Abstract

Vibrational motion of a harmonic oscillator was investigated with a focused continuous-wave (cw) CO2 Doppler lidar at 9.1-μm wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation. For vigorous vibration of the oscillator, the observed spectra may be indicating nonlinear motion.

© 2000 Optical Society of America

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References

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1997 (1)

1996 (4)

1981 (1)

1971 (1)

Bowdle, D. A.

Briers, J. D.

Chambers, D. M.

Chebbour, A.

Courteville, A.

Dandliker, R.

Ebert, R.

R. Ebert, “Remote vibration sensing for target reconnaissance,” in Proceedings of the Ninth Conference on Coherent Laser Radar [Defence Research Establishment (FOA), Linkoping, Sweden, 1997], pp. 224–227.

Gharbi, T.

Horrigan, F. A.

Jarzembski, M. A.

Jones, W. D.

Lerou, R. J. L.

R. J. L. Lerou, “Long range vibration sensing by lasers,” in Proceedings of the Ninth Conference on Coherent Laser Radar [Defence Research Establishment (FOA), Linkoping, Sweden, 1997], pp. 208–211.

Lucas, M.

Miles, T.

Rothberg, S.

Rothermel, J.

Sonnenschein, C. M.

Srivastava, V.

Willemin, J.-F.

Appl. Opt. (4)

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

Opt. Lett. (2)

Other (2)

R. J. L. Lerou, “Long range vibration sensing by lasers,” in Proceedings of the Ninth Conference on Coherent Laser Radar [Defence Research Establishment (FOA), Linkoping, Sweden, 1997], pp. 208–211.

R. Ebert, “Remote vibration sensing for target reconnaissance,” in Proceedings of the Ninth Conference on Coherent Laser Radar [Defence Research Establishment (FOA), Linkoping, Sweden, 1997], pp. 224–227.

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Figures (3)

Fig. 1
Fig. 1

Experimental arrangement for measuring backscatter using a cw CO2 Doppler lidar from a vibrating tuning fork that has been electrically driven.

Fig. 2
Fig. 2

Backscatter power spectra from a vibrating tuning fork that has been electrically driven (as shown in Fig. 1) as a function of applied voltage on the magnet for various cases of oscilloscope resolution. For all spectra the amplitude is 10 dB/div.

Fig. 3
Fig. 3

Backscatter power spectra from a pneumatic pump operating at 60 Hz for two cases of oscilloscope resolution. For both spectra the amplitude is 10 dB/div.

Tables (1)

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Table 1 Resonant f Modes for y0  λ = 9.1 μm

Equations (6)

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f=2v cos θλ,
f=4πy0cos(2πf0t)λf0.
fn=nf0,
tn=(2πf0)-1cos-1nλ4πy0.
yn=y01-nλ4πy021/2.
vn=nλf02.

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