Abstract

In the measurement of the amplitude of vibration of objects, holographic imaging techniques usually involve fringe counting; because of the limited resolution of the images, measurements of large amplitudes are not accessible. We demonstrate a technique that suppresses the necessity of fringe counting—frequency sideband imaging—where the order of the sideband is considered a marker of the amplitude. The measurement is completely local: no comparison with another reference point on the object is necessary. It involves a sharp variation of a signal, which makes it robust against perturbations. The method is demonstrated in an experiment made with a vibrating clarinet reed; phase modulations as large as 1000rad have been measured.

© 2009 Optical Society of America

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References

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2009 (1)

2006 (2)

2004 (1)

F. Zhang, J. Valera, I. Yamaguchi, M. Yokota, and G. Mills, Opt. Rev. 11, 297 (2004).
[CrossRef]

2003 (1)

1994 (2)

1971 (1)

1965 (1)

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table (Courier Dover, 1965).

Aleksoff, C.

Atlan, M.

Dunn, A.

Forget, B.

Gougeon, S.

Gross, M.

Hare, J.

Joud, F.

Jüptner, W.

Laloë, F.

Leval, J.

Lokberg, O.

O. Lokberg, J. Acoust. Soc. Am. 96, 2244 (1994).
[CrossRef]

Mills, G.

F. Zhang, J. Valera, I. Yamaguchi, M. Yokota, and G. Mills, Opt. Rev. 11, 297 (2004).
[CrossRef]

Mounier, D.

Picart, P.

Powell, R.

Rancillac, A.

Schnars, U.

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table (Courier Dover, 1965).

Stetson, K.

Valera, J.

F. Zhang, J. Valera, I. Yamaguchi, M. Yokota, and G. Mills, Opt. Rev. 11, 297 (2004).
[CrossRef]

Vitalis, T.

Yamaguchi, I.

F. Zhang, J. Valera, I. Yamaguchi, M. Yokota, and G. Mills, Opt. Rev. 11, 297 (2004).
[CrossRef]

Yokota, M.

F. Zhang, J. Valera, I. Yamaguchi, M. Yokota, and G. Mills, Opt. Rev. 11, 297 (2004).
[CrossRef]

Zhang, F.

F. Zhang, J. Valera, I. Yamaguchi, M. Yokota, and G. Mills, Opt. Rev. 11, 297 (2004).
[CrossRef]

Appl. Opt. (2)

J. Acoust. Soc. Am. (1)

O. Lokberg, J. Acoust. Soc. Am. 96, 2244 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (1)

Opt. Lett. (2)

Opt. Rev. (1)

F. Zhang, J. Valera, I. Yamaguchi, M. Yokota, and G. Mills, Opt. Rev. 11, 297 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Atlan and M. Gross, Rev. Sci. Instrum. 77, 116103 (2006).
[CrossRef]

Other (1)

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table (Courier Dover, 1965).

Supplementary Material (1)

» Media 1: JPG (505 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Relative intensities of the sidebands as a function of n for fixed Φ = 30.3 rad . The vertical lines show the intensities of the discrete n components of the real spectrum. The light gray shade shows the Doppler spectrum obtained from the vibration velocity distribution, with a continuous variable on the horizontal axis n = ( ν ν 0 ) ν A . Both spectra fall abruptly beyond n = ± 30.3 , which corresponds to the Doppler shift associated with the maximum velocity. (b) The dashed line shows the values n 1 as a function of Φ, where n 1 is the value of n giving the maximum intensity in the discrete spectrum; the solid line shows n 2 , where n 2 is the value of n for which the intensity is half the maximum, which gives a very good approximation of Φ. (c) The dashed and solid curves, respectively, show n 1 Φ and n 2 Φ as a function of Φ.

Fig. 2
Fig. 2

Cube of data obtained from the reconstructed holographic images of a vibrating clarinet reed; sideband images with n = 0 , 20 , 40 120 are shown in arbitrary linear scale. By choosing n, one moves the border of the illuminated region on the object, obtaining a local marker of the amplitude of vibration. The white dashed lines correspond to x = 249 and y = 750 , i.e., to the point chosen for Fig. 3.

Fig. 3
Fig. 3

Images corresponding to cuts of 3D data of the reconstructed images along the planes y = 750 (a) and x = 249 (b). (a) Deformation of the object along its axis. (b) Transverse cut with a slight vibration asymmetry. A logarithmic intensity scale is used.

Fig. 4
Fig. 4

(a) Image reconstructed with sideband n = 330 , with a large amplitude of vibration. (b) Equivalent of Fig. 3a, but with positive and negative n values quantized by steps Δ n = 10 ; one measures a maximum vibration amplitude of z max 60 μ m . An enlarged view of the n 0 part of the image is provided in supplementary material (Media 1). A logarithmic intensity scale is used.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

z ( t ) = z max sin ( 2 π ν A t ) .
φ ( t ) = 4 π z ( t ) λ = Φ sin ( 2 π ν A t ) ,
E ( t ) = E e j ( ν 0 t + φ ( t ) ) = E n J n ( Φ ) e j ( ν 0 + n ν A ) t ,
I n ( Φ ) = | E J n ( Φ ) | 2 .
ν 0 + n ν A ν LO ( n ) = ν CCD 4 .
H = m = 0 M 1 j m I m .

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