Abstract

We developed a multiplexed strain sensor system with high resolution using fiber Fabry-Perot interferometers (FFPI) as sensing elements. The temporal responses of the FFPIs excited by rectangular laser pulses are used to obtain the strain applied on each FFPI. The FFPIs are connected by cascaded couplers and delay fiber rolls for the time-domain multiplexing. A compact optoelectronic system performing closed-loop cyclic interrogation is employed to improve the sensing resolution and the frequency response. In the demonstration experiment, 3-channel strain sensing with resolutions better than 0.1 nε and frequency response higher than 100 Hz is realized.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
DFB fiber laser static strain sensor based on beat frequency interrogation with a reference fiber laser locked to a FBG resonator

Wenzhu Huang, Shengwen Feng, Wentao Zhang, and Fang Li
Opt. Express 24(11) 12321-12329 (2016)

Miniature interrogator for multiplexed FBG strain sensors based on a thermally tunable microring resonator array

Fan Yang, Wenjia Zhang, Shuangxiang Zhao, Qingwen Liu, Jifang Tao, and Zuyuan He
Opt. Express 27(5) 6037-6046 (2019)

Sensing the earth crustal deformation with nano-strain resolution fiber-optic sensors

Qingwen Liu, Zuyuan He, and Tomochika Tokunaga
Opt. Express 23(11) A428-A436 (2015)

References

  • View by:
  • |
  • |
  • |

  1. T. Yoshino, K. Kurosawa, K. Itoh, and T. Ose, “Fiber-optic Fabry-Perot interferometer and its sensor applications,” IEEE T. Microw. Theory 30, 1612–1621 (1982).
    [Crossref]
  2. A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
    [Crossref]
  3. M. A. Zumberge, F. K. Wyatt, D. X. Yu, and H. Hanada, “Optical fibers for measurement of earth strain,” Appl. Opt. 27, 4131–4138 (1988).
    [Crossref] [PubMed]
  4. T. Sato, R. Honda, and S. Shibata, “Ground strain measuring system using optical fiber sensors,” Proc. SPIE 3670, 470–479 (1999)
    [Crossref]
  5. Q. Liu, Z. He, and T. Tokunaga, “Sensing the earth crustal deformation with nano-strain resolution fiber-optic sensors,” Opt. Express 23, A428–A436 (2015).
    [Crossref] [PubMed]
  6. T. T. Lam, J. H. Chow, D. A. Shaddock, I. C. M. Littler, G. Gagliardi, M. B. Gray, and D. E. McClelland, “High-resolution absolute frequency referenced fiber optic sensor for quasi-static strain sensing,” Appl. Optics 49, 4029–4033 (2010).
    [Crossref]
  7. W. W. Morey, T. J. Bailey, W. H. Glenn, and G. Meltz, “Fiber Fabry-Perot interferometer using side exposed fiber Bragg gratings,” in “Optical Fiber Communication Conference,” (Optical Society of America, 1992), paper WA2.
  8. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [Crossref]
  9. A. Rosenthal, D. Razansky, and V. Ntziachristos, “High-sensitivity compact ultrasonic detector based on a π-phase-shifted fiber Bragg grating,” Opt. Lett. 36, 1833–1835 (2011).
    [Crossref] [PubMed]
  10. A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol. 17, 1849–1855 (1999).
    [Crossref]
  11. Q. Liu, T. Tokunaga, and Z. He, “Ultra-high-resolution large-dynamic-range optical fiber static strain sensor using Pound–Drever–Hall technique,” Opt. Lett. 36, 4044–4046 (2011).
    [Crossref] [PubMed]
  12. Q. Liu, T. Tokunaga, and Z. He, “Realization of nano static strain sensing with fiber Bragg gratings interrogated by narrow linewidth tunable lasers,” Opt. Express 19, 20214–20223 (2011).
    [Crossref] [PubMed]
  13. W. Huang, W. Zhang, and F. Li, “Swept optical ssb-sc modulation technique for high-resolution large-dynamic-range static strain measurement using FBG-FP sensors,” Opt. Lett. 40, 1406–1409 (2015).
    [Crossref] [PubMed]
  14. R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
    [Crossref]
  15. J. H. Chow, D. E. McClelland, M. B. Gray, and I. C. Littler, “Demonstration of a passive subpicostrain fiber strain sensor,” Opt. Lett. 30, 1923–1925 (2005).
    [Crossref] [PubMed]
  16. D. Gatti, G. Galzerano, D. Janner, S. Longhi, and P. Laporta, “Fiber strain sensor based on a π-phase-shifted Bragg grating and the Pound-Drever-Hall technique,” Opt. Express 16, 1945–1950 (2008).
    [Crossref] [PubMed]
  17. G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
    [Crossref] [PubMed]
  18. E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001).
    [Crossref]
  19. I. C. M. Littler, M. B. Gray, J. H. Chow, D. A. Shaddock, and D. E. McClelland, “Pico-strain multiplexed fiber optic sensor array operating down to infra-sonic frequencies,” Opt. Express 17, 11077–11087 (2009).
    [Crossref] [PubMed]
  20. J. Chen, Q. Liu, X. Fan, and Z. He, “Sub-nano-strain multiplexed fiber optic sensor array for quasi-static strain measurement,” IEEE. Photon. Technol. Lett. 28, 2311–2314 (2016).
    [Crossref]
  21. G. Hernández, Fabry-perot interferometers (Cambridge University, 1988).
  22. C. Roychoudhuri, “Response of Fabry–Perot interferometers to light pulses of very short duration,” J. Opt. Soc. Am. 65, 1418–1426 (1975).
    [Crossref]

2016 (1)

J. Chen, Q. Liu, X. Fan, and Z. He, “Sub-nano-strain multiplexed fiber optic sensor array for quasi-static strain measurement,” IEEE. Photon. Technol. Lett. 28, 2311–2314 (2016).
[Crossref]

2015 (2)

2011 (3)

2010 (2)

T. T. Lam, J. H. Chow, D. A. Shaddock, I. C. M. Littler, G. Gagliardi, M. B. Gray, and D. E. McClelland, “High-resolution absolute frequency referenced fiber optic sensor for quasi-static strain sensing,” Appl. Optics 49, 4029–4033 (2010).
[Crossref]

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

2005 (1)

2001 (1)

E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001).
[Crossref]

1999 (2)

A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol. 17, 1849–1855 (1999).
[Crossref]

T. Sato, R. Honda, and S. Shibata, “Ground strain measuring system using optical fiber sensors,” Proc. SPIE 3670, 470–479 (1999)
[Crossref]

1997 (2)

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[Crossref]

1988 (1)

1983 (1)

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

1982 (1)

T. Yoshino, K. Kurosawa, K. Itoh, and T. Ose, “Fiber-optic Fabry-Perot interferometer and its sensor applications,” IEEE T. Microw. Theory 30, 1612–1621 (1982).
[Crossref]

1975 (1)

Arie, A.

Askins, C.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Avino, S.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref] [PubMed]

Bailey, T. J.

W. W. Morey, T. J. Bailey, W. H. Glenn, and G. Meltz, “Fiber Fabry-Perot interferometer using side exposed fiber Bragg gratings,” in “Optical Fiber Communication Conference,” (Optical Society of America, 1992), paper WA2.

Black, E. D.

E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001).
[Crossref]

Chen, J.

J. Chen, Q. Liu, X. Fan, and Z. He, “Sub-nano-strain multiplexed fiber optic sensor array for quasi-static strain measurement,” IEEE. Photon. Technol. Lett. 28, 2311–2314 (2016).
[Crossref]

Chow, J. H.

Davis, M.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Drever, R. W. P.

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Erdogan, T.

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[Crossref]

Fan, X.

J. Chen, Q. Liu, X. Fan, and Z. He, “Sub-nano-strain multiplexed fiber optic sensor array for quasi-static strain measurement,” IEEE. Photon. Technol. Lett. 28, 2311–2314 (2016).
[Crossref]

Ferraro, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref] [PubMed]

Ford, G.

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Friebele, E.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Gagliardi, G.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref] [PubMed]

T. T. Lam, J. H. Chow, D. A. Shaddock, I. C. M. Littler, G. Gagliardi, M. B. Gray, and D. E. McClelland, “High-resolution absolute frequency referenced fiber optic sensor for quasi-static strain sensing,” Appl. Optics 49, 4029–4033 (2010).
[Crossref]

Galzerano, G.

Gatti, D.

Glenn, W. H.

W. W. Morey, T. J. Bailey, W. H. Glenn, and G. Meltz, “Fiber Fabry-Perot interferometer using side exposed fiber Bragg gratings,” in “Optical Fiber Communication Conference,” (Optical Society of America, 1992), paper WA2.

Gray, M. B.

Hall, F. V. K. J. L.

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Hanada, H.

He, Z.

Hernández, G.

G. Hernández, Fabry-perot interferometers (Cambridge University, 1988).

Honda, R.

T. Sato, R. Honda, and S. Shibata, “Ground strain measuring system using optical fiber sensors,” Proc. SPIE 3670, 470–479 (1999)
[Crossref]

Hough, J.

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Huang, W.

Itoh, K.

T. Yoshino, K. Kurosawa, K. Itoh, and T. Ose, “Fiber-optic Fabry-Perot interferometer and its sensor applications,” IEEE T. Microw. Theory 30, 1612–1621 (1982).
[Crossref]

Janner, D.

Kersey, A.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Koo, K.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Kurosawa, K.

T. Yoshino, K. Kurosawa, K. Itoh, and T. Ose, “Fiber-optic Fabry-Perot interferometer and its sensor applications,” IEEE T. Microw. Theory 30, 1612–1621 (1982).
[Crossref]

Lam, T. T.

T. T. Lam, J. H. Chow, D. A. Shaddock, I. C. M. Littler, G. Gagliardi, M. B. Gray, and D. E. McClelland, “High-resolution absolute frequency referenced fiber optic sensor for quasi-static strain sensing,” Appl. Optics 49, 4029–4033 (2010).
[Crossref]

Laporta, P.

Leblanc, M.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Li, F.

Lissak, B.

Littler, I. C.

Littler, I. C. M.

T. T. Lam, J. H. Chow, D. A. Shaddock, I. C. M. Littler, G. Gagliardi, M. B. Gray, and D. E. McClelland, “High-resolution absolute frequency referenced fiber optic sensor for quasi-static strain sensing,” Appl. Optics 49, 4029–4033 (2010).
[Crossref]

I. C. M. Littler, M. B. Gray, J. H. Chow, D. A. Shaddock, and D. E. McClelland, “Pico-strain multiplexed fiber optic sensor array operating down to infra-sonic frequencies,” Opt. Express 17, 11077–11087 (2009).
[Crossref] [PubMed]

Liu, Q.

Longhi, S.

McClelland, D. E.

Meltz, G.

W. W. Morey, T. J. Bailey, W. H. Glenn, and G. Meltz, “Fiber Fabry-Perot interferometer using side exposed fiber Bragg gratings,” in “Optical Fiber Communication Conference,” (Optical Society of America, 1992), paper WA2.

Morey, W. W.

W. W. Morey, T. J. Bailey, W. H. Glenn, and G. Meltz, “Fiber Fabry-Perot interferometer using side exposed fiber Bragg gratings,” in “Optical Fiber Communication Conference,” (Optical Society of America, 1992), paper WA2.

Munley, A.

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Natale, P.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref] [PubMed]

Ntziachristos, V.

Ose, T.

T. Yoshino, K. Kurosawa, K. Itoh, and T. Ose, “Fiber-optic Fabry-Perot interferometer and its sensor applications,” IEEE T. Microw. Theory 30, 1612–1621 (1982).
[Crossref]

Patrick, H.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Putnam, M.

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

Razansky, D.

Rosenthal, A.

Roychoudhuri, C.

Salza, M.

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref] [PubMed]

Sato, T.

T. Sato, R. Honda, and S. Shibata, “Ground strain measuring system using optical fiber sensors,” Proc. SPIE 3670, 470–479 (1999)
[Crossref]

Shaddock, D. A.

T. T. Lam, J. H. Chow, D. A. Shaddock, I. C. M. Littler, G. Gagliardi, M. B. Gray, and D. E. McClelland, “High-resolution absolute frequency referenced fiber optic sensor for quasi-static strain sensing,” Appl. Optics 49, 4029–4033 (2010).
[Crossref]

I. C. M. Littler, M. B. Gray, J. H. Chow, D. A. Shaddock, and D. E. McClelland, “Pico-strain multiplexed fiber optic sensor array operating down to infra-sonic frequencies,” Opt. Express 17, 11077–11087 (2009).
[Crossref] [PubMed]

Shibata, S.

T. Sato, R. Honda, and S. Shibata, “Ground strain measuring system using optical fiber sensors,” Proc. SPIE 3670, 470–479 (1999)
[Crossref]

Tokunaga, T.

Tur, M.

Ward, H.

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

Wyatt, F. K.

Yoshino, T.

T. Yoshino, K. Kurosawa, K. Itoh, and T. Ose, “Fiber-optic Fabry-Perot interferometer and its sensor applications,” IEEE T. Microw. Theory 30, 1612–1621 (1982).
[Crossref]

Yu, D. X.

Zhang, W.

Zumberge, M. A.

Am. J. Phys. (1)

E. D. Black, “An introduction to Pound–Drever–Hall laser frequency stabilization,” Am. J. Phys. 69, 79–87 (2001).
[Crossref]

Appl. Opt. (1)

Appl. Optics (1)

T. T. Lam, J. H. Chow, D. A. Shaddock, I. C. M. Littler, G. Gagliardi, M. B. Gray, and D. E. McClelland, “High-resolution absolute frequency referenced fiber optic sensor for quasi-static strain sensing,” Appl. Optics 49, 4029–4033 (2010).
[Crossref]

Appl. Phys. B (1)

R. W. P. Drever, F. V. K. J. L. Hall, J. Hough, G. Ford, A. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B 31, 97–105 (1983).
[Crossref]

IEEE T. Microw. Theory (1)

T. Yoshino, K. Kurosawa, K. Itoh, and T. Ose, “Fiber-optic Fabry-Perot interferometer and its sensor applications,” IEEE T. Microw. Theory 30, 1612–1621 (1982).
[Crossref]

IEEE. Photon. Technol. Lett. (1)

J. Chen, Q. Liu, X. Fan, and Z. He, “Sub-nano-strain multiplexed fiber optic sensor array for quasi-static strain measurement,” IEEE. Photon. Technol. Lett. 28, 2311–2314 (2016).
[Crossref]

J. Lightwave Technol. (3)

A. Kersey, M. Davis, H. Patrick, M. Leblanc, K. Koo, C. Askins, M. Putnam, and E. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15, 1442–1463 (1997).
[Crossref]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[Crossref]

A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol. 17, 1849–1855 (1999).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Express (4)

Opt. Lett. (4)

Proc. SPIE (1)

T. Sato, R. Honda, and S. Shibata, “Ground strain measuring system using optical fiber sensors,” Proc. SPIE 3670, 470–479 (1999)
[Crossref]

Science (1)

G. Gagliardi, M. Salza, S. Avino, P. Ferraro, and P. Natale, “Probing the ultimate limit of fiber-optic strain sensing,” Science 330, 1081–1084 (2010).
[Crossref] [PubMed]

Other (2)

W. W. Morey, T. J. Bailey, W. H. Glenn, and G. Meltz, “Fiber Fabry-Perot interferometer using side exposed fiber Bragg gratings,” in “Optical Fiber Communication Conference,” (Optical Society of America, 1992), paper WA2.

G. Hernández, Fabry-perot interferometers (Cambridge University, 1988).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 The temporal responses of a FFPI with R = 0.99 and NR = 313. (a) Theoretical temporal response Ir (ϕ, t) in time-domain by Eq. 2 under M0 = 50 (solid lines) or M0 = ∞ (dash lines) and phase mismatches ϕ = 0, ±0.005π, ±0.01π, ±0.015π, ±0.02π. (b) The pulse energy ratio Er (ϕ) by Eq. 3 and the steady state response Ir (ϕ) by Eq. 1 near a resonance point. Curves of Er (ϕ) with M0 = 10, 50, 250 are separately given.
Fig. 2
Fig. 2 Illustration of the dual pulse interrogation method. The left part of the figure shows the frequencies of the two laser pulses and a resonance of FFPI in frequency domain; the right part gives the diagrammatic illustration of the reflected pulse pairs under different ν and the curve of frequency deviation signal.
Fig. 3
Fig. 3 Schematic diagram of the experiment system. CIR: optical circulator; CP: optical coupler; AOM: acousto-optic modulator; RM: reflection mirror; PD: photo detector; A/D: analog-digital converter; SG: signal generator; RF-AMP: radio-frequency signal amplifier. Diagrammatic sketch of signals after the SG, PD1, and PD2 are also given below the diagram for ease of understanding.
Fig. 4
Fig. 4 (a) The measured reflected pulses of FFPI 1. Incident laser pulse duration is set to 0.5 μs, and their frequency deviation to the resonance center are 0, 0.75 MHz, 1.50 MHz, 2.25 MHz, and 3.00 MHz (correspond to phase mismatches of 0, 0.006π, 0.012π, 0.018π, and 0.024π respectively). Parasitic pulses can be observed within t > 0.5μs. (b) The measured frequency deviation signal curves of FFPI 1 and FFPI 2 with laser frequency shifts from 480 MHz to 680 MHz (AOM operating frequencies from 240 MHz to 340 MHz), 3 zero-crossing points appear at 500 MHz, 580 MHz, and 630 MHz.
Fig. 5
Fig. 5 Time-domain results in the experiment. (a) Measured strain on FFPI 1 when 100 nεpp, 10 Hz strain signal is applied. (b)–(d) Measured strain on FFPI 1, FFPI 2, and FFPI 3 respectively when constant strain are applied; the standard deviations of the results are also given.
Fig. 6
Fig. 6 Frequency-domain results in the experiment. (a) The power density spectra of measured strain on FFPI 1 when 0.1 Hz, 1 Hz, 10 Hz and 100 Hz strain signals are separately applied. (b) Power density spectra of simultaneous measured results from all the channels when 1 Hz strain signal is applied on FFPI 1 while constant strain on FFPI 2 and 3.

Equations (9)

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

I r ( ϕ ) = | r + n = 1 ( 1 r 2 ) r 2 n + 1 e i n ϕ | 2 = 1 1 1 + F sin 2 ( ϕ 2 ) , ϕ = 2 n L × 2 π λ , F = 4 R ( 1 R ) 2 , R = r 2 , N R = π 2 F ,
I r ( ϕ , t ) = { | r + n = 1 M ( 1 r 2 ) r 2 n + 1 e i n ϕ | 2 , 0 , | ( n = 1 M 0 ( r 2 n 1 τ e i n ϕ ) r 2 ( M M 0 ) τ | 2 , 0 t < T 0 , t = T 0 , t > T 0 , M = t t 0 , M 0 = T 0 t 0 , I i ( t ) = u ( t ) u ( t T 0 )
E r ( ϕ ) = 0 T 0 I r ( ϕ , t ) d t 0 T 0 I t ( ϕ , t ) d t = 1 T 0 0 T 0 I r ( ϕ , t ) d t .
D ( v ) = E r ( 2 π v v F S R ϕ d ) E r ( 2 π v v F S R + ϕ d ) ,
Δ ε = k 1 Δ v ,
D 1 ( 1 ) ( v 1 0 ) , D 2 ( 1 ) ( v 2 0 ) , , D N ( 1 ) ( v N 0 ) .
δ v i 1 = K i 1 D i ( 1 ) ( v i 0 ) , i = 1 , 2 , , N .
v i 1 = v i 0 + δ v i 1 = v i 0 + K i 1 D i ( 1 ) ( v i 0 ) , i = 1 , 2 , , N .
v i k = v i k 1 + K i 1 D i ( k ) ( v i k 1 ) , i = 1 , 2 , , N .

Metrics