Abstract

We proposed and experimentally demonstrated a compact micro-displacement sensor with high sensitivity based on a long-period fiber grating (LPG) with an air-cavity. The sensor head is obtained by composing an air-cavity with the ends of a LPG and a single mode fiber (SMF). The wavelength shift of the LPG has a linear relationship with the length of the air gap which agrees well with the theoretical analysis. The experimental results show that the sensitivity is ~0.22 nm/µm within the micro-displacement range of 0 to 140 µm.

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References

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  1. H. G. Xu, T. Ono, and M. Esashi, “Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors,” J. Micromech. Microeng.16(12), 2747–2754 (2006).
    [CrossRef]
  2. S. Fericean and R. Droxler, “New noncontacting inductive analog proximity and inductive linear displacement sensors for industrial automation,” IEEE Sens. J.7(11), 1538–1545 (2007).
    [CrossRef]
  3. J. H. Ng, X. Zhou, X. Yang, and J. Hao, “A simple temperature-insensitive fiber Bragg grating displacement sensor,” Opt. Commun.273(2), 398–401 (2007).
    [CrossRef]
  4. X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
    [CrossRef]
  5. Y. Zhu, P. Shum, C. Lu, M. Lacquet, P. Swart, A. Chtcherbakov, and S. Spammer, “Temperature insensitive measurements of static displacements using a fiber Bragg grating,” Opt. Express11(16), 1918–1924 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-16-1918 .
    [CrossRef] [PubMed]
  6. Y. Zhao, H. Huang, and Q. Wang, “Interrogation technique using a novel spectra bandwidth measurement method with a blazed FBG and a fiber-optic array for an FBG displacement sensor,” Sens. Actuators A Phys.165(2), 185–188 (2011).
    [CrossRef]
  7. C. Shen and C. Zhong, “Novel temperature-insensitive fiber Bragg grating sensor for displacement Measurement,” Sens. Actuators A Phys.170(1–2), 51–54 (2011).
    [CrossRef]
  8. T. Guo, C. Chen, and J. Albert, “Non-uniform-tilt-modulated fiber Bragg grating for temperature-immune micro-displacement measurement,” Meas. Sci. Technol.20(3), 034007 (2009).
    [CrossRef]
  9. Q. Jiang and D. Hu, “Microdisplacement sensor based on tilted fiber Bragg grating transversal load effect,” IEEE Sens. J.11(9), 1776–1779 (2011).
    [CrossRef]
  10. J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
    [CrossRef]
  11. Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
    [CrossRef] [PubMed]
  12. Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).
  13. X. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long period fiber gratings,” J. Lightwave Technol.20(2), 255–266 (2002).
    [CrossRef]
  14. W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
    [CrossRef]
  15. C.-L. Zhao, L. Xiao, J. Ju, M. S. Demokan, and W. Jin, “Strain and temperature characteristics of a long-period grating written in a photonic crystal fiber and its application as a temperature-insensitive strain sensor,” J. Lightwave Technol.26(2), 220–227 (2008).
    [CrossRef]

2011 (5)

Y. Zhao, H. Huang, and Q. Wang, “Interrogation technique using a novel spectra bandwidth measurement method with a blazed FBG and a fiber-optic array for an FBG displacement sensor,” Sens. Actuators A Phys.165(2), 185–188 (2011).
[CrossRef]

C. Shen and C. Zhong, “Novel temperature-insensitive fiber Bragg grating sensor for displacement Measurement,” Sens. Actuators A Phys.170(1–2), 51–54 (2011).
[CrossRef]

Q. Jiang and D. Hu, “Microdisplacement sensor based on tilted fiber Bragg grating transversal load effect,” IEEE Sens. J.11(9), 1776–1779 (2011).
[CrossRef]

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

2009 (1)

T. Guo, C. Chen, and J. Albert, “Non-uniform-tilt-modulated fiber Bragg grating for temperature-immune micro-displacement measurement,” Meas. Sci. Technol.20(3), 034007 (2009).
[CrossRef]

2008 (1)

2007 (2)

S. Fericean and R. Droxler, “New noncontacting inductive analog proximity and inductive linear displacement sensors for industrial automation,” IEEE Sens. J.7(11), 1538–1545 (2007).
[CrossRef]

J. H. Ng, X. Zhou, X. Yang, and J. Hao, “A simple temperature-insensitive fiber Bragg grating displacement sensor,” Opt. Commun.273(2), 398–401 (2007).
[CrossRef]

2006 (2)

J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
[CrossRef]

H. G. Xu, T. Ono, and M. Esashi, “Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors,” J. Micromech. Microeng.16(12), 2747–2754 (2006).
[CrossRef]

2005 (1)

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

2003 (1)

2002 (1)

2001 (1)

Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).

Albert, J.

T. Guo, C. Chen, and J. Albert, “Non-uniform-tilt-modulated fiber Bragg grating for temperature-immune micro-displacement measurement,” Meas. Sci. Technol.20(3), 034007 (2009).
[CrossRef]

Baptista, J. M.

J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
[CrossRef]

Bennion, I.

Chan, C. C.

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

Chen, C.

T. Guo, C. Chen, and J. Albert, “Non-uniform-tilt-modulated fiber Bragg grating for temperature-immune micro-displacement measurement,” Meas. Sci. Technol.20(3), 034007 (2009).
[CrossRef]

Chtcherbakov, A.

Chung, Y.

Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).

Demokan, M. S.

Ding, L.

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

Dong, X.

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

Dong, X. Y.

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

Droxler, R.

S. Fericean and R. Droxler, “New noncontacting inductive analog proximity and inductive linear displacement sensors for industrial automation,” IEEE Sens. J.7(11), 1538–1545 (2007).
[CrossRef]

Esashi, M.

H. G. Xu, T. Ono, and M. Esashi, “Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors,” J. Micromech. Microeng.16(12), 2747–2754 (2006).
[CrossRef]

Fericean, S.

S. Fericean and R. Droxler, “New noncontacting inductive analog proximity and inductive linear displacement sensors for industrial automation,” IEEE Sens. J.7(11), 1538–1545 (2007).
[CrossRef]

Frazão, O.

J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
[CrossRef]

Guo, T.

T. Guo, C. Chen, and J. Albert, “Non-uniform-tilt-modulated fiber Bragg grating for temperature-immune micro-displacement measurement,” Meas. Sci. Technol.20(3), 034007 (2009).
[CrossRef]

Han, W. T.

Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).

Han, Y. G.

Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).

Hao, J.

J. H. Ng, X. Zhou, X. Yang, and J. Hao, “A simple temperature-insensitive fiber Bragg grating displacement sensor,” Opt. Commun.273(2), 398–401 (2007).
[CrossRef]

Hu, D.

Q. Jiang and D. Hu, “Microdisplacement sensor based on tilted fiber Bragg grating transversal load effect,” IEEE Sens. J.11(9), 1776–1779 (2011).
[CrossRef]

Hu, L.

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

Huang, H.

Y. Zhao, H. Huang, and Q. Wang, “Interrogation technique using a novel spectra bandwidth measurement method with a blazed FBG and a fiber-optic array for an FBG displacement sensor,” Sens. Actuators A Phys.165(2), 185–188 (2011).
[CrossRef]

Jiang, Q.

Q. Jiang and D. Hu, “Microdisplacement sensor based on tilted fiber Bragg grating transversal load effect,” IEEE Sens. J.11(9), 1776–1779 (2011).
[CrossRef]

Jin, S.

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

Jin, W.

Jin, Y.

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

Ju, J.

Lacquet, M.

Lee, B. H.

Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).

Lu, C.

Ng, J. H.

J. H. Ng, X. Zhou, X. Yang, and J. Hao, “A simple temperature-insensitive fiber Bragg grating displacement sensor,” Opt. Commun.273(2), 398–401 (2007).
[CrossRef]

Ngo, N. Q.

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

Ono, T.

H. G. Xu, T. Ono, and M. Esashi, “Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors,” J. Micromech. Microeng.16(12), 2747–2754 (2006).
[CrossRef]

Peak, U. C.

Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).

Rego, G.

J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
[CrossRef]

Santos, J. L.

J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
[CrossRef]

Santos, S. F.

J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
[CrossRef]

Shao, L.-Y.

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

Shen, C.

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

C. Shen and C. Zhong, “Novel temperature-insensitive fiber Bragg grating sensor for displacement Measurement,” Sens. Actuators A Phys.170(1–2), 51–54 (2011).
[CrossRef]

Shu, X.

Shum, P.

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

Y. Zhu, P. Shum, C. Lu, M. Lacquet, P. Swart, A. Chtcherbakov, and S. Spammer, “Temperature insensitive measurements of static displacements using a fiber Bragg grating,” Opt. Express11(16), 1918–1924 (2003), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-16-1918 .
[CrossRef] [PubMed]

Spammer, S.

Swart, P.

Wang, Q.

Y. Zhao, H. Huang, and Q. Wang, “Interrogation technique using a novel spectra bandwidth measurement method with a blazed FBG and a fiber-optic array for an FBG displacement sensor,” Sens. Actuators A Phys.165(2), 185–188 (2011).
[CrossRef]

Wang, Y.

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

Xiao, L.

Xu, H. G.

H. G. Xu, T. Ono, and M. Esashi, “Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors,” J. Micromech. Microeng.16(12), 2747–2754 (2006).
[CrossRef]

Yang, X.

J. H. Ng, X. Zhou, X. Yang, and J. Hao, “A simple temperature-insensitive fiber Bragg grating displacement sensor,” Opt. Commun.273(2), 398–401 (2007).
[CrossRef]

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

Zhang, L.

Zhao, C.-L.

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

C.-L. Zhao, L. Xiao, J. Ju, M. S. Demokan, and W. Jin, “Strain and temperature characteristics of a long-period grating written in a photonic crystal fiber and its application as a temperature-insensitive strain sensor,” J. Lightwave Technol.26(2), 220–227 (2008).
[CrossRef]

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

Zhao, Y.

Y. Zhao, H. Huang, and Q. Wang, “Interrogation technique using a novel spectra bandwidth measurement method with a blazed FBG and a fiber-optic array for an FBG displacement sensor,” Sens. Actuators A Phys.165(2), 185–188 (2011).
[CrossRef]

Zhong, C.

C. Shen and C. Zhong, “Novel temperature-insensitive fiber Bragg grating sensor for displacement Measurement,” Sens. Actuators A Phys.170(1–2), 51–54 (2011).
[CrossRef]

Zhou, W.

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

Zhou, X.

J. H. Ng, X. Zhou, X. Yang, and J. Hao, “A simple temperature-insensitive fiber Bragg grating displacement sensor,” Opt. Commun.273(2), 398–401 (2007).
[CrossRef]

Zhu, Y.

IEEE Sens. J. (2)

S. Fericean and R. Droxler, “New noncontacting inductive analog proximity and inductive linear displacement sensors for industrial automation,” IEEE Sens. J.7(11), 1538–1545 (2007).
[CrossRef]

Q. Jiang and D. Hu, “Microdisplacement sensor based on tilted fiber Bragg grating transversal load effect,” IEEE Sens. J.11(9), 1776–1779 (2011).
[CrossRef]

IEICE Trans. Electron. E (1)

Y. G. Han, B. H. Lee, W. T. Han, U. C. Peak, and Y. Chung, “Controllable transmission characteristics of multi-channel long period fiber gratings,” IEICE Trans. Electron. E84-C(5), 610–614 (2001).

J. Lightwave Technol. (2)

J. Micromech. Microeng. (1)

H. G. Xu, T. Ono, and M. Esashi, “Precise motion control of a nanopositioning PZT microstage using integrated capacitive displacement sensors,” J. Micromech. Microeng.16(12), 2747–2754 (2006).
[CrossRef]

Meas. Sci. Technol. (1)

T. Guo, C. Chen, and J. Albert, “Non-uniform-tilt-modulated fiber Bragg grating for temperature-immune micro-displacement measurement,” Meas. Sci. Technol.20(3), 034007 (2009).
[CrossRef]

Opt. Commun. (2)

J. M. Baptista, S. F. Santos, G. Rego, O. Frazão, and J. L. Santos, “Micro-displacement or bending measurement using a long-period fibre grating in a self-referenced fibre optic intensity sensor,” Opt. Commun.260(1), 8–11 (2006).
[CrossRef]

J. H. Ng, X. Zhou, X. Yang, and J. Hao, “A simple temperature-insensitive fiber Bragg grating displacement sensor,” Opt. Commun.273(2), 398–401 (2007).
[CrossRef]

Opt. Express (1)

Rev. Sci. Instrum. (1)

Y. Wang, C.-L. Zhao, L. Hu, X. Dong, Y. Jin, C. Shen, and S. Jin, “A tilt sensor with a compact dimension based on a long-period fiber grating,” Rev. Sci. Instrum.82(9), 093106 (2011).
[CrossRef] [PubMed]

Sens. Actuators A Phys. (3)

Y. Zhao, H. Huang, and Q. Wang, “Interrogation technique using a novel spectra bandwidth measurement method with a blazed FBG and a fiber-optic array for an FBG displacement sensor,” Sens. Actuators A Phys.165(2), 185–188 (2011).
[CrossRef]

C. Shen and C. Zhong, “Novel temperature-insensitive fiber Bragg grating sensor for displacement Measurement,” Sens. Actuators A Phys.170(1–2), 51–54 (2011).
[CrossRef]

W. Zhou, X. Dong, L.-Y. Shao, C. C. Chan, C.-L. Zhao, and P. Shum, “Compact refractometer based on extrinsic-phase-shift fiber Bragg grating,” Sens. Actuators A Phys.168(1), 46–50 (2011).
[CrossRef]

Smart Mater. Struct. (1)

X. Y. Dong, X. Yang, C.-L. Zhao, L. Ding, P. Shum, and N. Q. Ngo, “A novel temperature-insensitive fiber Bragg grating sensor for displacement measurement,” Smart Mater. Struct.14(2), N7–N10 (2005).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup of the proposed sensor.

Fig. 2
Fig. 2

Transmission spectra of the original LPG (in red), and the LPG with air cavity (in black).

Fig. 3
Fig. 3

Transmission spectra of the LPG with air cavity at different displacement variations.

Fig. 4
Fig. 4

The relationships of the dip wavelength with the displacement variations of the air cavity (in red) and cavity with LPG (in blue).

Fig. 5
Fig. 5

Transmission spectra of the air cavity at different displacement variation. The measured dip wavelength is marked by black arrows.

Tables (1)

Tables Icon

Table 1 Performance Comparison of Optical Fiber Grating Displacement Sensors

Equations (14)

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

{ a co (L)=exp(i( β co - 1 2 Δ β ν )L)[ a co (0)( cossL+i Δ β ν 2s sinsL )+ a cl ν (0) iκ s sinsL ] a cl ν (L)=exp(i( β cl ν - 1 2 Δ β ν )L)[ a co (0) i κ s sinsL+ a cl ν (0)( cossLi Δ β ν 2s sinsL ) ]
Δ β ν = β co β cl ν 2π Λ
s= ( κ κ+ Δ β ν 2 4 ) 1 2
M= [ A E B F ]/ t gap 2
A= e if /α-α r gap 2 e -if
B=- r gap e if /α+α r gap e -if
E= r gap e if /α-α r gap e -if
F=- r gap 2 e if /α+α e -if
r gap = n eff -n gap n eff +n gap
t gap = 1- r gap 2
f= 2π n gap L gap λ
[ a co a cl ν ]=M·[ a co (L) a cl ν (L) ]
[ a co ]= [ A B ]/ t gap 2 [ a co (L) a cl ν (L) ]
λ= 2π n gap Δ L gap C + 2π n gap L gap0 C

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