Fig. 4

Plot of the visibility of the piezoelectric disk as a function of the amplitude of vibration.

Equations (10)

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K = σ I ,
I = 0 I P ( I ) d I ,
P M ( I ) = ( M ) M I M 1 I M Γ ( M ) e M I I ,
I SSI ( M 1 , M 2 ) = | { I L I U ( I I L ) P M 1 ( I ) d I + I U ( I U ) P M 1 ( I ) d I } { I L I U ( I I L ) P M 2 ( I ) d I + I U ( I U ) P M 2 ( I ) d I } | ,
I SSI ( M 1 , M 2 ) = | I L I U ( I I L ) { P M 1 ( I ) P M 2 ( I ) } d I + ( I U ) I U { P M 1 ( I ) P M 2 ( I ) } d I | .
I SSI ( M 1 , M 2 ) | I L I U ( I I L ) { P M 1 ( I ) P M 2 ( I ) } d I | .
K n = γ n γ n 2 2 ( 1 e 2 γ n ) ,
γ n = τ n T .
V = | I 1 I 2 I 1 + I 2 | ,
d = 1.22 ( 1 + m ) λ f ,

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