Abstract

We report a demonstration of phase-resolved vibrometry, in which out-of-plane sinusoidal motion is assessed by heterodyne holography. In heterodyne holography, the beam in the reference channel is an optical local oscillator (LO). It is frequency-shifted with respect to the illumination beam to enable frequency conversion within the sensor bandwidth. The proposed scheme introduces a strobe LO, where the reference beam is frequency-shifted and modulated in amplitude, to alleviate the issue of phase retrieval. The strobe LO is both tuned around the first optical modulation sideband at the vibration frequency, and modulated in amplitude to freeze selected mechanical vibration states sequentially. The phase map of the vibration can then be derived from the demodulation of successive vibration states.

© 2013 Optical Society of America

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References

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  1. R. L. Powell and K. A. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).
    [CrossRef]
  2. J. Levitt and K. Stetson, Appl. Opt. 15, 195 (1976).
    [CrossRef]
  3. P. Picart, J. Leval, D. Mounier, and S. Gougeon, Opt. Lett. 28, 1900 (2003).
    [CrossRef]
  4. G. Pedrini, W. Osten, and M. E. Gusev, Appl. Opt. 45, 3456 (2006).
    [CrossRef]
  5. C. C. Aleksoff, Appl. Opt. 10, 1329 (1971).
    [CrossRef]
  6. F. Joud, F. Laloë, M. Atlan, J. Hare, and M. Gross, Opt. Express 17, 2774 (2009).
    [CrossRef]
  7. O. J. Løkberg and K. Høgmoen, Appl. Opt. 15, 2701(1976).
    [CrossRef]
  8. S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, Opt. Lasers Eng. 36, 77 (2001).
    [CrossRef]
  9. J. Leval, P. Picart, J. P. Boileau, and J. C. Pascal, Appl. Opt. 44, 5763 (2005).
    [CrossRef]
  10. M. Hernandez-Montes, F. Mendoza Santoyo, C. Perez Lopez, S. Muñoz Solís, and J. Esquivel, Opt. Lasers Eng. 49, 698 (2011).
    [CrossRef]
  11. M. Atlan, M. Gross, and E. Absil, Opt. Lett. 32, 1456 (2007).
    [CrossRef]
  12. B. M. Hennelly and J. T. Sheridan, J. Opt. Soc. Am. A 22, 928 (2005).
    [CrossRef]
  13. B. Samson, F. Verpillat, M. Gross, and M. Atlan, Opt. Lett. 36, 1449 (2011).
    [CrossRef]

2011 (2)

M. Hernandez-Montes, F. Mendoza Santoyo, C. Perez Lopez, S. Muñoz Solís, and J. Esquivel, Opt. Lasers Eng. 49, 698 (2011).
[CrossRef]

B. Samson, F. Verpillat, M. Gross, and M. Atlan, Opt. Lett. 36, 1449 (2011).
[CrossRef]

2009 (1)

2007 (1)

2006 (1)

2005 (2)

2003 (1)

2001 (1)

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, Opt. Lasers Eng. 36, 77 (2001).
[CrossRef]

1976 (2)

1971 (1)

1965 (1)

Absil, E.

Aleksoff, C. C.

Atlan, M.

Boileau, J. P.

Bosseboeuf, A.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, Opt. Lasers Eng. 36, 77 (2001).
[CrossRef]

Danaie, K.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, Opt. Lasers Eng. 36, 77 (2001).
[CrossRef]

Esquivel, J.

M. Hernandez-Montes, F. Mendoza Santoyo, C. Perez Lopez, S. Muñoz Solís, and J. Esquivel, Opt. Lasers Eng. 49, 698 (2011).
[CrossRef]

Gilles, J.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, Opt. Lasers Eng. 36, 77 (2001).
[CrossRef]

Gougeon, S.

Gross, M.

Gusev, M. E.

Hare, J.

Hennelly, B. M.

Hernandez-Montes, M.

M. Hernandez-Montes, F. Mendoza Santoyo, C. Perez Lopez, S. Muñoz Solís, and J. Esquivel, Opt. Lasers Eng. 49, 698 (2011).
[CrossRef]

Høgmoen, K.

Joud, F.

Laloë, F.

Leval, J.

Levitt, J.

Løkberg, O. J.

Mendoza Santoyo, F.

M. Hernandez-Montes, F. Mendoza Santoyo, C. Perez Lopez, S. Muñoz Solís, and J. Esquivel, Opt. Lasers Eng. 49, 698 (2011).
[CrossRef]

Mounier, D.

Muñoz Solís, S.

M. Hernandez-Montes, F. Mendoza Santoyo, C. Perez Lopez, S. Muñoz Solís, and J. Esquivel, Opt. Lasers Eng. 49, 698 (2011).
[CrossRef]

Osten, W.

Pascal, J. C.

Pedrini, G.

Perez Lopez, C.

M. Hernandez-Montes, F. Mendoza Santoyo, C. Perez Lopez, S. Muñoz Solís, and J. Esquivel, Opt. Lasers Eng. 49, 698 (2011).
[CrossRef]

Petitgrand, S.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, Opt. Lasers Eng. 36, 77 (2001).
[CrossRef]

Picart, P.

Powell, R. L.

Samson, B.

Sheridan, J. T.

Stetson, K.

Stetson, K. A.

Verpillat, F.

Yahiaoui, R.

S. Petitgrand, R. Yahiaoui, K. Danaie, A. Bosseboeuf, and J. Gilles, Opt. Lasers Eng. 36, 77 (2001).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Sketch of the optical setup.

Fig. 2.
Fig. 2.

Chronogram of signal acquisition over (a) n and (b) m×n successive frames. Sine: mechanical excitation signal, pulse: strobe LO signal.

Fig. 3.
Fig. 3.

Out-of-plane vibration maps of a silicon wafer excited at (a, b) 142 kHz and (c, d) 151 kHz. Amplitude maps (a, c), in arbitrary units; black, nodes; white, antinodes. Phase maps (b, d): black, 0 rad; white, πrad.

Fig. 4.
Fig. 4.

(a) Amplitude (black, nodes; white, antinodes) and (b–d) phase maps of a vibrating sheet of paper with (c) no phase shift and (d) π phase shift between the excitation and the strobe illumination. The phase image rendered without strobe demodulation does not exhibit the vibration phase retardation (b). Dark and light gray regions within the object in (c) and (d) are in phase opposition, as shown in cuts reported in Fig. 5.

Fig. 5.
Fig. 5.

(a) Cuts of the vibrating object, along AB and AB in Figs. 4(c) and 4(d). (b) Measured phase of an antinode in Fig. 4 (circles) versus phase detuning between the excitation and the illumination patterns (lines).

Equations (3)

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ωP=ωM+ωS/(nm).
Mp=k=1nIk+(p1)nexp(2iπkn).
Q=p=1m|Mp|2exp(2iπpm).

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