Abstract

Aiming at realizing a static strain sensor of nano-strain resolution, which is required in most geophysical applications, this paper presents a thorough analysis on the strain resolution of a fiber Bragg grating (FBG) static strain sensor interrogated with a narrow linewidth tunable laser. The main noise sources of the sensor are discussed, and the strain resolution is deduced with a cross-correlation algorithm. The theoretical prediction agrees well with our experimental result, and the analysis is further validated by numerical simulations. Based on the analysis, the paper provides the guidelines for optimizing this type of sensor to realize ultra-high resolution. It is shown that with properly designed FBGs and interrogation systems, nano static strain resolution can be realized, as we recently demonstrated in experiment.

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References

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  1. A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
    [CrossRef]
  2. M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
    [CrossRef]
  3. B. Lissak, A. Arie, and M. Tur, “Highly sensitive dynamic strain measurements by locking lasers to fiber Bragg gratings,” Opt. Lett. 23(24), 1930–1932 (1998).
    [CrossRef] [PubMed]
  4. D. Gatti, G. Galzerano, D. Janner, S. Longhi, and P. Laporta, “Fiber strain sensor based on a pi-phase-shifted Bragg grating and the Pound-Drever-Hall technique,” Opt. Express 16(3), 1945–1950 (2008).
    [CrossRef] [PubMed]
  5. A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol. 17(10), 1849–1855 (1999).
    [CrossRef]
  6. J. H. Chow, I. C. M. Littler, D. E. McClelland, and M. B. Gray, “Quasi-static fiber strain sensing with absolute frequency referencing,” in 19th International Coference on Optical Fiber Sensors, D. Sampson, ed. (Perth, Australia, 2008), 700429.
  7. Q. Liu, Z. He, T. Tokunaga, and K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Proc. of SPIE 4th European Workshop on Optical Fiber Sensors (Porto, 2010) 7653, 97–100.
  8. C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
    [CrossRef]
  9. G. Meltz, W. W. Morey, and W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14(15), 823–825 (1989).
    [CrossRef] [PubMed]

2008

M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
[CrossRef]

D. Gatti, G. Galzerano, D. Janner, S. Longhi, and P. Laporta, “Fiber strain sensor based on a pi-phase-shifted Bragg grating and the Pound-Drever-Hall technique,” Opt. Express 16(3), 1945–1950 (2008).
[CrossRef] [PubMed]

2007

C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
[CrossRef]

1999

1998

1997

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

1989

Arie, A.

Askins, C. G.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Bhattacharya, D. K.

M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
[CrossRef]

Chakraborty, A. K.

M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
[CrossRef]

Dasgupta, K.

M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
[CrossRef]

Davis, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Friebele, E. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Galzerano, G.

Gangopadhyay, T. K.

M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
[CrossRef]

Gatti, D.

Glenn, W. H.

Huang, C.

C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
[CrossRef]

Janner, D.

Jing, W. C.

C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
[CrossRef]

Kersey, A. D.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Koo, K. P.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Laporta, P.

LeBlanc, M.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Lissak, B.

Liu, K.

C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
[CrossRef]

Longhi, S.

Majumder, M.

M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
[CrossRef]

Meltz, G.

Morey, W. W.

Patrick, H. J.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Peng, G. D.

C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
[CrossRef]

Putnam, M. A.

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Tur, M.

Zhang, Y. M.

C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
[CrossRef]

IEEE Photon. Technol. Lett.

C. Huang, W. C. Jing, K. Liu, Y. M. Zhang, and G. D. Peng, “Demodulation of fiber Bragg grating sensor using cross-correlation algorithm,” IEEE Photon. Technol. Lett. 19(9), 707–709 (2007).
[CrossRef]

J. Lightwave Technol.

A. Arie, B. Lissak, and M. Tur, “Static fiber-Bragg grating strain sensing using frequency-locked lasers,” J. Lightwave Technol. 17(10), 1849–1855 (1999).
[CrossRef]

A. D. Kersey, M. A. Davis, H. J. Patrick, M. LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E. J. Friebele, “Fiber grating sensors,” J. Lightwave Technol. 15(8), 1442–1463 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

Sens. Actuators A Phys.

M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fibre Bragg gratings in structural health monitoring - Present status and applications,” Sens. Actuators A Phys. 147(1), 150–164 (2008).
[CrossRef]

Other

J. H. Chow, I. C. M. Littler, D. E. McClelland, and M. B. Gray, “Quasi-static fiber strain sensing with absolute frequency referencing,” in 19th International Coference on Optical Fiber Sensors, D. Sampson, ed. (Perth, Australia, 2008), 700429.

Q. Liu, Z. He, T. Tokunaga, and K. Hotate, “An ultra-high-resolution FBG static-strain sensor for geophysics applications,” in Proc. of SPIE 4th European Workshop on Optical Fiber Sensors (Porto, 2010) 7653, 97–100.

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Figures (8)

Fig. 1
Fig. 1

Typical system configuration of an FBG sensor interrogated with a tunable laser. CP, coupler; CIR, circulator; FBG ref., FBG for referencing; FBG sens., FBG for sensing.

Fig. 2
Fig. 2

Relative intensity noise level vs. integration time of a photo-detector (Agilent 81635A).

Fig. 3
Fig. 3

Wavelength repeatability induced reflectivity error in measurement. Blue and Red line: two measured spectra with wavelength fluctuation, where δλ1 and δλ2 are the wavelength differences between two repeated measurements.

Fig. 4
Fig. 4

The cross-correlation curve around the peak. Black dashed line: cross-correlation product without noise; Red line: original correlation product with noise; Dashed red line: shifted correlation product with noise. Gray zone: the region of cross-correlation curve fluctuates with noise.

Fig. 5
Fig. 5

Calculated resolution vs. simulated resolution.

Fig. 6
Fig. 6

Strain resolution vs. bandwidth of FBG with different shapes.

Fig. 7
Fig. 7

Strain resolution vs. FBG bandwidth under different wavelength inaccuracy of the laser source.

Fig. 8
Fig. 8

Strain resolution vs. FBG bandwidth under different intensity-noise level.

Tables (1)

Tables Icon

Table 1 Sensor Parameters in Ref. 7

Equations (10)

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C( j )= i=N N R( λ i+j )R( λ i+ε ) .
C'( j )= i=N N R( λ i+j )R( λ i ) + 2 i=N N R( λ i+j )N( λ i ) = C R ( j )+ C N ( j ).
Δ N ( j )= i=N N 2 R( λ i )N( λ i ) i=N N 2 R( λ ij )N( λ i ) = 2 jdλ( i=N N R'( λ ij/2 )Δ R elec + i=N N R'( λ ij/2 )R'( λ i )δλ ) = Δ N,elec ( j )+ Δ N,λ ( j ).
σ( Δ N )= σ 2 ( Δ N,elec )+ σ 2 ( Δ N,λ ) .
C R ( j )+ σ( Δ N ( j ) ) 2 C R ( 0 ).
R( λ )=exp( ( 2( λ λ 0 ) λ width ) 2n )=exp( ( 2i w ) 2n ).
C R ( 0 ) C R ( j ) ( 0.972n+0.28 ) w j 2 ,
σ( Δ N,elec )2j n 2 +0.26n+0.3 w 2 4 σ( Δ R elec ),
σ( Δ N,λ )j 20 n 2 9 w σ( δλ ) wdλ .
λ R,best =1.54 dλσ( Δ R elec )σ( δλ ) .

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