Abstract

Real-time vibration measurement with a high accuracy is described in which a He-Ne laser interferometer and a feedback control system are used. The measured vibration waveform is calculated as the sum of two measured waveforms obtained from the controller output signal and the feedback signal in the feedback system, respectively. This calculation method provides an exact measured vibration amplitude with error less than about 8 nanometers at the vibration frequency of 100 Hz. The vibration amplitude measured from only the controller output signal has an error less than about 21 nanometers. The maximum measurable amplitude decreases from 1935nm to 903 nm when the vibration frequency increases from 50 Hz to 500 Hz.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25(18), 3137–3140 (1986).
    [Crossref]
  2. O. Sasaki and K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27(19), 4139–4142 (1988).
    [Crossref]
  3. M. J. Connelly, J. H. Galeti, and C. Kitano, “Michelson interferometer vibrometer using self-correcting synthetic-heterodyne demodulation,” Appl. Opt. 54(18), 5734–5738 (2015).
    [Crossref]
  4. J. H. Galeti, C. Kitano, and J. Connelly, “Improved synthetic-heterodyne Michelson interferometer vibrometer using phase and gain control feedback,” Appl. Opt. 54(35), 10418–10424 (2015).
    [Crossref]
  5. O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
    [Crossref]
  6. T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
    [Crossref]

2015 (2)

1997 (1)

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

1990 (1)

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

1988 (1)

1986 (1)

Connelly, J.

Connelly, M. J.

Galeti, J. H.

Kitano, C.

Maruyama, T.

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

Okada, T.

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

Okazaki, H.

Sasaki, O.

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

O. Sasaki and K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27(19), 4139–4142 (1988).
[Crossref]

O. Sasaki and H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25(18), 3137–3140 (1986).
[Crossref]

Suzuki, T.

T. Suzuki, T. Okada, O. Sasaki, and T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36(9), 2496–2502 (1997).
[Crossref]

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

Takahashi, K.

O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29(12), 1511–1515 (1990).
[Crossref]

O. Sasaki and K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27(19), 4139–4142 (1988).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Laser interferometer for vibration measurement with a feedback system. L1 and L2: lens, PZT: piezoelectric transducer, FBSG; feedback signal generator, FBC: feedback controller, BS: beam splitter, PD: photodiode, OSCSCO: oscilloscope.
Fig. 2.
Fig. 2. Flow chart of the feedback system.
Fig. 3.
Fig. 3. Feedback signal SF(t) without feedback control system.
Fig. 4.
Fig. 4. Sinusoidal vibration dC(t) obtained from the control signal VC(t).
Fig. 5.
Fig. 5. Sinusoidal vibration dF(t) obtained from the feedback signal SF(t).
Fig. 6.
Fig. 6. Measured sinusoidal vibration d(t)=dC(t)+dF(t).
Fig. 7.
Fig. 7. Maximum measurable amplitude at different vibration frequencies.

Tables (1)

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Table 1. Experimental result at different applied voltages.

Equations (7)

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S ( t ) = A + B cos [ Z cos ( ω c t ) + α ( t ) ] ,
Z = ( 4 π / λ ) a , α ( t ) = α D ( t ) α C ( t ) + α 0 ,
S ( t ) = A + B cos α [ J 0 ( Z ) 2 J 2 ( Z ) cos ( 2 ω c t ) + ] B sin α [ 2 J 1 ( Z ) cos ( ω c t ) 2 J 3 ( Z ) cos ( 3 ω c t ) + ] ,
S F ( t ) = K sin α ( t ) = K sin [ α D ( t ) α C ( t ) ] ,
S F ( t ) = K [ α D ( t ) α C ( t ) ] .
d ( t ) = ( λ / 4 π ) α D ( t ) = ( λ / 4 π ) [ α C ( t ) + S F ( t ) / K ] = d C ( t ) + d F ( t ) ,
a D = a C + a F .

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