Abstract

For a competitive sensor, both the sensitivity enhancement and calibration convenience are important. However, for surface-mounted fiber grating strain sensors, researchers in previous studies have seldom addressed these two capabilities simultaneously. Using the coupled-mode theory, we calculated the voltage signals from the filtered spectral-power interrogation system for a fiber Bragg grating with a glued grating or with a glue-free grating subject to different strain fields. Under a grating zone (the targeted surface), a one-dimensional linearly varied strain field, described by both the parameters of the average strain and the strain gradient, was considered. Finally, a simple and easy formula is provided (the improved-bonding linearly chirped fiber grating) to achieve both the sensitivity enhancement and calibration convenience at the same time for the strain sensor.

© 2010 Optical Society of America

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References

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  1. K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
    [CrossRef]
  2. M. Majumder, T. K. Gangopadhyay, A. K. Chakraborty, K. Dasgupta, and D. K. Bhattacharya, “Fiber Bragg gratings in structural health monitoring-present status and applications,” Sens. Actuators A 147, 150–164 (2008).
    [CrossRef]
  3. R. M. Measures, S. Melle, and K. Liu, “Wavelength demodulated Bragg grating fiber optic sensing systems for addressing smart structures critical issues,” Smart Mater. Struct. 1, 36–44 (1992).
    [CrossRef]
  4. R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
    [CrossRef]
  5. V. P. Wnuk, A. Mendez, S. Ferguson, and T. Graver, “Process for mounting and packaging of fiber Bragg grating strain sensors for use in harsh environment applications,” Proc. SPIE 5758, 46–53 (2005).
    [CrossRef]
  6. J. Azana, M. A. Muriel, L. R. Chen, and W. E. Smith, “Fiber Bragg grating period reconstruction using time-frequency signal analysis and application to distributed sensing,” J. Lightwave Technol. 19, 646–654 (2001).
    [CrossRef]
  7. M. C. Parker and S. D. Walker, “A unified Fourier transform theory for photonic crystal and FBG filters in the strong coupling regime,” IEEE Photonics Technol. Lett. 14, 1321–1323 (2002).
    [CrossRef]
  8. P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fibre Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
    [CrossRef]
  9. M. LeBlanc, S. Y. Huang, M. M. Ohn, and R. M. Measures, “Tunable chirping of a fibre Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
    [CrossRef]
  10. S. Y. Huang, M. LeBlanc, M. M. Ohn, and R. M. Measures, “Bragg intragrating structural sensing,” Appl. Opt. 34, 5003–5009 (1995).
    [CrossRef] [PubMed]
  11. M. LeBlanc, S. Y. Huang, M. M. Ohn, R. M. Measures, A. Guemes, and A. Othonos, “Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis,” Opt. Lett. 21, 1405–1407 (1996).
    [CrossRef] [PubMed]
  12. S. Y. Huang, M. M. Ohn, and R. M. Measures, “Phase-based Bragg intragrating distributed strain sensor,” Appl. Opt. 35, 1135–1142 (1996).
    [CrossRef] [PubMed]
  13. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  14. W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
    [CrossRef]
  15. J. R. Pierce, “Coupling of modes of propagation,” J. Appl. Phys. 25, 179–183 (1954).
    [CrossRef]
  16. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
    [CrossRef]
  17. S. Ferguson, D. Snyder, T. Graver, and A. Mendez, “FlexPatch: a rugged miniature FBG strain sensor,” Proc. SPIE 6530, 653004 (2007).
    [CrossRef]

2008 (1)

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

2007 (1)

S. Ferguson, D. Snyder, T. Graver, and A. Mendez, “FlexPatch: a rugged miniature FBG strain sensor,” Proc. SPIE 6530, 653004 (2007).
[CrossRef]

2005 (1)

V. P. Wnuk, A. Mendez, S. Ferguson, and T. Graver, “Process for mounting and packaging of fiber Bragg grating strain sensors for use in harsh environment applications,” Proc. SPIE 5758, 46–53 (2005).
[CrossRef]

2002 (1)

M. C. Parker and S. D. Walker, “A unified Fourier transform theory for photonic crystal and FBG filters in the strong coupling regime,” IEEE Photonics Technol. Lett. 14, 1321–1323 (2002).
[CrossRef]

2001 (1)

1998 (1)

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
[CrossRef]

1997 (2)

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

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

1996 (2)

1995 (1)

1994 (2)

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fibre Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

M. LeBlanc, S. Y. Huang, M. M. Ohn, and R. M. Measures, “Tunable chirping of a fibre Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

1992 (1)

R. M. Measures, S. Melle, and K. Liu, “Wavelength demodulated Bragg grating fiber optic sensing systems for addressing smart structures critical issues,” Smart Mater. Struct. 1, 36–44 (1992).
[CrossRef]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

1959 (1)

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

1954 (1)

J. R. Pierce, “Coupling of modes of propagation,” J. Appl. Phys. 25, 179–183 (1954).
[CrossRef]

Azana, J.

Bennion, I.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
[CrossRef]

Bhattacharya, D. K.

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

Chakraborty, A. K.

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

Chen, L. R.

Dasgupta, K.

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

Eggleton, B. J.

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fibre Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

Erdogan, T.

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

Everall, L. A.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
[CrossRef]

Fallon, R. W.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
[CrossRef]

Ferguson, S.

S. Ferguson, D. Snyder, T. Graver, and A. Mendez, “FlexPatch: a rugged miniature FBG strain sensor,” Proc. SPIE 6530, 653004 (2007).
[CrossRef]

V. P. Wnuk, A. Mendez, S. Ferguson, and T. Graver, “Process for mounting and packaging of fiber Bragg grating strain sensors for use in harsh environment applications,” Proc. SPIE 5758, 46–53 (2005).
[CrossRef]

Gangopadhyay, T. K.

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

Graver, T.

S. Ferguson, D. Snyder, T. Graver, and A. Mendez, “FlexPatch: a rugged miniature FBG strain sensor,” Proc. SPIE 6530, 653004 (2007).
[CrossRef]

V. P. Wnuk, A. Mendez, S. Ferguson, and T. Graver, “Process for mounting and packaging of fiber Bragg grating strain sensors for use in harsh environment applications,” Proc. SPIE 5758, 46–53 (2005).
[CrossRef]

Guemes, A.

Hill, K. O.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

Hill, P. C.

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fibre Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

Huang, S. Y.

LeBlanc, M.

Liu, K.

R. M. Measures, S. Melle, and K. Liu, “Wavelength demodulated Bragg grating fiber optic sensing systems for addressing smart structures critical issues,” Smart Mater. Struct. 1, 36–44 (1992).
[CrossRef]

Majumder, M.

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

Measures, R. M.

Melle, S.

R. M. Measures, S. Melle, and K. Liu, “Wavelength demodulated Bragg grating fiber optic sensing systems for addressing smart structures critical issues,” Smart Mater. Struct. 1, 36–44 (1992).
[CrossRef]

Meltz, G.

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

Mendez, A.

S. Ferguson, D. Snyder, T. Graver, and A. Mendez, “FlexPatch: a rugged miniature FBG strain sensor,” Proc. SPIE 6530, 653004 (2007).
[CrossRef]

V. P. Wnuk, A. Mendez, S. Ferguson, and T. Graver, “Process for mounting and packaging of fiber Bragg grating strain sensors for use in harsh environment applications,” Proc. SPIE 5758, 46–53 (2005).
[CrossRef]

Muriel, M. A.

Ohn, M. M.

Othonos, A.

Parker, M. C.

M. C. Parker and S. D. Walker, “A unified Fourier transform theory for photonic crystal and FBG filters in the strong coupling regime,” IEEE Photonics Technol. Lett. 14, 1321–1323 (2002).
[CrossRef]

Pierce, J. R.

J. R. Pierce, “Coupling of modes of propagation,” J. Appl. Phys. 25, 179–183 (1954).
[CrossRef]

Post, D.

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Primak, W.

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

Smith, W. E.

Snyder, D.

S. Ferguson, D. Snyder, T. Graver, and A. Mendez, “FlexPatch: a rugged miniature FBG strain sensor,” Proc. SPIE 6530, 653004 (2007).
[CrossRef]

Walker, S. D.

M. C. Parker and S. D. Walker, “A unified Fourier transform theory for photonic crystal and FBG filters in the strong coupling regime,” IEEE Photonics Technol. Lett. 14, 1321–1323 (2002).
[CrossRef]

Williams, J. A. R.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
[CrossRef]

Wnuk, V. P.

V. P. Wnuk, A. Mendez, S. Ferguson, and T. Graver, “Process for mounting and packaging of fiber Bragg grating strain sensors for use in harsh environment applications,” Proc. SPIE 5758, 46–53 (2005).
[CrossRef]

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

Zhang, L.

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (2)

P. C. Hill and B. J. Eggleton, “Strain gradient chirp of fibre Bragg gratings,” Electron. Lett. 30, 1172–1174 (1994).
[CrossRef]

M. LeBlanc, S. Y. Huang, M. M. Ohn, and R. M. Measures, “Tunable chirping of a fibre Bragg grating using a tapered cantilever bed,” Electron. Lett. 30, 2163–2165 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919–933 (1973).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. C. Parker and S. D. Walker, “A unified Fourier transform theory for photonic crystal and FBG filters in the strong coupling regime,” IEEE Photonics Technol. Lett. 14, 1321–1323 (2002).
[CrossRef]

J. Appl. Phys. (2)

W. Primak and D. Post, “Photoelastic constants of vitreous silica and its elastic coefficient of refractive index,” J. Appl. Phys. 30, 779–788 (1959).
[CrossRef]

J. R. Pierce, “Coupling of modes of propagation,” J. Appl. Phys. 25, 179–183 (1954).
[CrossRef]

J. Lightwave Technol. (3)

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

K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15, 1263–1276 (1997).
[CrossRef]

J. Azana, M. A. Muriel, L. R. Chen, and W. E. Smith, “Fiber Bragg grating period reconstruction using time-frequency signal analysis and application to distributed sensing,” J. Lightwave Technol. 19, 646–654 (2001).
[CrossRef]

Meas. Sci. Technol. (1)

R. W. Fallon, L. Zhang, L. A. Everall, J. A. R. Williams, and I. Bennion, “All-fibre optical sensing system: Bragg grating sensor interrogated by a long-period grating,” Meas. Sci. Technol. 9, 1969–1973 (1998).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

S. Ferguson, D. Snyder, T. Graver, and A. Mendez, “FlexPatch: a rugged miniature FBG strain sensor,” Proc. SPIE 6530, 653004 (2007).
[CrossRef]

V. P. Wnuk, A. Mendez, S. Ferguson, and T. Graver, “Process for mounting and packaging of fiber Bragg grating strain sensors for use in harsh environment applications,” Proc. SPIE 5758, 46–53 (2005).
[CrossRef]

Sens. Actuators A (1)

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

Smart Mater. Struct. (1)

R. M. Measures, S. Melle, and K. Liu, “Wavelength demodulated Bragg grating fiber optic sensing systems for addressing smart structures critical issues,” Smart Mater. Struct. 1, 36–44 (1992).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Layout of the system considered in this research.

Fig. 2
Fig. 2

Discretization of an FBG from node number 0 (where z = 0 ) to N (where z = l ), and the related one-dimensional strain field.

Fig. 3
Fig. 3

Comparison between a result of numerical computations and its corresponding exact solution for a strain-free uniform pitched grating with l = 2 mm , Λ 0 = 500 nm , n 0 = 1.482 , δ n = 10 3 , and h = 1 .

Fig. 4
Fig. 4

Typical relationship between voltage signals, average strains, and strain gradients: (a) In the three-dimensional graph, the curved surface is for the TBFBG strain sensor, and the plane is for the IBFBG strain sensor. (b) In contour lines for the curved surface for the TBFBG, the values labeled on the contours are the corresponding voltage values.

Fig. 5
Fig. 5

First series of profiles for the strain paths with the constant ratio r = ε ave / g = 0.70 , 0.75, 0.83, 1.00, 1.50, 1.75, 2.16, 3.00, 5.50, and infinity (cm). These calculated results were obtained for ε 0 (the strain at z = 0 ) from 0.002 to + 0.002 with a constant difference of 0.0004 in ε 0 . Symbols (total of 99 triangles) are the calculated results.

Fig. 6
Fig. 6

Second series of profiles for the strain paths with the constant parameter ε ave from 0.008 to + 0.008 . Symbols (total of 121 triangles) are the calculated results in which g = 0.010 to + 0.010 cm 1 with a constant difference of 0.002 cm 1 in g.

Fig. 7
Fig. 7

Third series of profiles for the strain paths in which the constant parameter g = 0 to 0.010 cm 1 . Symbols (total of 66 triangles) are the calculated results in which ε ave = 0.008 to + 0.008 with a constant difference of 0.0016 in ε ave .

Fig. 8
Fig. 8

Reflection spectra for the constant ratio r = ε ave / g = 0.70 cm [the conditions (triangles) of the top curve shown in Fig. 5] in which ε ave = 0.007 to + 0.007 with a constant difference of 0.0014 in ε ave .

Fig. 9
Fig. 9

Reflection spectra for the constant parameter ε ave = 0.0 [the conditions (triangles) of the middle curve shown in Fig. 6] in which g = 0.010 to + 0.010 cm 1 with a constant difference of 0.002 cm 1 in g.

Fig. 10
Fig. 10

Reflection spectra for the constant parameter g = 0.010 cm 1 [the conditions (triangles) of the top straight line shown in Fig. 7] in which ε ave = 0.008 , 0, and + 0.008 . This figure only shows the three spectra with their complete shapes rather than the 11 interweaving spectra because of their overlapping in the finite bandwidth.

Fig. 11
Fig. 11

Relationship between the average strains and the central wavelengths of the spectra based on the calculated spectra for the results shown in Figs. 4 to 6 with a total of 286 data points.

Fig. 12
Fig. 12

Relationship between the strain gradients and the areas of spectra based on the calculated spectra for the results shown in Figs. 4 to 6 with a total of 286 data points.

Fig. 13
Fig. 13

Comparison of the typical relationships (among voltage signals, average strains, and strain gradients) between the improved-bonding linearly chirped fiber grating (the steep upper plane) and the IBFBG (the lower flattish plane).

Equations (18)

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n eff ( z ) = n 0 + δ n ( z ) · { h + cos [ 2 π Λ ( z ) z ] } ,
ε ( z ) = ε ave + ( z l 2 ) · g ,
Λ s = Λ 0 · { 1 + ε ave + g 2 · [ Λ 0 · ( 2 m 1 ) l ] } ,
n s = ( n 0 + h · δ n ) · ( 1 0.047125 · ε ( z ) ) .
σ ^ 2 π λ · n s π Λ s ,
κ π λ · δ n ,
V ( ε ) = Δ V ( ε ) + V B = k λ 1 λ 2 S ( λ ) · F ( λ ) · R ( ε , λ ) · P ( λ ) · d λ ,
L ( λ ) k · S ( λ ) · F ( λ ) · P ( λ ) .
L ( λ ) = L 0 + s 2 · ( λ λ a ) , λ [ λ a , λ b ] ,
Δ V ( ε ) = λ a λ b R ( λ ) L ( λ ) d λ ,
V B = λ 1 λ a R ( λ ) L ( λ ) d λ + λ b λ 2 R ( λ ) L ( λ ) d λ .
d A d z = j σ ^ A + j κ B ,
d B d z = j σ ^ B j κ A ,
R ( ε , λ ) = | B ( z = 0 , ε , λ ) A ( z = 0 , ε , λ ) | 2 .
d d z [ A B ] = [ j σ ^ j κ j κ j σ ^ ] · [ A B ] .
Δ V = Δ z · M · V .
V n = V n + 1 Δ V n + 1 = V n + 1 M n + 1 · V n + 1 · Δ z = ( I Δ z · M n + 1 ) · V n + 1 = T n + 1 · V n + 1 ,
V 0 = ( i = 1 N T i ) · V N .

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