Abstract

A novel high-speed and high-sensitivity displacement measurement sensing system, based on the phase-locked low-coherence interferometry, is presented. The sensing system is realized by comprising the Michelson fiber-optic interferometer. In order to obtain quadrature signals at the interferometer outputs, a 3×3 fused silica fiber-optic directional coupler is used. Therefore, the usage of the interferometer phase modulation as well as the usage of the lock-in amplification has been avoided. In this way, the speed of such a realized sensing system is significantly increased in comparison with the standard phase-locked interferometric systems that can be found elsewhere in the literature. The bandwidth of the realized sensing system is limited by the first resonance frequency of the used piezo actuator to 4.6 kHz. The estimated noise floor in the displacement measurement is approximately 180pm/Hz.

© 2012 Optical Society of America

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References

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  1. A. V. Zvyagin, I. Eix, and D. D. Sampson, “High-speed, high-sensitivity, gated surface profiling with closed-loop optical coherence topography,” Appl. Opt. 41, 2179–2184 (2002).
    [CrossRef]
  2. T. Suzuki, O. Sasaki, K. Higuchi, and T. Maruyama, “Phase-locked laser diode interferometer: high-speed feedback control system,” Appl. Opt. 30, 3622–3626 (1991).
    [CrossRef]
  3. D. C. Leiner, “Real-time phase microscopy using a phase-lock interferometer,” Rev. Sci. Instrum. 49, 1702–1705(1978).
    [CrossRef]
  4. J.-Y. Liu, I. Yamaguchi, J.-I. Kato, and T. Nakajima, “Real-time surface shape measurement by an active interferometer,” Opt. Rev. 4, 216–220 (1997).
    [CrossRef]
  5. J. L. Lauer and S. S. Fung, “Surface topographical changes measured by phase-locked interferometry,” NASA Contract. Rep. 3757 (NASA, 1984).
  6. L. M. Manojlović, “A simple white-light fiber-optic interferometric sensing system for absolute position measurement,” Opt. Laser Eng. 48, 486–490 (2010).
    [CrossRef]
  7. S. K. Sheem, “Optical fiber interferometer with [3×3] directional coupler: analysis,” J. Appl. Phys. 52, 3865–3872 (1981).
    [CrossRef]
  8. R. G. Priest, “Analysis of fiber interferometer utilizing 3×3 fiber coupler,” IEEE Trans. Microw. Theory Tech. MTT-30, 1589–1591 (1982).
    [CrossRef]
  9. K. P. Koo, A. B. Tvente, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3×3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618(1982).
    [CrossRef]
  10. Z. Zhao, M. S. Demokan, and M. MacAlpine, “Improved demodulation scheme for fiber optic interferometers using an asymetric 3×3 coupler,” J. Lightwave Technol. 15, 2059–2068 (1997).
    [CrossRef]
  11. L. M. Manojlović, “A novel common path interferometric technique for vibration measurement based on two fiber-optic couplers,” IEEE Sens. J. 11, 1541–1547 (2011).
    [CrossRef]
  12. M. C. Tomic, J. M. Elazar, and Z. V. Djinovic, “Low-coherence interferometric method for measurement of displacement based on a 3×3 fibre-optic directional coupler,” J. Opt. A: Pure Appl. Opt. 4, S381–S386 (2002).
    [CrossRef]
  13. Z. Djinovic, M. Tomic, and C. Gamauf, “Fiber-optic interferometric sensor of magnetic field for structural health monitoring,” Procedia Eng. 5, 1103–1106 (2010).
    [CrossRef]
  14. C. W. de Silva, Modeling and Control of Engineering Systems (CRC, 2009).
  15. A. Visioli, Practical PID Control (Springer-Verlag, 2006).

2011

L. M. Manojlović, “A novel common path interferometric technique for vibration measurement based on two fiber-optic couplers,” IEEE Sens. J. 11, 1541–1547 (2011).
[CrossRef]

2010

L. M. Manojlović, “A simple white-light fiber-optic interferometric sensing system for absolute position measurement,” Opt. Laser Eng. 48, 486–490 (2010).
[CrossRef]

Z. Djinovic, M. Tomic, and C. Gamauf, “Fiber-optic interferometric sensor of magnetic field for structural health monitoring,” Procedia Eng. 5, 1103–1106 (2010).
[CrossRef]

2002

A. V. Zvyagin, I. Eix, and D. D. Sampson, “High-speed, high-sensitivity, gated surface profiling with closed-loop optical coherence topography,” Appl. Opt. 41, 2179–2184 (2002).
[CrossRef]

M. C. Tomic, J. M. Elazar, and Z. V. Djinovic, “Low-coherence interferometric method for measurement of displacement based on a 3×3 fibre-optic directional coupler,” J. Opt. A: Pure Appl. Opt. 4, S381–S386 (2002).
[CrossRef]

1997

J.-Y. Liu, I. Yamaguchi, J.-I. Kato, and T. Nakajima, “Real-time surface shape measurement by an active interferometer,” Opt. Rev. 4, 216–220 (1997).
[CrossRef]

Z. Zhao, M. S. Demokan, and M. MacAlpine, “Improved demodulation scheme for fiber optic interferometers using an asymetric 3×3 coupler,” J. Lightwave Technol. 15, 2059–2068 (1997).
[CrossRef]

1991

1982

R. G. Priest, “Analysis of fiber interferometer utilizing 3×3 fiber coupler,” IEEE Trans. Microw. Theory Tech. MTT-30, 1589–1591 (1982).
[CrossRef]

K. P. Koo, A. B. Tvente, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3×3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618(1982).
[CrossRef]

1981

S. K. Sheem, “Optical fiber interferometer with [3×3] directional coupler: analysis,” J. Appl. Phys. 52, 3865–3872 (1981).
[CrossRef]

1978

D. C. Leiner, “Real-time phase microscopy using a phase-lock interferometer,” Rev. Sci. Instrum. 49, 1702–1705(1978).
[CrossRef]

Dandridge, A.

K. P. Koo, A. B. Tvente, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3×3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618(1982).
[CrossRef]

de Silva, C. W.

C. W. de Silva, Modeling and Control of Engineering Systems (CRC, 2009).

Demokan, M. S.

Z. Zhao, M. S. Demokan, and M. MacAlpine, “Improved demodulation scheme for fiber optic interferometers using an asymetric 3×3 coupler,” J. Lightwave Technol. 15, 2059–2068 (1997).
[CrossRef]

Djinovic, Z.

Z. Djinovic, M. Tomic, and C. Gamauf, “Fiber-optic interferometric sensor of magnetic field for structural health monitoring,” Procedia Eng. 5, 1103–1106 (2010).
[CrossRef]

Djinovic, Z. V.

M. C. Tomic, J. M. Elazar, and Z. V. Djinovic, “Low-coherence interferometric method for measurement of displacement based on a 3×3 fibre-optic directional coupler,” J. Opt. A: Pure Appl. Opt. 4, S381–S386 (2002).
[CrossRef]

Eix, I.

Elazar, J. M.

M. C. Tomic, J. M. Elazar, and Z. V. Djinovic, “Low-coherence interferometric method for measurement of displacement based on a 3×3 fibre-optic directional coupler,” J. Opt. A: Pure Appl. Opt. 4, S381–S386 (2002).
[CrossRef]

Fung, S. S.

J. L. Lauer and S. S. Fung, “Surface topographical changes measured by phase-locked interferometry,” NASA Contract. Rep. 3757 (NASA, 1984).

Gamauf, C.

Z. Djinovic, M. Tomic, and C. Gamauf, “Fiber-optic interferometric sensor of magnetic field for structural health monitoring,” Procedia Eng. 5, 1103–1106 (2010).
[CrossRef]

Higuchi, K.

Kato, J.-I.

J.-Y. Liu, I. Yamaguchi, J.-I. Kato, and T. Nakajima, “Real-time surface shape measurement by an active interferometer,” Opt. Rev. 4, 216–220 (1997).
[CrossRef]

Koo, K. P.

K. P. Koo, A. B. Tvente, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3×3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618(1982).
[CrossRef]

Lauer, J. L.

J. L. Lauer and S. S. Fung, “Surface topographical changes measured by phase-locked interferometry,” NASA Contract. Rep. 3757 (NASA, 1984).

Leiner, D. C.

D. C. Leiner, “Real-time phase microscopy using a phase-lock interferometer,” Rev. Sci. Instrum. 49, 1702–1705(1978).
[CrossRef]

Liu, J.-Y.

J.-Y. Liu, I. Yamaguchi, J.-I. Kato, and T. Nakajima, “Real-time surface shape measurement by an active interferometer,” Opt. Rev. 4, 216–220 (1997).
[CrossRef]

MacAlpine, M.

Z. Zhao, M. S. Demokan, and M. MacAlpine, “Improved demodulation scheme for fiber optic interferometers using an asymetric 3×3 coupler,” J. Lightwave Technol. 15, 2059–2068 (1997).
[CrossRef]

Manojlovic, L. M.

L. M. Manojlović, “A novel common path interferometric technique for vibration measurement based on two fiber-optic couplers,” IEEE Sens. J. 11, 1541–1547 (2011).
[CrossRef]

L. M. Manojlović, “A simple white-light fiber-optic interferometric sensing system for absolute position measurement,” Opt. Laser Eng. 48, 486–490 (2010).
[CrossRef]

Maruyama, T.

Nakajima, T.

J.-Y. Liu, I. Yamaguchi, J.-I. Kato, and T. Nakajima, “Real-time surface shape measurement by an active interferometer,” Opt. Rev. 4, 216–220 (1997).
[CrossRef]

Priest, R. G.

R. G. Priest, “Analysis of fiber interferometer utilizing 3×3 fiber coupler,” IEEE Trans. Microw. Theory Tech. MTT-30, 1589–1591 (1982).
[CrossRef]

Sampson, D. D.

Sasaki, O.

Sheem, S. K.

S. K. Sheem, “Optical fiber interferometer with [3×3] directional coupler: analysis,” J. Appl. Phys. 52, 3865–3872 (1981).
[CrossRef]

Suzuki, T.

Tomic, M.

Z. Djinovic, M. Tomic, and C. Gamauf, “Fiber-optic interferometric sensor of magnetic field for structural health monitoring,” Procedia Eng. 5, 1103–1106 (2010).
[CrossRef]

Tomic, M. C.

M. C. Tomic, J. M. Elazar, and Z. V. Djinovic, “Low-coherence interferometric method for measurement of displacement based on a 3×3 fibre-optic directional coupler,” J. Opt. A: Pure Appl. Opt. 4, S381–S386 (2002).
[CrossRef]

Tvente, A. B.

K. P. Koo, A. B. Tvente, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3×3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618(1982).
[CrossRef]

Visioli, A.

A. Visioli, Practical PID Control (Springer-Verlag, 2006).

Yamaguchi, I.

J.-Y. Liu, I. Yamaguchi, J.-I. Kato, and T. Nakajima, “Real-time surface shape measurement by an active interferometer,” Opt. Rev. 4, 216–220 (1997).
[CrossRef]

Zhao, Z.

Z. Zhao, M. S. Demokan, and M. MacAlpine, “Improved demodulation scheme for fiber optic interferometers using an asymetric 3×3 coupler,” J. Lightwave Technol. 15, 2059–2068 (1997).
[CrossRef]

Zvyagin, A. V.

Appl. Opt.

Appl. Phys. Lett.

K. P. Koo, A. B. Tvente, and A. Dandridge, “Passive stabilization scheme for fiber interferometers using (3×3) fiber directional coupler,” Appl. Phys. Lett. 41, 616–618(1982).
[CrossRef]

IEEE Sens. J.

L. M. Manojlović, “A novel common path interferometric technique for vibration measurement based on two fiber-optic couplers,” IEEE Sens. J. 11, 1541–1547 (2011).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

R. G. Priest, “Analysis of fiber interferometer utilizing 3×3 fiber coupler,” IEEE Trans. Microw. Theory Tech. MTT-30, 1589–1591 (1982).
[CrossRef]

J. Appl. Phys.

S. K. Sheem, “Optical fiber interferometer with [3×3] directional coupler: analysis,” J. Appl. Phys. 52, 3865–3872 (1981).
[CrossRef]

J. Lightwave Technol.

Z. Zhao, M. S. Demokan, and M. MacAlpine, “Improved demodulation scheme for fiber optic interferometers using an asymetric 3×3 coupler,” J. Lightwave Technol. 15, 2059–2068 (1997).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

M. C. Tomic, J. M. Elazar, and Z. V. Djinovic, “Low-coherence interferometric method for measurement of displacement based on a 3×3 fibre-optic directional coupler,” J. Opt. A: Pure Appl. Opt. 4, S381–S386 (2002).
[CrossRef]

Opt. Laser Eng.

L. M. Manojlović, “A simple white-light fiber-optic interferometric sensing system for absolute position measurement,” Opt. Laser Eng. 48, 486–490 (2010).
[CrossRef]

Opt. Rev.

J.-Y. Liu, I. Yamaguchi, J.-I. Kato, and T. Nakajima, “Real-time surface shape measurement by an active interferometer,” Opt. Rev. 4, 216–220 (1997).
[CrossRef]

Procedia Eng.

Z. Djinovic, M. Tomic, and C. Gamauf, “Fiber-optic interferometric sensor of magnetic field for structural health monitoring,” Procedia Eng. 5, 1103–1106 (2010).
[CrossRef]

Rev. Sci. Instrum.

D. C. Leiner, “Real-time phase microscopy using a phase-lock interferometer,” Rev. Sci. Instrum. 49, 1702–1705(1978).
[CrossRef]

Other

J. L. Lauer and S. S. Fung, “Surface topographical changes measured by phase-locked interferometry,” NASA Contract. Rep. 3757 (NASA, 1984).

C. W. de Silva, Modeling and Control of Engineering Systems (CRC, 2009).

A. Visioli, Practical PID Control (Springer-Verlag, 2006).

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Figures (11)

Fig. 1.
Fig. 1.

Block schematic of the proposed phase-locked low-coherence interferometric setup for the high-speed and high-sensitivity displacement measurement. LDD, laser diode driver; SLD, superluminescent diode; FOC, fiber-optic coupler; PD1 and PD2, photodetectors; A, inverting amplifier; TIA, transimpedance amplifier; PI, PI controller; F, filter; B, variable source of constant voltage; Σ, summation circuit; HVA, high voltage amplifier; and PA, piezo actuator.

Fig. 2.
Fig. 2.

PD signal difference at the TIA output.

Fig. 3.
Fig. 3.

Displacement of the SM and RM when the SM oscillates at a frequency of 1 kHz and with an amplitude of 60 nm.

Fig. 4.
Fig. 4.

Equivalent PSD of the measured SM displacement.

Fig. 5.
Fig. 5.

Amplitude frequency characteristic of the realized sensing system. The measured data are represented by the dashed curve, and the calculated data are represented by the solid curve.

Fig. 6.
Fig. 6.

Amplitude frequency characteristic of RM and SM displacements.

Fig. 7.
Fig. 7.

Amplitude transfer function between the SM and RM position difference and SM.

Fig. 8.
Fig. 8.

Maximal allowable SM vibration amplitudes.

Fig. 9.
Fig. 9.

Measured output voltage signal versus the actual displacement of the SM. The measured data are represented by the solid curve given in front of the diagram and the linear fit of the measured data is also represented by the solid curve positioned behind the measured data.

Fig. 10.
Fig. 10.

Left: SM and RM position difference measured at the TIA output. Right: Histogram of the measured position difference together with the fitted normal distribution.

Fig. 11.
Fig. 11.

Transimpedance amplifier.

Equations (27)

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PSF=13rFP0,PRF=13rFP0,
PSM,RM=13(1rF)2rM[1+(λ0lnw2πa2DS,R)2]1f(φS,R)P0,
P1,2=P1,2F+P1,2V,P1,2F=13(PRF+PSF),P1,2V=13[PSM+PRM+2PSMPRMcos(θ±2π3)],
θ=4πλ0(xSxR),
ΔI=233RKPSMPRMsinθ,
ΔI233RKPSMPRMθ.
VTIA8π33RTRKλ0PSMPRM(xSxR)=S(xSxR),
S=8π3(1rF)2rMRTRKP09λ0[1+(DSd)2][1+(DRd)2],
d=2πa2λ0lnw.
xR(s)xS(s)=11+1S·P(s)G(s)F(s)C(s),
Vout(s)xS(s)=S·F(s)C(s)1+S·P(s)G(s)F(s)C(s),
KV=lims0sS·P(s)G(s)F(s)C(s)=SG0k0KPτI,
Δx=vSKV=τIvSG0k0SKP.
vS<λ0SG0k0KP8τI.
Δx(s)xS(s)=11+S·P(s)G(s)F(s)C(s),
|Δx(jω)xS(jω)|=1|1+S·P(jω)G(jω)F(jω)C(jω)|.
|xS(jω)|<λ08|1+S·P(jω)G(jω)F(jω)C(jω)|.
in2¯=inPD2¯+inA+2¯(1+RFRL)2+inA2¯(1+RLRF)2+enF2¯+enL2¯+enA2¯(RF+RL)2,
inPD2¯=2qRKP1,2+4kBTRPD2qRKP1,2,enF2¯=4kBTRF,enL2¯=4kBTRL,
in2¯2qRKP1,2+4kBTRT+inA2¯[1(1+RFRL)2+1(1+RLRF)2],
in2¯2qRKP1,2+4kBTRT+12inA2¯,
σΔx=1S2vnTIA2¯B,
P1=B1+B2cosθB3sinθ,P2=B1+ΔB1+(B2+ΔB2)cosθ+(B3+ΔB3)sinθ,
ΔP=ΔB1+ΔB2cosθ+(2B3+ΔB3)sinθ.
ΔθΔB1+ΔB22B3.
Δθ36(2ΔB1B1+ΔB2B2).
ΔxFOC324πλ0(2ΔB1B1+ΔB2B2).

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