Abstract

A novel method is presented for of measuring absolute displacement with a synthesized wavelength interferometer. The optical phase of the interferometer is simultaneously modulated with a frequency-modulated laser diode and optical path-length difference. The error signal originating from the intensity modulation of the source is eliminated by a signal processing circuit. In addition, a lock-in technique is used to demodulate the envelope of the interferometric signal. The displacement signal is derived by the self-mixing technique.

© 1999 Optical Society of America

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References

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  1. W. M. Wang, K. T. V. Grattan, W. J. O. Boyle, A. W. Palmer, “Active optical feedback in a dual-diode laser configuration applied to displacement measurements with a wide dynamic-range,” Appl. Opt. 33, 1795–1801 (1994).
    [CrossRef] [PubMed]
  2. A. J. Denboef, “Interferometric laser range-finder using a frequency modulated diode-laser,” Appl. Opt. 26, 4545–4550 (1987).
    [CrossRef]
  3. M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier-transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
    [CrossRef] [PubMed]
  4. E. Fischer, E. Dalhoff, S. Herim, U. Hofbauer, H. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 34, 5589–5594 (1995).
    [CrossRef] [PubMed]
  5. A. J. Denboef, “Two-wavelength scanning spot interferometer using single-frequency diode-laser,” Appl. Opt. 27, 306–311 (1988).
    [CrossRef]
  6. Y. J. Rao, D. A. Jackson, L. Zhang, I. Bennion, “Dual-cavity interferometric wavelength-shift detection for in-fiber Bragg grating sensors,” Opt. Lett. 21, 1556–1558 (1996).
    [CrossRef] [PubMed]
  7. K. P. Koo, A. D. Kersey, “Bragg grating-based laser sensors system with interferometric interrogation and wavelength-division multiplexing,” J. Lightwave Technol. 13, 1243–1249 (1995).
    [CrossRef]
  8. P. Y. Chien, R. P. Pan, C. L. Pan, “Double phase modulation approach to an interferometric system,” Opt. Commun. 93, 39–43 (1992).
    [CrossRef]
  9. R. Onodera, Y. Ishii, “Effect of beat frequency on the measured phase of laser-diode heterodyne interferometry,” Appl. Opt. 22, 4355–4360 (1996).
    [CrossRef]
  10. V. Mahal, A. Arie, “Distance measurements using two frequency-stabilized Nd–YAG lasers,” Appl. Opt. 35, 3010–3015 (1996).
    [CrossRef] [PubMed]

1996 (3)

1995 (2)

E. Fischer, E. Dalhoff, S. Herim, U. Hofbauer, H. Tiziani, “Absolute interferometric distance measurement using a FM-demodulation technique,” Appl. Opt. 34, 5589–5594 (1995).
[CrossRef] [PubMed]

K. P. Koo, A. D. Kersey, “Bragg grating-based laser sensors system with interferometric interrogation and wavelength-division multiplexing,” J. Lightwave Technol. 13, 1243–1249 (1995).
[CrossRef]

1994 (1)

1992 (1)

P. Y. Chien, R. P. Pan, C. L. Pan, “Double phase modulation approach to an interferometric system,” Opt. Commun. 93, 39–43 (1992).
[CrossRef]

1991 (1)

1988 (1)

1987 (1)

Arie, A.

Bennion, I.

Boyle, W. J. O.

Chien, P. Y.

P. Y. Chien, R. P. Pan, C. L. Pan, “Double phase modulation approach to an interferometric system,” Opt. Commun. 93, 39–43 (1992).
[CrossRef]

Dalhoff, E.

Denboef, A. J.

Fischer, E.

Grattan, K. T. V.

Herim, S.

Hofbauer, U.

Ishii, Y.

R. Onodera, Y. Ishii, “Effect of beat frequency on the measured phase of laser-diode heterodyne interferometry,” Appl. Opt. 22, 4355–4360 (1996).
[CrossRef]

Jackson, D. A.

Kersey, A. D.

K. P. Koo, A. D. Kersey, “Bragg grating-based laser sensors system with interferometric interrogation and wavelength-division multiplexing,” J. Lightwave Technol. 13, 1243–1249 (1995).
[CrossRef]

Koo, K. P.

K. P. Koo, A. D. Kersey, “Bragg grating-based laser sensors system with interferometric interrogation and wavelength-division multiplexing,” J. Lightwave Technol. 13, 1243–1249 (1995).
[CrossRef]

Mahal, V.

Onodera, R.

R. Onodera, Y. Ishii, “Effect of beat frequency on the measured phase of laser-diode heterodyne interferometry,” Appl. Opt. 22, 4355–4360 (1996).
[CrossRef]

Palmer, A. W.

Pan, C. L.

P. Y. Chien, R. P. Pan, C. L. Pan, “Double phase modulation approach to an interferometric system,” Opt. Commun. 93, 39–43 (1992).
[CrossRef]

Pan, R. P.

P. Y. Chien, R. P. Pan, C. L. Pan, “Double phase modulation approach to an interferometric system,” Opt. Commun. 93, 39–43 (1992).
[CrossRef]

Rao, Y. J.

Suematsu, M.

Takeda, M.

Tiziani, H.

Wang, W. M.

Zhang, L.

Appl. Opt. (7)

J. Lightwave Technol. (1)

K. P. Koo, A. D. Kersey, “Bragg grating-based laser sensors system with interferometric interrogation and wavelength-division multiplexing,” J. Lightwave Technol. 13, 1243–1249 (1995).
[CrossRef]

Opt. Commun. (1)

P. Y. Chien, R. P. Pan, C. L. Pan, “Double phase modulation approach to an interferometric system,” Opt. Commun. 93, 39–43 (1992).
[CrossRef]

Opt. Lett. (1)

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Figures (7)

Fig. 1
Fig. 1

Experimental setup of the tested system.

Fig. 2
Fig. 2

Electric signal processing diagram of lock-in and self-mixing detection techniques.

Fig. 3
Fig. 3

Experimental results for (a) the optical interferometer under double modulation, and (b) the demodulated output signal.

Fig. 4
Fig. 4

Experimental results for (a) the demodulated signal, (b) the gating signal, (c) the gated signal and (d) the self-mixing signal.

Fig. 5
Fig. 5

Measured displacement output over several centimeters in range.

Fig. 6
Fig. 6

Long-term stability of the system under a fixed displacement.

Fig. 7
Fig. 7

Measured output with displacement step changes of 100 µm.

Equations (10)

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ν=νo+νm sin ωmt,
Err, t=1/2Eotexpj2πνt, Etr, t=1/2Eotexpj2πνt,
Err, t=1/4Eot-Lr/cexpj2πνt-Lr/c, Etr, t=1/4Eot-Lt/cexpj2πνt-Lt/c.
Iout=1/16Err, t+Etr, t·Err, t+Etr, t*=1/16|Eot-Lr/c|2+|Eot-Lt/c|2+2Eot-Lr/c·Eo*t-Lt/ccos2πνLt/c-Lr/c=Io/161+m sin ωmt1+cos2πνo+νm sin ωmtLt/c-Lr/c=Io/161+m sin ωmt[1+cosϕt-ϕr+ϕm sin ωmt,
ϕt=2πνoLt/c, ϕr=2πνoLr/c, ϕm=2πνmLt-Lr/c.
Iout=Io/16cosϕt-ϕr+ϕm sin ωmt=Io/16cosϕt-ϕrcosϕm sin ωmt-sinϕt-ϕrsinϕm sin ωmt=Io/16cosϕt-ϕrJ0ϕm+2J2ϕmcos2ωmt++sinϕt-ϕr[2J1ϕmsinωmt+2J3ϕmsin3ωmt+,
I3ω=Io/16sinϕt-ϕrJ3ϕm.
Ld=Lo+Lp sin ωpt,
I3ω=Io/16sin2πνo/cLo+Lp sin ωpt×2J32πνm/cLo+Lp sin ωpt.
Ienv=KJ32πνm/cLo+Lp sin ωpt=KJ32πνm/cLo,

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