Abstract

We propose and demonstrate sub-micron displacement sensing and sensitivity enhancement using a two-frequency interferometer and a Kerr phase-interrogator. Displacement induces phase variation on a sinusoidally modulated optical signal by changing the length of the path that either of the signal’s two spectral components propagates through. A Kerr phase-interrogator converts the resulting phase variation into power variation allowing for sub-micron displacement sensing. The sensitivity of this novel displacement sensor is enhanced beyond the wavelength-limited sensitivity of the widely used Michelson interferometric displacement sensor. The proposed approach for sensitivity enhancement creates a whole new class of sensors with ultra-high sensitivity.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  10. C. Baker, Y. Lu, and X. Bao, “Chromatic-dispersion measurement by modulation phase-shift method using a Kerr phase-interrogator,” Opt. Express 22, 22314–22319 (2014).
    [Crossref] [PubMed]
  11. M. Rochette, C. Baker, and R. Ahmad, “All-optical polarization-mode dispersion monitor for return-to-zero optical signals at 40 gbits/s and beyond,” Opt. Lett. 35, 3703–3705 (2010).
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2014 (4)

2010 (1)

1996 (1)

1990 (1)

S. Bartlett, F. Farahi, and D. Jackson, “A dual resolution noncontact vibration and displacement sensor based upon a two wavelength source,” Rev. Sci. Instrum. 61, 1014–1017 (1990).
[Crossref]

1982 (2)

B. Costa, D. Mazzoni, M. Puleo, and E. Vezzoni, “Phase shift technique for the measurement of chromatic dispersion in optical fibers using led’s,” IEEE J. Quantum Electron. 18, 1509–1515 (1982).
[Crossref]

S. C. Rashleigh, “Wavelength dependence of birefringence in highly birefringent fibers,” Opt. Lett. 7, 294–296 (1982).
[Crossref] [PubMed]

1973 (1)

1972 (1)

C. R. Brown, G. R. Brown, and D. H. Niblett, “Measurement of small strain amplitudes in internal friction experiments by means of a laser interferometer,” J. Phys. E 5, 966 (1972).
[Crossref]

1970 (1)

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

Ahmad, R.

Andrews, F. A.

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

Baker, C.

Bao, X.

Bartlett, S.

S. Bartlett, F. Farahi, and D. Jackson, “A dual resolution noncontact vibration and displacement sensor based upon a two wavelength source,” Rev. Sci. Instrum. 61, 1014–1017 (1990).
[Crossref]

Boskovic, A.

Brown, C. R.

C. R. Brown, G. R. Brown, and D. H. Niblett, “Measurement of small strain amplitudes in internal friction experiments by means of a laser interferometer,” J. Phys. E 5, 966 (1972).
[Crossref]

Brown, G. R.

C. R. Brown, G. R. Brown, and D. H. Niblett, “Measurement of small strain amplitudes in internal friction experiments by means of a laser interferometer,” J. Phys. E 5, 966 (1972).
[Crossref]

Chen, L.

Chernikov, S. V.

Costa, B.

B. Costa, D. Mazzoni, M. Puleo, and E. Vezzoni, “Phase shift technique for the measurement of chromatic dispersion in optical fibers using led’s,” IEEE J. Quantum Electron. 18, 1509–1515 (1982).
[Crossref]

Eberhardt, F. J.

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

Farahi, F.

S. Bartlett, F. Farahi, and D. Jackson, “A dual resolution noncontact vibration and displacement sensor based upon a two wavelength source,” Rev. Sci. Instrum. 61, 1014–1017 (1990).
[Crossref]

Gruner-Nielsen, L.

Jackson, D.

S. Bartlett, F. Farahi, and D. Jackson, “A dual resolution noncontact vibration and displacement sensor based upon a two wavelength source,” Rev. Sci. Instrum. 61, 1014–1017 (1990).
[Crossref]

Levring, O. A.

Lu, Y.

Mazzoni, D.

B. Costa, D. Mazzoni, M. Puleo, and E. Vezzoni, “Phase shift technique for the measurement of chromatic dispersion in optical fibers using led’s,” IEEE J. Quantum Electron. 18, 1509–1515 (1982).
[Crossref]

Niblett, D. H.

C. R. Brown, G. R. Brown, and D. H. Niblett, “Measurement of small strain amplitudes in internal friction experiments by means of a laser interferometer,” J. Phys. E 5, 966 (1972).
[Crossref]

Pernick, B. J.

Puleo, M.

B. Costa, D. Mazzoni, M. Puleo, and E. Vezzoni, “Phase shift technique for the measurement of chromatic dispersion in optical fibers using led’s,” IEEE J. Quantum Electron. 18, 1509–1515 (1982).
[Crossref]

Rashleigh, S. C.

Rochette, M.

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[Crossref]

Song, J.

Taylor, J. R.

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[Crossref]

Vezzoni, E.

B. Costa, D. Mazzoni, M. Puleo, and E. Vezzoni, “Phase shift technique for the measurement of chromatic dispersion in optical fibers using led’s,” IEEE J. Quantum Electron. 18, 1509–1515 (1982).
[Crossref]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

B. Costa, D. Mazzoni, M. Puleo, and E. Vezzoni, “Phase shift technique for the measurement of chromatic dispersion in optical fibers using led’s,” IEEE J. Quantum Electron. 18, 1509–1515 (1982).
[Crossref]

J. Acoust. Soc. Am. (1)

F. J. Eberhardt and F. A. Andrews, “Laser heterodyne system for measurement and analysis of vibration,” J. Acoust. Soc. Am. 48, 603–609 (1970).
[Crossref]

J. Lightwave Technol. (1)

J. Phys. E (1)

C. R. Brown, G. R. Brown, and D. H. Niblett, “Measurement of small strain amplitudes in internal friction experiments by means of a laser interferometer,” J. Phys. E 5, 966 (1972).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

S. Bartlett, F. Farahi, and D. Jackson, “A dual resolution noncontact vibration and displacement sensor based upon a two wavelength source,” Rev. Sci. Instrum. 61, 1014–1017 (1990).
[Crossref]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematic of the sub-micron displacement measurement setup based on a Kerr phase-interrogator and a two-frequency IDS. RF: radio-frequency; CW: continuous-wave; EOM: electro-optic modulator; PSD: power spectral density; PC: polarization controller; FPS: fiber polarization splitter; FPC: fiber polarization combiner; PM: polarization maintaining; PBS: polarization beam splitter; M: mirror; and EDFA: Erbium-doped fiber amplifier.
Fig. 2
Fig. 2 Normalized power of the first order-sideband as a function of phase calculated using Eq. (5) for ϕSPM = 0.5, 5, 10, and 50.
Fig. 3
Fig. 3 Exact and approximate values of P1 as a function of ϕ calculated using Eq. (5) and Eq. (6) with a) ϕSPM = 5, b) ϕSPM = 10, and c) ϕSPM = 1000.
Fig. 4
Fig. 4 Experimentally measured and theoretically calculated side-band power as a function of displacement for ϕSPM < 0.5.
Fig. 5
Fig. 5 Experimental measurements of power as a function of displacement for ϕSPM = 5.

Equations (7)

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A = P p / 2 cos ( π f s t + ϕ ) ,
A = P p / 2 cos ( π f s t + ϕ ) ,
P 1 = P 1 max cos 2 ( ϕ )
σ = max { | d P 1 / d D | / P 1 max } = 2 π / λ 1 .
P 1 ( ϕ ) = P p × { J 1 2 [ ( ϕ S P M / 2 ) cos ( ϕ ) ] + J 2 2 [ ( ϕ S P M / 2 ) cos ( ϕ ) ] }
P 1 ( ϕ ) = P 1 max sin 2 [ 0.36 × ϕ S P M × ( ϕ π / 2 m π ) ]
σ = max { | d P 1 / d D | / P 1 max } = 0.36 ϕ S P M × ( 2 π / λ 1 ) ,

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