Abstract

An instrument for noncontact measurement of differential vibrations is developed, based on the self-mixing interferometer. As no reference arm is available in the self-mixing configuration, the differential mode is obtained by electronic subtraction of signals from two (nominally equal) vibrometer channels, taking advantage that channels are servo stabilized and thus insensitive to speckle and other sources of amplitude fluctuation. We show that electronic subtraction is nearly as effective as field superposition. Common-mode suppression is 2530dB, the dynamic range (amplitude) is in excess of 100μm, and the minimum measurable (differential) amplitude is 20nm on a B=10kHz bandwidth. The instrument has been used to measure vibrations of two metal samples kept in contact, revealing the hysteresis cycle in the microslip and gross-slip regimes, which are of interest in the study of friction induced vibration damping of gas turbine blades for aircraft applications.

© 2006 Optical Society of America

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References

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  1. S. Donati, Electro-Optical Instrumentation--Sensing and Measuring with Lasers (Prentice Hall, 2004).
  2. G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A 4, S283-S294 (2002).
    [CrossRef]
  3. S. Donati, G. Giuliani, and S. Merlo, "Laser diode feedback interferometer for measurement of displacements without ambiguity," IEEE J. Quantum Electron. 31, 113-119 (1995).
    [CrossRef]
  4. M. Norgia, S. Donati, and A. D'Alessandro, "Interferometric measurement of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
    [CrossRef]
  5. M. Norgia and S. Donati, "A displacement measuring Instrument utilizing self-mixing inteferometry," IEEE Trans. Instrum. Meas. 52, 1765-1769 (2003).
    [CrossRef]
  6. F. Gouaux, N. Servagent, and T. Bosch, "Absolute distance measurement with an optical feedback interferometer," Appl. Opt. 37, 6684-6689 (1998).
    [CrossRef]
  7. G. Giuliani, S. Bozzi-Pietra, and S. Donati, "Self-mixing laser diode vibrometer," Meas. Sci. Technol. 14, 24-32 (2003).
    [CrossRef]
  8. N. Servagent, T. Bosch, and M. Lescure, "A laser displacement sensor using the self-mixing effect for modal analysis and defect detection," IEEE Trans. Instrum. Meas. 46, 847-850 (1997).
    [CrossRef]
  9. G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
    [CrossRef]
  10. J. H. Griffin, "A review of friction damping of turbine blade vibration," Int. J. Turbo Jet Eng. 7, 297-307 (1990).
    [CrossRef]
  11. A. V. Srinivasan, "Flutter and resonant vibration characteristics of engine blades," J. Eng. Gas Turbines Power 119, 742-775 (1997).
    [CrossRef]
  12. S. Filippi, A. Akay, and M. M. Gola, "Measurement of tangential contact hysteresis during microslip," J. Tribol. 126, 482-489 (2004).
    [CrossRef]

2004 (1)

S. Filippi, A. Akay, and M. M. Gola, "Measurement of tangential contact hysteresis during microslip," J. Tribol. 126, 482-489 (2004).
[CrossRef]

2003 (2)

M. Norgia and S. Donati, "A displacement measuring Instrument utilizing self-mixing inteferometry," IEEE Trans. Instrum. Meas. 52, 1765-1769 (2003).
[CrossRef]

G. Giuliani, S. Bozzi-Pietra, and S. Donati, "Self-mixing laser diode vibrometer," Meas. Sci. Technol. 14, 24-32 (2003).
[CrossRef]

2002 (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A 4, S283-S294 (2002).
[CrossRef]

2001 (2)

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
[CrossRef]

M. Norgia, S. Donati, and A. D'Alessandro, "Interferometric measurement of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

1998 (1)

1997 (2)

N. Servagent, T. Bosch, and M. Lescure, "A laser displacement sensor using the self-mixing effect for modal analysis and defect detection," IEEE Trans. Instrum. Meas. 46, 847-850 (1997).
[CrossRef]

A. V. Srinivasan, "Flutter and resonant vibration characteristics of engine blades," J. Eng. Gas Turbines Power 119, 742-775 (1997).
[CrossRef]

1995 (1)

S. Donati, G. Giuliani, and S. Merlo, "Laser diode feedback interferometer for measurement of displacements without ambiguity," IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

1990 (1)

J. H. Griffin, "A review of friction damping of turbine blade vibration," Int. J. Turbo Jet Eng. 7, 297-307 (1990).
[CrossRef]

Akay, A.

S. Filippi, A. Akay, and M. M. Gola, "Measurement of tangential contact hysteresis during microslip," J. Tribol. 126, 482-489 (2004).
[CrossRef]

Bosch, T.

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A 4, S283-S294 (2002).
[CrossRef]

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
[CrossRef]

F. Gouaux, N. Servagent, and T. Bosch, "Absolute distance measurement with an optical feedback interferometer," Appl. Opt. 37, 6684-6689 (1998).
[CrossRef]

N. Servagent, T. Bosch, and M. Lescure, "A laser displacement sensor using the self-mixing effect for modal analysis and defect detection," IEEE Trans. Instrum. Meas. 46, 847-850 (1997).
[CrossRef]

Bozzi-Pietra, S.

G. Giuliani, S. Bozzi-Pietra, and S. Donati, "Self-mixing laser diode vibrometer," Meas. Sci. Technol. 14, 24-32 (2003).
[CrossRef]

D'Alessandro, A.

M. Norgia, S. Donati, and A. D'Alessandro, "Interferometric measurement of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

Donati, S.

M. Norgia and S. Donati, "A displacement measuring Instrument utilizing self-mixing inteferometry," IEEE Trans. Instrum. Meas. 52, 1765-1769 (2003).
[CrossRef]

G. Giuliani, S. Bozzi-Pietra, and S. Donati, "Self-mixing laser diode vibrometer," Meas. Sci. Technol. 14, 24-32 (2003).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A 4, S283-S294 (2002).
[CrossRef]

M. Norgia, S. Donati, and A. D'Alessandro, "Interferometric measurement of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo, "Laser diode feedback interferometer for measurement of displacements without ambiguity," IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

S. Donati, Electro-Optical Instrumentation--Sensing and Measuring with Lasers (Prentice Hall, 2004).

Filippi, S.

S. Filippi, A. Akay, and M. M. Gola, "Measurement of tangential contact hysteresis during microslip," J. Tribol. 126, 482-489 (2004).
[CrossRef]

Giuliani, G.

G. Giuliani, S. Bozzi-Pietra, and S. Donati, "Self-mixing laser diode vibrometer," Meas. Sci. Technol. 14, 24-32 (2003).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A 4, S283-S294 (2002).
[CrossRef]

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
[CrossRef]

S. Donati, G. Giuliani, and S. Merlo, "Laser diode feedback interferometer for measurement of displacements without ambiguity," IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

Gola, M. M.

S. Filippi, A. Akay, and M. M. Gola, "Measurement of tangential contact hysteresis during microslip," J. Tribol. 126, 482-489 (2004).
[CrossRef]

Gouaux, F.

Griffin, J. H.

J. H. Griffin, "A review of friction damping of turbine blade vibration," Int. J. Turbo Jet Eng. 7, 297-307 (1990).
[CrossRef]

Lescure, M.

N. Servagent, T. Bosch, and M. Lescure, "A laser displacement sensor using the self-mixing effect for modal analysis and defect detection," IEEE Trans. Instrum. Meas. 46, 847-850 (1997).
[CrossRef]

Merlo, S.

S. Donati, G. Giuliani, and S. Merlo, "Laser diode feedback interferometer for measurement of displacements without ambiguity," IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

Norgia, M.

M. Norgia and S. Donati, "A displacement measuring Instrument utilizing self-mixing inteferometry," IEEE Trans. Instrum. Meas. 52, 1765-1769 (2003).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A 4, S283-S294 (2002).
[CrossRef]

M. Norgia, S. Donati, and A. D'Alessandro, "Interferometric measurement of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

Passerini, M.

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
[CrossRef]

Servagent, N.

F. Gouaux, N. Servagent, and T. Bosch, "Absolute distance measurement with an optical feedback interferometer," Appl. Opt. 37, 6684-6689 (1998).
[CrossRef]

N. Servagent, T. Bosch, and M. Lescure, "A laser displacement sensor using the self-mixing effect for modal analysis and defect detection," IEEE Trans. Instrum. Meas. 46, 847-850 (1997).
[CrossRef]

Srinivasan, A. V.

A. V. Srinivasan, "Flutter and resonant vibration characteristics of engine blades," J. Eng. Gas Turbines Power 119, 742-775 (1997).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

S. Donati, G. Giuliani, and S. Merlo, "Laser diode feedback interferometer for measurement of displacements without ambiguity," IEEE J. Quantum Electron. 31, 113-119 (1995).
[CrossRef]

M. Norgia, S. Donati, and A. D'Alessandro, "Interferometric measurement of displacement on a diffusing target by a speckle tracking technique," IEEE J. Quantum Electron. 37, 800-806 (2001).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

M. Norgia and S. Donati, "A displacement measuring Instrument utilizing self-mixing inteferometry," IEEE Trans. Instrum. Meas. 52, 1765-1769 (2003).
[CrossRef]

N. Servagent, T. Bosch, and M. Lescure, "A laser displacement sensor using the self-mixing effect for modal analysis and defect detection," IEEE Trans. Instrum. Meas. 46, 847-850 (1997).
[CrossRef]

Int. J. Turbo Jet Eng. (1)

J. H. Griffin, "A review of friction damping of turbine blade vibration," Int. J. Turbo Jet Eng. 7, 297-307 (1990).
[CrossRef]

J. Eng. Gas Turbines Power (1)

A. V. Srinivasan, "Flutter and resonant vibration characteristics of engine blades," J. Eng. Gas Turbines Power 119, 742-775 (1997).
[CrossRef]

J. Opt. A (1)

G. Giuliani, M. Norgia, S. Donati, and T. Bosch, "Laser diode self-mixing technique for sensing applications," J. Opt. A 4, S283-S294 (2002).
[CrossRef]

J. Tribol. (1)

S. Filippi, A. Akay, and M. M. Gola, "Measurement of tangential contact hysteresis during microslip," J. Tribol. 126, 482-489 (2004).
[CrossRef]

Meas. Sci. Technol. (1)

G. Giuliani, S. Bozzi-Pietra, and S. Donati, "Self-mixing laser diode vibrometer," Meas. Sci. Technol. 14, 24-32 (2003).
[CrossRef]

Opt. Eng. (1)

G. Giuliani, S. Donati, M. Passerini, and T. Bosch, "Angle measurement by injection detection in a laser diode," Opt. Eng. 40, 95-99 (2001).
[CrossRef]

Other (1)

S. Donati, Electro-Optical Instrumentation--Sensing and Measuring with Lasers (Prentice Hall, 2004).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the optical head: an 825 nm semiconductor laser (DL) is used as the source, and its monitor photodiode (PD) is mounted internally in the package, behind the rear mirror, is the detector of the SMI. An anamorphic objective lens is used to collimate the beam and direct it onto the diffusing target. A transimpedance amplifier brings the photocurrent to a level large enough for subsequent signal processing.

Fig. 2
Fig. 2

Driving the target with a sine wave, the SMI signal resembles the normal (Bessel-like) interferometric signal at low injection levels ( C 0.5 ) . At increased C factors, the signal is progressively distorted and then becomes a sawtoothlike waveform (bottom, C 3.5 ).

Fig. 3
Fig. 3

Working at C > 1 , the SMI can be stabilized at half-fringe (left) by a simple feedback loop (right) feeding back to the bias current of the DL from the amplified SMI signal.

Fig. 4
Fig. 4

Block scheme of the self-mixing differential vibrometer based on the electronic subtraction of output signals of two nominally identical channels.

Fig. 5
Fig. 5

Top, geometric arrangement of the two optical heads and targets, showing the laser beams in normal operation (solid lines) and during calibration (dashed lines). Bottom, arrangement of the forces applied to the rig assembly carrying the two beadlike targets.

Fig. 6
Fig. 6

Maximum measurable peak-to-peak vibration amplitude for the two individual vibrometer channels as a function of frequency, and minimum detectable signal (at S / N = 1 ). Measurements are relative to a white paper surface, placed at a 40 cm distance from the optical heads.

Fig. 7
Fig. 7

Picture of the assembled differential vibrometer.

Fig. 8
Fig. 8

(a) Time-domain traces for the tangential force (as in Fig. 5) and the differential displacement for the case of gross slip of the contact between the two vibrating samples. The master sample is driven by at 84 Hz , and it vibrates harmonically with an amplitude of 100 μm peak to peak. Bottom trace is the corresponding displacement waveform (amplitude 20 μm peak to peak). (b) Plot of the tangential force–differential displacement revealing the hysteresis.

Equations (6)

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P ( ϕ ) = P 0 [ 1 + m F ( ϕ ) ] ,
Δ V = R I 0 sin Δ Φ R I 0 ΔΦ ,
I ph = I ph 0 + I 0 cos ΔΦ .
Δ I bias = G m A Δ V ,
A loop = 2 k s ( α λ / λ ) I 0 G m A R ,
Δ V = [ α λ G m ] - 1 Δ s ( λ / s ) .

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