Abstract

Simultaneous measurement of temperature and pressure with a single fiber Bragg grating (FBG) based on a broadened reflection spectrum is proposed and experimentally demonstrated. A novel double-hole structure of a cantilever beam is designed, and a FBG is affixed on the nonuniform strain area of the cantilever beam. The Bragg reflection bandwidth is sensitive to the spatially gradient strain but is free from the spatially uniform temperature. The wavelength peak shift and the bandwidth broadening of the FBG with a change of temperature and pressure allow for simultaneous discrimination between the temperature and the pressure effects. Standard deviation errors of 1.4°C   and   1 .8   kPa were obtained with temperature and pressure ranges of 20°C100  °C and 080  kPa, respectively. This novel and low-cost sensor approach has considerable potential applications for temperature-insensitive strain measurement.

© 2006 Optical Society of America

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  1. W. W. Morey, G. Meltz, and W. H. Glenn, "Bragg grating temperature and strain sensors," in Proceedings of the Sixth International Optical Fiber Sensor Conference (Springer, 1989), Vol. 44, pp. 526-531.
  2. Y. Zhao and Y. B. Liao, "Discrimination methods and demodulation techniques for fiber Bragg grating sensors," Opt. Lasers Eng. 41, 1-18 (2004).
    [CrossRef]
  3. P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
    [CrossRef]
  4. M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, "Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors," Electron. Lett. 30, 1085-1087 (1994).
    [CrossRef]
  5. E. Udd, D. Nelson, C. Lawrence, J. R. Spingarn, and B. Ferguson, "Three axis strain and temperature sensor," in Eleventh Optical Fiber Sensor Conference, Y.Ohtsuka and T.Yoshino, eds. (Japan Society of Applied Physics, 1996), pp. 244-247.
  6. S. W. James, M. L. Dockney, and R. P. Tatam, "Simultaneous independent temperature and strain measurement using in-fiber Bragg grating sensors," Electron. Lett. 32, 1133-1134 (1996).
    [CrossRef]
  7. G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).
  8. J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).
  9. J. Jung, N. Park, and B. Lee, "Simultaneous measurement of strain and temperature by use of a single fiber Bragg grating written in an erbium:ytterbium-doped fiber," Appl. Opt. 39, 1118-1120 (2000).
    [CrossRef]
  10. P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
    [CrossRef]
  11. X. Y. Dong, Y. Q. Liu, Z. G. Liu, and X. Y. Dong, "Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor," Opt. Commun. 192, 213-217 (2001).
    [CrossRef]
  12. Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).
  13. H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
    [CrossRef]
  14. T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).
  15. C. Fernandez-Valdivielso, I. R. Matias, and F. J. Arregui, "Simultaneous measurement of strain and temperature using a fiber Bragg grating and a thermochromic material," Sens. Actuators A 101, 107-116 (2002).
    [CrossRef]
  16. D. I. Forsyth, S. A. Wade, T. Sun, X. Chen, and K. T. V. Grattan, "Dual temperature and strain measurement with the combined fluorescence lifetime and Bragg wavelength shift approach in doped optical fiber," Appl. Opt. 41, 6585-6592 (2002).
    [CrossRef] [PubMed]
  17. M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, "Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis," Opt. Lett. 21, 1405-1407 (1996).
    [CrossRef] [PubMed]
  18. J. Hannah and M. J. Hillier, Applied Mechanics, 3rd ed. (Longmans, 1995), pp. 310-312.
  19. T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

2004 (2)

Y. Zhao and Y. B. Liao, "Discrimination methods and demodulation techniques for fiber Bragg grating sensors," Opt. Lasers Eng. 41, 1-18 (2004).
[CrossRef]

T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

2002 (2)

C. Fernandez-Valdivielso, I. R. Matias, and F. J. Arregui, "Simultaneous measurement of strain and temperature using a fiber Bragg grating and a thermochromic material," Sens. Actuators A 101, 107-116 (2002).
[CrossRef]

D. I. Forsyth, S. A. Wade, T. Sun, X. Chen, and K. T. V. Grattan, "Dual temperature and strain measurement with the combined fluorescence lifetime and Bragg wavelength shift approach in doped optical fiber," Appl. Opt. 41, 6585-6592 (2002).
[CrossRef] [PubMed]

2001 (1)

X. Y. Dong, Y. Q. Liu, Z. G. Liu, and X. Y. Dong, "Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor," Opt. Commun. 192, 213-217 (2001).
[CrossRef]

2000 (2)

Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).

J. Jung, N. Park, and B. Lee, "Simultaneous measurement of strain and temperature by use of a single fiber Bragg grating written in an erbium:ytterbium-doped fiber," Appl. Opt. 39, 1118-1120 (2000).
[CrossRef]

1999 (1)

P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
[CrossRef]

1996 (3)

S. W. James, M. L. Dockney, and R. P. Tatam, "Simultaneous independent temperature and strain measurement using in-fiber Bragg grating sensors," Electron. Lett. 32, 1133-1134 (1996).
[CrossRef]

M. LeBlanc, S. Y. Huang, M. Ohn, and R. M. Measures, "Distributed strain measurement based on a fiber Bragg grating and its reflection spectrum analysis," Opt. Lett. 21, 1405-1407 (1996).
[CrossRef] [PubMed]

H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
[CrossRef]

1995 (1)

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

1994 (1)

M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, "Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors," Electron. Lett. 30, 1085-1087 (1994).
[CrossRef]

Araujo, F. M.

P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
[CrossRef]

Archambault, J. L.

M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, "Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors," Electron. Lett. 30, 1085-1087 (1994).
[CrossRef]

Arregui, F. J.

C. Fernandez-Valdivielso, I. R. Matias, and F. J. Arregui, "Simultaneous measurement of strain and temperature using a fiber Bragg grating and a thermochromic material," Sens. Actuators A 101, 107-116 (2002).
[CrossRef]

Bennion, I.

T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).

Berthou, H.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Brady, G. P.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).

Cavaleiro, P. M.

P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
[CrossRef]

Chen, C. Y.

T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

Chen, X.

Dakin, J. P.

M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, "Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors," Electron. Lett. 30, 1085-1087 (1994).
[CrossRef]

Depeursinge, Y.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Dockney, M. L.

S. W. James, M. L. Dockney, and R. P. Tatam, "Simultaneous independent temperature and strain measurement using in-fiber Bragg grating sensors," Electron. Lett. 32, 1133-1134 (1996).
[CrossRef]

Dong, X. Y.

X. Y. Dong, Y. Q. Liu, Z. G. Liu, and X. Y. Dong, "Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor," Opt. Commun. 192, 213-217 (2001).
[CrossRef]

X. Y. Dong, Y. Q. Liu, Z. G. Liu, and X. Y. Dong, "Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor," Opt. Commun. 192, 213-217 (2001).
[CrossRef]

Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).

Dunphy, J. R.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Farahi, F.

P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
[CrossRef]

Ferdinand, P.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Ferguson, B.

E. Udd, D. Nelson, C. Lawrence, J. R. Spingarn, and B. Ferguson, "Three axis strain and temperature sensor," in Eleventh Optical Fiber Sensor Conference, Y.Ohtsuka and T.Yoshino, eds. (Japan Society of Applied Physics, 1996), pp. 244-247.

Fernandez-Valdivielso, C.

C. Fernandez-Valdivielso, I. R. Matias, and F. J. Arregui, "Simultaneous measurement of strain and temperature using a fiber Bragg grating and a thermochromic material," Sens. Actuators A 101, 107-116 (2002).
[CrossRef]

Fernando, G.

T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).

Ferragu, O.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Ferraro, P.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Ferreira, L. A.

P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
[CrossRef]

Forsyth, D. I.

Glenn, W. H.

W. W. Morey, G. Meltz, and W. H. Glenn, "Bragg grating temperature and strain sensors," in Proceedings of the Sixth International Optical Fiber Sensor Conference (Springer, 1989), Vol. 44, pp. 526-531.

Grattan, K. T. V.

Guo, T.

T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

Guo, Z. Y.

Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).

Hannah, J.

J. Hannah and M. J. Hillier, Applied Mechanics, 3rd ed. (Longmans, 1995), pp. 310-312.

Hillier, M. J.

J. Hannah and M. J. Hillier, Applied Mechanics, 3rd ed. (Longmans, 1995), pp. 310-312.

Huang, S. Y.

Imparato, S. I.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Jackson, D. A.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).

T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).

James, S. W.

S. W. James, M. L. Dockney, and R. P. Tatam, "Simultaneous independent temperature and strain measurement using in-fiber Bragg grating sensors," Electron. Lett. 32, 1133-1134 (1996).
[CrossRef]

Jarret, B.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Jia, Z. A.

T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

Jung, J.

Kalli, K.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).

Kersey, A. D.

H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
[CrossRef]

Kotrosios, G.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Lawrence, C.

E. Udd, D. Nelson, C. Lawrence, J. R. Spingarn, and B. Ferguson, "Three axis strain and temperature sensor," in Eleventh Optical Fiber Sensor Conference, Y.Ohtsuka and T.Yoshino, eds. (Japan Society of Applied Physics, 1996), pp. 244-247.

LeBlanc, M.

Lechien, J. L.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Lee, B.

Lescop, B.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Liao, Y. B.

Y. Zhao and Y. B. Liao, "Discrimination methods and demodulation techniques for fiber Bragg grating sensors," Opt. Lasers Eng. 41, 1-18 (2004).
[CrossRef]

Liu, T.

T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).

Liu, Y. Q.

X. Y. Dong, Y. Q. Liu, Z. G. Liu, and X. Y. Dong, "Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor," Opt. Commun. 192, 213-217 (2001).
[CrossRef]

Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).

Liu, Z. G.

X. Y. Dong, Y. Q. Liu, Z. G. Liu, and X. Y. Dong, "Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor," Opt. Commun. 192, 213-217 (2001).
[CrossRef]

Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).

Magne, S.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Marty, V.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Matias, I. R.

C. Fernandez-Valdivielso, I. R. Matias, and F. J. Arregui, "Simultaneous measurement of strain and temperature using a fiber Bragg grating and a thermochromic material," Sens. Actuators A 101, 107-116 (2002).
[CrossRef]

Measures, R. M.

Meltz, G.

W. W. Morey, G. Meltz, and W. H. Glenn, "Bragg grating temperature and strain sensors," in Proceedings of the Sixth International Optical Fiber Sensor Conference (Springer, 1989), Vol. 44, pp. 526-531.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Michel, J. B.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Morey, W. W.

W. W. Morey, G. Meltz, and W. H. Glenn, "Bragg grating temperature and strain sensors," in Proceedings of the Sixth International Optical Fiber Sensor Conference (Springer, 1989), Vol. 44, pp. 526-531.

Nelson, D.

E. Udd, D. Nelson, C. Lawrence, J. R. Spingarn, and B. Ferguson, "Three axis strain and temperature sensor," in Eleventh Optical Fiber Sensor Conference, Y.Ohtsuka and T.Yoshino, eds. (Japan Society of Applied Physics, 1996), pp. 244-247.

Neuman, V.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Ohn, M.

Park, N.

Patrick, H. J.

H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
[CrossRef]

Pedrazzani, J. R.

H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
[CrossRef]

Pierre, G.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Qiao, X. G.

T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

Rao, Y. J.

T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).

Reekie, L.

M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, "Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors," Electron. Lett. 30, 1085-1087 (1994).
[CrossRef]

Renouf, C.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Rougeault, S.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Santos, J. L.

P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
[CrossRef]

Signorazzi, M.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Spingarn, J. R.

E. Udd, D. Nelson, C. Lawrence, J. R. Spingarn, and B. Ferguson, "Three axis strain and temperature sensor," in Eleventh Optical Fiber Sensor Conference, Y.Ohtsuka and T.Yoshino, eds. (Japan Society of Applied Physics, 1996), pp. 244-247.

Stevens, W.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Sun, A.

T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

Sun, T.

Tatam, R. P.

S. W. James, M. L. Dockney, and R. P. Tatam, "Simultaneous independent temperature and strain measurement using in-fiber Bragg grating sensors," Electron. Lett. 32, 1133-1134 (1996).
[CrossRef]

Toscano, D.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Udd, E.

E. Udd, D. Nelson, C. Lawrence, J. R. Spingarn, and B. Ferguson, "Three axis strain and temperature sensor," in Eleventh Optical Fiber Sensor Conference, Y.Ohtsuka and T.Yoshino, eds. (Japan Society of Applied Physics, 1996), pp. 244-247.

Van Uffelen, M.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Vannucci, A.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Varasi, M.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Varelas, D.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Vengsarkar, A. M.

H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
[CrossRef]

Verbandt, Y.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Voet, M. R. H.

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Voto, C.

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

Wade, S. A.

Webb, D. J.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).

Williams, G. M.

H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
[CrossRef]

Xu, M. G.

M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, "Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors," Electron. Lett. 30, 1085-1087 (1994).
[CrossRef]

Zhang, L.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).

T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).

Zhang, Y.

Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).

Zhao, Y.

Y. Zhao and Y. B. Liao, "Discrimination methods and demodulation techniques for fiber Bragg grating sensors," Opt. Lasers Eng. 41, 1-18 (2004).
[CrossRef]

Acta Photon. Sin. (1)

T. Guo, X. G. Qiao, Z. A. Jia, A. Sun, and C. Y. Chen, "Investigation of fiber Bragg grating for pressure sensing based on reflected wave's broadened bandwidth," Acta Photon. Sin. 33, 288-290 (2004).

Appl. Opt. (2)

Chin. J. Lasers A (1)

Y. Q. Liu, Z. Y. Guo, Y. Zhang, Z. G. Liu, and X. Y. Dong, "Research on the simultaneous measurement of pressure and temperature using one fiber grating," Chin. J. Lasers A 27, 1002-1006 (2000).

Electron. Lett. (2)

M. G. Xu, J. L. Archambault, L. Reekie, and J. P. Dakin, "Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors," Electron. Lett. 30, 1085-1087 (1994).
[CrossRef]

S. W. James, M. L. Dockney, and R. P. Tatam, "Simultaneous independent temperature and strain measurement using in-fiber Bragg grating sensors," Electron. Lett. 32, 1133-1134 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

P. M. Cavaleiro, F. M. Araujo, L. A. Ferreira, J. L. Santos, and F. Farahi, "Simultaneous measurement of strain and temperature using Bragg gratings written in germanosilicate and boron-codoped germanosilicate fibers," IEEE Photon. Technol. Lett. 11, 1635-1637 (1999).
[CrossRef]

H. J. Patrick, G. M. Williams, A. D. Kersey, J. R. Pedrazzani, and A. M. Vengsarkar, "Hybrid fiber Bragg grating/long period fiber grating sensor for strain/temperature discrimination," IEEE Photon. Technol. Lett. 8, 1223-1225 (1996).
[CrossRef]

J. Lightwave Technol. (1)

P. Ferdinand, O. Ferragu, J. L. Lechien, B. Lescop, S. Magne, V. Marty, S. Rougeault, G. Kotrosios, V. Neuman, Y. Depeursinge, J. B. Michel, M. Van Uffelen, D. Varelas, H. Berthou, G. Pierre, C. Renouf, B. Jarret, Y. Verbandt, W. Stevens, M. R. H. Voet, and D. Toscano, "Mine operating accurate stability control with optical fiber sensing and Bragg grating technology: the BRITE-EuRam STABILOS project," J. Lightwave Technol. 13, 1303-1313 (1995).
[CrossRef]

Opt. Commun. (1)

X. Y. Dong, Y. Q. Liu, Z. G. Liu, and X. Y. Dong, "Simultaneous displacement and temperature measurement with cantilever-based fiber Bragg grating sensor," Opt. Commun. 192, 213-217 (2001).
[CrossRef]

Opt. Lasers Eng. (1)

Y. Zhao and Y. B. Liao, "Discrimination methods and demodulation techniques for fiber Bragg grating sensors," Opt. Lasers Eng. 41, 1-18 (2004).
[CrossRef]

Opt. Lett. (1)

Sens. Actuators A (1)

C. Fernandez-Valdivielso, I. R. Matias, and F. J. Arregui, "Simultaneous measurement of strain and temperature using a fiber Bragg grating and a thermochromic material," Sens. Actuators A 101, 107-116 (2002).
[CrossRef]

Other (6)

J. Hannah and M. J. Hillier, Applied Mechanics, 3rd ed. (Longmans, 1995), pp. 310-312.

T. Liu, G. Fernando, Y. J. Rao, D. A. Jackson, L. Zhang, and I. Bennion, "Simultaneous strain and temperature measurements in composites using a multiplexed fibre Bragg grating sensor and an extrinsic Fabry-Perot sensor," in Smart Sensing, Processing, and Instrumentation, R.O.Claus, ed., Proc. SPIE 3042, 203-212 (1997).

W. W. Morey, G. Meltz, and W. H. Glenn, "Bragg grating temperature and strain sensors," in Proceedings of the Sixth International Optical Fiber Sensor Conference (Springer, 1989), Vol. 44, pp. 526-531.

E. Udd, D. Nelson, C. Lawrence, J. R. Spingarn, and B. Ferguson, "Three axis strain and temperature sensor," in Eleventh Optical Fiber Sensor Conference, Y.Ohtsuka and T.Yoshino, eds. (Japan Society of Applied Physics, 1996), pp. 244-247.

G. P. Brady, K. Kalli, D. J. Webb, D. A. Jackson, L. Zhang, and I. Bennion, "Recent developments in optical fibre sensing using fibre Bragg gratings," in Fiber Optic and Laser Sensors XIV, R.P.De Paula and J.W.BertholdIII, eds., Proc. SPIE 2839, 8-19 (1996).

J. R. Dunphy, G. Meltz, M. Varasi, A. Vannucci, M. Signorazzi, P. Ferraro, S. I. Imparato, and C. Voto, "Embedded optical sensor capable of strain and temperature measurement using a single diffraction grating," U.S. patent 5,399,854 (21 March 1994).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the structure of the double-hole cantilever beam.

Fig. 2
Fig. 2

Reflection spectra of the FBG at 0 kPa (a), 40 kPa (b), and 80 kPa (c) with a temperature of 26 °C.

Fig. 3
Fig. 3

Reflection spectra of the FBG at 20 °C (a) and 100 °C (b) without any pressure applied on it.

Fig. 4
Fig. 4

Experimental arrangement for simultaneous temperature and pressure measurements.

Fig. 5
Fig. 5

Plot of λ B , λ BW versus temperature in the absence of applied pressure.

Fig. 6
Fig. 6

Plot of λ B , λ BW versus pressure at a temperature of 26 °C.

Fig. 7
Fig. 7

Bragg reflection power versus pressure.

Fig. 8
Fig. 8

Bragg reflection power versus temperature.

Equations (10)

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

ϵ = σ E = ( L x ) H 2 E I P ,
Δ ϵ = ( L x ) H l 2 E I 2 P .
Δ λ B = 2 n eff Λ { [ ( 1 p e ) ( L x ) H / ( 2 E I ) ] P + [ ξ + ( 1 p e ) α sub ] Δ T } ,
Δ λ B W = n eff Λ ( 1 p e ) ( L x ) H l E I 2 P ,
[ Δ λ B Δ λ B W ] = [ K P 1 K T 1 K P 2 0 ] [ P Δ T ] ,
K P 1 = n eff Λ ( 1 p e ) ( L x ) H / ( E I ) ,
K T 1 = 2 n eff Λ [ ξ + ( 1 p e ) α sub ] ,
K P 2 = n eff Λ ( 1 p e ) ( L x ) H l / ( E I 2 ) .
[ Δ λ B Δ λ B W ] = [ 0.0094 0.028 0.0132 0 ] [ P Δ T ] .
[ Δ λ B Δ P B ] = [ 0.0094 0.028 0.0336 0 ] [ P Δ T ] .

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