Abstract

The factors limiting the resolution of displacement sensors based on the extrinsic Fabry–Perot interferometer were studied. An analytical model giving the dependency of extrinsic Fabry–Perot interferometric (EFPI) resolution on the parameters of an optical setup and a sensor interrogator was developed. The proposed model enables one to either estimate the limit of possible resolution achievable with a given setup, or derive the requirements for optical elements and/or a sensor interrogator necessary for attaining the desired sensor resolution. An experiment supporting the analytical derivations was performed, demonstrating a large dynamic measurement range (with cavity length from tens of microns to 5 mm), a high baseline resolution (from 14 pm), and good agreement with the model.

© 2014 Optical Society of America

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References

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  1. E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2006).
  2. J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high-temperature sensing with sapphire fiber air gap-based extrinsic Fabry–Perot interferometers,” Opt. Lett. 35, 619–621 (2010).
    [CrossRef]
  3. Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
    [CrossRef]
  4. W. Wang and F. Li, “Large-range liquid level sensor based on an optical fibre extrinsic Fabry–Perot interferometer,” Opt. Lasers Eng. 52, 201–205 (2014).
    [CrossRef]
  5. D. Tosi, S. Poeggel, G. Leen, and E. Lewis, “Adaptive filter-based interrogation of high-sensitivity fiber optic Fabry–Perot interferometry sensors,” Sens. Actuators A, Phys. 206, 144–150 (2014).
    [CrossRef]
  6. R.-Q. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry–Pérot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26, 217–219 (2014).
    [CrossRef]
  7. X. Zhou and Q. Yu, “Wide-range displacement sensor based on fiber optic Fabry–Perot interferometer for subnanometer measurement,” IEEE Sens. J. 11, 1602–1606 (2011).
    [CrossRef]
  8. N. Ushakov, L. Liokumovich, and A. Medvedev, “EFPI signal processing method providing picometer-level resolution in cavity length measurement,” Proc. SPIE 8789, 87890Y (2013).
    [CrossRef]
  9. Y. Jiang and C. Tang, “Passive interrogation of an extrinsic Fabry–Pérot interferometer using a three-wavelength method,” Opt. Eng. 48, 064401 (2009).
    [CrossRef]
  10. Q. Wang and Z. Ma, “Feedback-stabilized interrogation technique for optical Fabry–Perot acoustic sensor using a tunable fiber laser,” Opt. Laser Technol. 51, 43–46 (2013).
    [CrossRef]
  11. F. Depiereux, P. Lehmann, T. Pfeifer, and R. Schmitt, “Fiber optical sensor with miniaturized probe head and nanometer accuracy based on spatially modulated low-coherence interferogram analysis,” Appl. Opt. 46, 3425–3431 (2007).
    [CrossRef]
  12. E. D. Moore, “Advances in swept-wavelength interferometry for precision measurements,” Ph.D. dissertation (University of Colorado, 2011).
  13. Z. Wang and Y. Jiang, “Wavenumber scanning-based Fourier-transform white light interferometry,” Appl. Opt. 51, 5512–5516 (2012).
    [CrossRef]
  14. Q. Wang, Ch. Qin, D. Wang, and Y. Zhao, “Investigation on stability of extrinsic Fabry–Perot interferometric pressure sensors for high-temperature/high-pressure underground applications,” Instrum. Sci. Technol. 41, 143–153 (2013).
    [CrossRef]
  15. F. Shen and A. Wang, “Frequency-estimation-based signal-processing algorithm for white light optical fiber Fabry–Perot interferometers,” Appl. Opt. 44, 5206–5214 (2005).
    [CrossRef]
  16. B. Yu, A. Wang, and G. R. Pickrell, “Analysis of fiber Fabry–Perot interferometric sensors using low-coherence light sources,” J. Lightwave Technol. 24, 1758–1767 (2006).
    [CrossRef]
  17. C. Ma and A. Wang, “Signal processing of white light interferometric low-finesse fiber optic Fabry–Perot sensors,” Appl. Opt. 52, 127–138 (2013).
    [CrossRef]
  18. E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express 16, 13139–13149 (2008).
    [CrossRef]
  19. M. Han, Y. Zhang, F. Shen, G. R. Pickrell, and A. Wang, “Signal-processing algorithm for white light optical fiber extrinsic Fabry–Perot interferometric sensors,” Opt. Lett. 29, 1736–1738 (2004).
    [CrossRef]
  20. H. Fu and P. Y. Kam, “MAP/ML estimation of the frequency and phase of a single sinusoid in noise,” IEEE Trans. Signal Process. 55, 834–845 (2007).
    [CrossRef]
  21. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).
  22. D. Marcuse, “Loss analysis of single-mode fiber splices,” AT&T Tech. J. 56, 703–718 (1977).

2014

W. Wang and F. Li, “Large-range liquid level sensor based on an optical fibre extrinsic Fabry–Perot interferometer,” Opt. Lasers Eng. 52, 201–205 (2014).
[CrossRef]

D. Tosi, S. Poeggel, G. Leen, and E. Lewis, “Adaptive filter-based interrogation of high-sensitivity fiber optic Fabry–Perot interferometry sensors,” Sens. Actuators A, Phys. 206, 144–150 (2014).
[CrossRef]

R.-Q. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry–Pérot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26, 217–219 (2014).
[CrossRef]

2013

N. Ushakov, L. Liokumovich, and A. Medvedev, “EFPI signal processing method providing picometer-level resolution in cavity length measurement,” Proc. SPIE 8789, 87890Y (2013).
[CrossRef]

Q. Wang and Z. Ma, “Feedback-stabilized interrogation technique for optical Fabry–Perot acoustic sensor using a tunable fiber laser,” Opt. Laser Technol. 51, 43–46 (2013).
[CrossRef]

Q. Wang, Ch. Qin, D. Wang, and Y. Zhao, “Investigation on stability of extrinsic Fabry–Perot interferometric pressure sensors for high-temperature/high-pressure underground applications,” Instrum. Sci. Technol. 41, 143–153 (2013).
[CrossRef]

C. Ma and A. Wang, “Signal processing of white light interferometric low-finesse fiber optic Fabry–Perot sensors,” Appl. Opt. 52, 127–138 (2013).
[CrossRef]

2012

2011

X. Zhou and Q. Yu, “Wide-range displacement sensor based on fiber optic Fabry–Perot interferometer for subnanometer measurement,” IEEE Sens. J. 11, 1602–1606 (2011).
[CrossRef]

2010

J. Wang, B. Dong, E. Lally, J. Gong, M. Han, and A. Wang, “Multiplexed high-temperature sensing with sapphire fiber air gap-based extrinsic Fabry–Perot interferometers,” Opt. Lett. 35, 619–621 (2010).
[CrossRef]

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

2009

Y. Jiang and C. Tang, “Passive interrogation of an extrinsic Fabry–Pérot interferometer using a three-wavelength method,” Opt. Eng. 48, 064401 (2009).
[CrossRef]

2008

2007

2006

2005

2004

1977

D. Marcuse, “Loss analysis of single-mode fiber splices,” AT&T Tech. J. 56, 703–718 (1977).

Chen, G.

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

Depiereux, F.

Dong, B.

Fu, H.

H. Fu and P. Y. Kam, “MAP/ML estimation of the frequency and phase of a single sinusoid in noise,” IEEE Trans. Signal Process. 55, 834–845 (2007).
[CrossRef]

Gong, J.

Han, M.

Huang, Y.

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

Jiang, Y.

Z. Wang and Y. Jiang, “Wavenumber scanning-based Fourier-transform white light interferometry,” Appl. Opt. 51, 5512–5516 (2012).
[CrossRef]

Y. Jiang and C. Tang, “Passive interrogation of an extrinsic Fabry–Pérot interferometer using a three-wavelength method,” Opt. Eng. 48, 064401 (2009).
[CrossRef]

Kam, P. Y.

H. Fu and P. Y. Kam, “MAP/ML estimation of the frequency and phase of a single sinusoid in noise,” IEEE Trans. Signal Process. 55, 834–845 (2007).
[CrossRef]

Lally, E.

Leen, G.

D. Tosi, S. Poeggel, G. Leen, and E. Lewis, “Adaptive filter-based interrogation of high-sensitivity fiber optic Fabry–Perot interferometry sensors,” Sens. Actuators A, Phys. 206, 144–150 (2014).
[CrossRef]

Lehmann, P.

Lewis, E.

D. Tosi, S. Poeggel, G. Leen, and E. Lewis, “Adaptive filter-based interrogation of high-sensitivity fiber optic Fabry–Perot interferometry sensors,” Sens. Actuators A, Phys. 206, 144–150 (2014).
[CrossRef]

Li, F.

W. Wang and F. Li, “Large-range liquid level sensor based on an optical fibre extrinsic Fabry–Perot interferometer,” Opt. Lasers Eng. 52, 201–205 (2014).
[CrossRef]

Liokumovich, L.

N. Ushakov, L. Liokumovich, and A. Medvedev, “EFPI signal processing method providing picometer-level resolution in cavity length measurement,” Proc. SPIE 8789, 87890Y (2013).
[CrossRef]

Lv, R.-Q.

R.-Q. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry–Pérot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26, 217–219 (2014).
[CrossRef]

Ma, C.

Ma, Z.

Q. Wang and Z. Ma, “Feedback-stabilized interrogation technique for optical Fabry–Perot acoustic sensor using a tunable fiber laser,” Opt. Laser Technol. 51, 43–46 (2013).
[CrossRef]

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” AT&T Tech. J. 56, 703–718 (1977).

McLeod, R. R.

Medvedev, A.

N. Ushakov, L. Liokumovich, and A. Medvedev, “EFPI signal processing method providing picometer-level resolution in cavity length measurement,” Proc. SPIE 8789, 87890Y (2013).
[CrossRef]

Moore, E. D.

E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express 16, 13139–13149 (2008).
[CrossRef]

E. D. Moore, “Advances in swept-wavelength interferometry for precision measurements,” Ph.D. dissertation (University of Colorado, 2011).

Pfeifer, T.

Pickrell, G. R.

Poeggel, S.

D. Tosi, S. Poeggel, G. Leen, and E. Lewis, “Adaptive filter-based interrogation of high-sensitivity fiber optic Fabry–Perot interferometry sensors,” Sens. Actuators A, Phys. 206, 144–150 (2014).
[CrossRef]

Qin, Ch.

Q. Wang, Ch. Qin, D. Wang, and Y. Zhao, “Investigation on stability of extrinsic Fabry–Perot interferometric pressure sensors for high-temperature/high-pressure underground applications,” Instrum. Sci. Technol. 41, 143–153 (2013).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

Schmitt, R.

Shen, F.

Tang, C.

Y. Jiang and C. Tang, “Passive interrogation of an extrinsic Fabry–Pérot interferometer using a three-wavelength method,” Opt. Eng. 48, 064401 (2009).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

Tosi, D.

D. Tosi, S. Poeggel, G. Leen, and E. Lewis, “Adaptive filter-based interrogation of high-sensitivity fiber optic Fabry–Perot interferometry sensors,” Sens. Actuators A, Phys. 206, 144–150 (2014).
[CrossRef]

Udd, E.

E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2006).

Ushakov, N.

N. Ushakov, L. Liokumovich, and A. Medvedev, “EFPI signal processing method providing picometer-level resolution in cavity length measurement,” Proc. SPIE 8789, 87890Y (2013).
[CrossRef]

Wang, A.

Wang, D.

R.-Q. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry–Pérot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26, 217–219 (2014).
[CrossRef]

Q. Wang, Ch. Qin, D. Wang, and Y. Zhao, “Investigation on stability of extrinsic Fabry–Perot interferometric pressure sensors for high-temperature/high-pressure underground applications,” Instrum. Sci. Technol. 41, 143–153 (2013).
[CrossRef]

Wang, J.

Wang, Q.

R.-Q. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry–Pérot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26, 217–219 (2014).
[CrossRef]

Q. Wang and Z. Ma, “Feedback-stabilized interrogation technique for optical Fabry–Perot acoustic sensor using a tunable fiber laser,” Opt. Laser Technol. 51, 43–46 (2013).
[CrossRef]

Q. Wang, Ch. Qin, D. Wang, and Y. Zhao, “Investigation on stability of extrinsic Fabry–Perot interferometric pressure sensors for high-temperature/high-pressure underground applications,” Instrum. Sci. Technol. 41, 143–153 (2013).
[CrossRef]

Wang, W.

W. Wang and F. Li, “Large-range liquid level sensor based on an optical fibre extrinsic Fabry–Perot interferometer,” Opt. Lasers Eng. 52, 201–205 (2014).
[CrossRef]

Wang, Z.

Wei, T.

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

Xiao, H.

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

Yu, B.

Yu, Q.

X. Zhou and Q. Yu, “Wide-range displacement sensor based on fiber optic Fabry–Perot interferometer for subnanometer measurement,” IEEE Sens. J. 11, 1602–1606 (2011).
[CrossRef]

Zhang, Y.

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

M. Han, Y. Zhang, F. Shen, G. R. Pickrell, and A. Wang, “Signal-processing algorithm for white light optical fiber extrinsic Fabry–Perot interferometric sensors,” Opt. Lett. 29, 1736–1738 (2004).
[CrossRef]

Zhao, Y.

R.-Q. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry–Pérot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26, 217–219 (2014).
[CrossRef]

Q. Wang, Ch. Qin, D. Wang, and Y. Zhao, “Investigation on stability of extrinsic Fabry–Perot interferometric pressure sensors for high-temperature/high-pressure underground applications,” Instrum. Sci. Technol. 41, 143–153 (2013).
[CrossRef]

Zhou, X.

X. Zhou and Q. Yu, “Wide-range displacement sensor based on fiber optic Fabry–Perot interferometer for subnanometer measurement,” IEEE Sens. J. 11, 1602–1606 (2011).
[CrossRef]

Zhou, Z.

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

Appl. Opt.

AT&T Tech. J.

D. Marcuse, “Loss analysis of single-mode fiber splices,” AT&T Tech. J. 56, 703–718 (1977).

IEEE Photon. Technol. Lett.

R.-Q. Lv, Y. Zhao, D. Wang, and Q. Wang, “Magnetic fluid-filled optical fiber Fabry–Pérot sensor for magnetic field measurement,” IEEE Photon. Technol. Lett. 26, 217–219 (2014).
[CrossRef]

IEEE Sens. J.

X. Zhou and Q. Yu, “Wide-range displacement sensor based on fiber optic Fabry–Perot interferometer for subnanometer measurement,” IEEE Sens. J. 11, 1602–1606 (2011).
[CrossRef]

IEEE Trans. Signal Process.

H. Fu and P. Y. Kam, “MAP/ML estimation of the frequency and phase of a single sinusoid in noise,” IEEE Trans. Signal Process. 55, 834–845 (2007).
[CrossRef]

Instrum. Sci. Technol.

Q. Wang, Ch. Qin, D. Wang, and Y. Zhao, “Investigation on stability of extrinsic Fabry–Perot interferometric pressure sensors for high-temperature/high-pressure underground applications,” Instrum. Sci. Technol. 41, 143–153 (2013).
[CrossRef]

J. Lightwave Technol.

Meas. Sci. Technol.

Y. Huang, T. Wei, Z. Zhou, Y. Zhang, G. Chen, and H. Xiao, “An extrinsic Fabry–Perot interferometer-based large strain sensor with high resolution,” Meas. Sci. Technol. 21, 105308 (2010).
[CrossRef]

Opt. Eng.

Y. Jiang and C. Tang, “Passive interrogation of an extrinsic Fabry–Pérot interferometer using a three-wavelength method,” Opt. Eng. 48, 064401 (2009).
[CrossRef]

Opt. Express

Opt. Laser Technol.

Q. Wang and Z. Ma, “Feedback-stabilized interrogation technique for optical Fabry–Perot acoustic sensor using a tunable fiber laser,” Opt. Laser Technol. 51, 43–46 (2013).
[CrossRef]

Opt. Lasers Eng.

W. Wang and F. Li, “Large-range liquid level sensor based on an optical fibre extrinsic Fabry–Perot interferometer,” Opt. Lasers Eng. 52, 201–205 (2014).
[CrossRef]

Opt. Lett.

Proc. SPIE

N. Ushakov, L. Liokumovich, and A. Medvedev, “EFPI signal processing method providing picometer-level resolution in cavity length measurement,” Proc. SPIE 8789, 87890Y (2013).
[CrossRef]

Sens. Actuators A, Phys.

D. Tosi, S. Poeggel, G. Leen, and E. Lewis, “Adaptive filter-based interrogation of high-sensitivity fiber optic Fabry–Perot interferometry sensors,” Sens. Actuators A, Phys. 206, 144–150 (2014).
[CrossRef]

Other

E. Udd, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2006).

E. D. Moore, “Advances in swept-wavelength interferometry for precision measurements,” Ph.D. dissertation (University of Colorado, 2011).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

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Figures (5)

Fig. 1.
Fig. 1.

Relation of LR stdev and SNR of additive white noise.

Fig. 2.
Fig. 2.

Relation of the optical power, reflected to the interrogator and the additive noise level—measured (points) and fitted (line).

Fig. 3.
Fig. 3.

Experimental setup.

Fig. 4.
Fig. 4.

Fringe visibility (a) and signal-to-noise ratio (b) for different reflectivities of the second mirror; experimental (points) and analytical, calculated according to Eqs. (A8) and (16) (solid curves).

Fig. 5.
Fig. 5.

Baseline measurement resolutions for different reflectivities of the second mirror; experimental (points) and theoretical, calculated according to Eq. (18) (solid curves).

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

SFP(L,λ)=S0(L,λ)+S(L,λ),
S(L,λ)=Smcos(4πnL/λ+γ(L,λ)),
R(L)=S(λ)S(L,λ)=i[SiSi(L)]2.
δLΔλ0·L0/λ0.
SiSi(L0)Sm4πnL0δ·Δ·iλ02sin(4πnL0λi+γ).
δλ0/2nL0,
SiSi(L0)Sm4πnL0δλi/λ02sin(4πnL0/λi+γ).
SiSi(L0)Sm4πnL0δλi/λ02.
SNR3=Sm2/2(σδλSm4πnL0/λ02)2=2λ04(8πnL0σδλ)2,
Si2(R1R2*)1/2cos(4πnL0/λi+γ)·P0+δsi,
R2*(λ,L)=R2(πnw02)2L2λ2+(πnw02)2.
σs=aPb,
SNR4=Sm2/2σs2=2P022ba2R1R2*(R1+R2*)2b.
SNR4=2D2R1R2*(L),
SNR4=2R1R2*RIN2·(R1+R2*)2=0.5·(VRIN)2,
SNR=1/(SNR31+SNR41).
σLr(SNR)=C·SNR1/2,
σLr=[C2SNR+σΔλ2L02λ02]1/2.
A(r,z)=w0w(z)exp[rw(z)jz·r2zRw2(z)jatan(zzR)],
w(z)=w01+(z/zR)2,zR=πnw02λ.
ηF(L)=A(r,0)·A*(r,2L)dφdr[|A(r,0)|2dφdr|A(r,2L)|2dφdr]1/2.
ηF=2w0w(2L)·ejψ[(w02+w2(2L))2+4w04L2/zR2]1/2,
ψ=atan[LzR·(4L2zR2+3)].
η=(πnw02)2L2λ2+(πnw02)2.
Sm=πnw02R1R2L2λ2+(πnw02)2.
V=2R1R2R1·[(Lλ/πnw02)2+1]1/2+R2.
λ4πnLλ|λ0=4πnLλ02,
λψ(L)|λ0=3(πnw02)3·L[(Lλ)2+(πnw02)2]·[(2Lλ)2+(πnw02)2].

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