Abstract

A compact sensor based on step-changed arc-induced long-period fiber gratings was implemented to discriminate between temperature and strain. The proposed sensor consists of a single long-period grating with two sections written consecutively in the SMF-28 fiber using the electric arc discharge technique. The two sections have the same period but different fabrication parameters. The operation of the sensor relies on the existence of a difference between the values of temperature and strain sensitivity of two neighboring resonances observed in the spectrum of the step-changed grating. The temperature and strain resolutions obtained for the sensor are 0.2°C and 35με, respectively.

© 2007 Optical Society of America

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  1. V. Bhatia, D. Campbell, R. O. Claus, and A. M. Vengsarkar, "Simultaneous strain and temperature measurement with long-period gratings," Opt. Lett. 22, 648-650 (1997).
    [CrossRef] [PubMed]
  2. O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
    [CrossRef]
  3. K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
    [CrossRef]
  4. Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
    [CrossRef]
  5. G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of temperature and strain based on arc-induced long-period fibre gratings," Electron. Lett. 41, 60-62 (2005).
    [CrossRef]
  6. G. Rego, O. Okhotnikov, E. Dianov, and V. Sulimov, "High temperature stability of long-period fiber gratings produced using an electric arc," J. Lightwave Technol. 19, 1574-1579 (2001).
    [CrossRef]
  7. G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Arc-induced long-period fiber gratings," Fiber Integr. Opt. 24, 245-259 (2005).
    [CrossRef]
  8. X. Shu, L. Zhang, and I. Bennion, "Sensitivity characteristics of long-period fiber gratings," J. Lightwave Technol. 20, 255-266 (2002).
    [CrossRef]
  9. F. Dürr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. M. Dianov, H. G. Limberger, and R. P. Salathé, "Tomographic stress profiling of arc-induced long-period fiber gratings," J. Lightwave Technol. 23, 3947-3953 (2005).
    [CrossRef]
  10. G. Rego, F. Dürr, P. V. S. Marques, and H. G. Limberger, "Strong asymmetric stresses arc-induced in preannealed nitrogen-doped fibres," Electron. Lett. 42, 334-335 (2006).
    [CrossRef]
  11. G. Humbert and A. Malki, "Electric-arc-induced gratings in nonhydrogenated fibers: fabrication and high-temperature characterizations," J. Opt. A 4, 194-198 (2002).
    [CrossRef]
  12. O. Ivanov, "Coupling of hybrid modes in strained and heated fibers," Opt. Commun. 239, 311-321 (2004).
    [CrossRef]
  13. V. Bhatia, "Applications of long-period gratings to single and multiparameter sensing," Opt. Express 4, 457-466 (1999).
    [CrossRef] [PubMed]
  14. B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
    [CrossRef]
  15. Y.-G. Han and S. B. Lee, "Effect of initial coupling strength on transmission characteristics of long-period fiber grating and its sensing application," in Optical Fiber Sensors,Proc. SPIE 5855, 675-678 (2005).
    [CrossRef]

2006 (1)

G. Rego, F. Dürr, P. V. S. Marques, and H. G. Limberger, "Strong asymmetric stresses arc-induced in preannealed nitrogen-doped fibres," Electron. Lett. 42, 334-335 (2006).
[CrossRef]

2005 (4)

Y.-G. Han and S. B. Lee, "Effect of initial coupling strength on transmission characteristics of long-period fiber grating and its sensing application," in Optical Fiber Sensors,Proc. SPIE 5855, 675-678 (2005).
[CrossRef]

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of temperature and strain based on arc-induced long-period fibre gratings," Electron. Lett. 41, 60-62 (2005).
[CrossRef]

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Arc-induced long-period fiber gratings," Fiber Integr. Opt. 24, 245-259 (2005).
[CrossRef]

F. Dürr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. M. Dianov, H. G. Limberger, and R. P. Salathé, "Tomographic stress profiling of arc-induced long-period fiber gratings," J. Lightwave Technol. 23, 3947-3953 (2005).
[CrossRef]

2004 (3)

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

O. Ivanov, "Coupling of hybrid modes in strained and heated fibers," Opt. Commun. 239, 311-321 (2004).
[CrossRef]

2003 (1)

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

2002 (3)

X. Shu, L. Zhang, and I. Bennion, "Sensitivity characteristics of long-period fiber gratings," J. Lightwave Technol. 20, 255-266 (2002).
[CrossRef]

G. Humbert and A. Malki, "Electric-arc-induced gratings in nonhydrogenated fibers: fabrication and high-temperature characterizations," J. Opt. A 4, 194-198 (2002).
[CrossRef]

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

2001 (1)

1999 (1)

1997 (1)

Araújo, F. M.

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

Bennion, I.

Bhatia, V.

Campbell, D.

Chan, H. L. W.

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

Choy, C. L.

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

Chung, Y.

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

Claus, R. O.

Demokan, M. S.

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

Dianov, E.

Dianov, E. M.

Dürr, F.

G. Rego, F. Dürr, P. V. S. Marques, and H. G. Limberger, "Strong asymmetric stresses arc-induced in preannealed nitrogen-doped fibres," Electron. Lett. 42, 334-335 (2006).
[CrossRef]

F. Dürr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. M. Dianov, H. G. Limberger, and R. P. Salathé, "Tomographic stress profiling of arc-induced long-period fiber gratings," J. Lightwave Technol. 23, 3947-3953 (2005).
[CrossRef]

Ferreira, L. A.

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

Frazão, O.

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

Guan, B. O.

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

Han, K. J.

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

Han, Y.-G.

Y.-G. Han and S. B. Lee, "Effect of initial coupling strength on transmission characteristics of long-period fiber grating and its sensing application," in Optical Fiber Sensors,Proc. SPIE 5855, 675-678 (2005).
[CrossRef]

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

Humbert, G.

G. Humbert and A. Malki, "Electric-arc-induced gratings in nonhydrogenated fibers: fabrication and high-temperature characterizations," J. Opt. A 4, 194-198 (2002).
[CrossRef]

Ivanov, O.

O. Ivanov, "Coupling of hybrid modes in strained and heated fibers," Opt. Commun. 239, 311-321 (2004).
[CrossRef]

Jung, J.

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

Kang, J.

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

Kim, C.-S.

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

Kwon, J.

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

Lee, B.

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

Lee, S.

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

Lee, S. B.

Y.-G. Han and S. B. Lee, "Effect of initial coupling strength on transmission characteristics of long-period fiber grating and its sensing application," in Optical Fiber Sensors,Proc. SPIE 5855, 675-678 (2005).
[CrossRef]

Lee, Y. W.

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

Limberger, H. G.

G. Rego, F. Dürr, P. V. S. Marques, and H. G. Limberger, "Strong asymmetric stresses arc-induced in preannealed nitrogen-doped fibres," Electron. Lett. 42, 334-335 (2006).
[CrossRef]

F. Dürr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. M. Dianov, H. G. Limberger, and R. P. Salathé, "Tomographic stress profiling of arc-induced long-period fiber gratings," J. Lightwave Technol. 23, 3947-3953 (2005).
[CrossRef]

Malki, A.

G. Humbert and A. Malki, "Electric-arc-induced gratings in nonhydrogenated fibers: fabrication and high-temperature characterizations," J. Opt. A 4, 194-198 (2002).
[CrossRef]

Marques, P. S.

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of temperature and strain based on arc-induced long-period fibre gratings," Electron. Lett. 41, 60-62 (2005).
[CrossRef]

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Arc-induced long-period fiber gratings," Fiber Integr. Opt. 24, 245-259 (2005).
[CrossRef]

Marques, P. V. S.

G. Rego, F. Dürr, P. V. S. Marques, and H. G. Limberger, "Strong asymmetric stresses arc-induced in preannealed nitrogen-doped fibres," Electron. Lett. 42, 334-335 (2006).
[CrossRef]

F. Dürr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. M. Dianov, H. G. Limberger, and R. P. Salathé, "Tomographic stress profiling of arc-induced long-period fiber gratings," J. Lightwave Technol. 23, 3947-3953 (2005).
[CrossRef]

Okhotnikov, O.

Paek, U.-C.

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

Rego, G.

G. Rego, F. Dürr, P. V. S. Marques, and H. G. Limberger, "Strong asymmetric stresses arc-induced in preannealed nitrogen-doped fibres," Electron. Lett. 42, 334-335 (2006).
[CrossRef]

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Arc-induced long-period fiber gratings," Fiber Integr. Opt. 24, 245-259 (2005).
[CrossRef]

F. Dürr, G. Rego, P. V. S. Marques, S. L. Semjonov, E. M. Dianov, H. G. Limberger, and R. P. Salathé, "Tomographic stress profiling of arc-induced long-period fiber gratings," J. Lightwave Technol. 23, 3947-3953 (2005).
[CrossRef]

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of temperature and strain based on arc-induced long-period fibre gratings," Electron. Lett. 41, 60-62 (2005).
[CrossRef]

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

G. Rego, O. Okhotnikov, E. Dianov, and V. Sulimov, "High temperature stability of long-period fiber gratings produced using an electric arc," J. Lightwave Technol. 19, 1574-1579 (2001).
[CrossRef]

Roh, S.

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

Salathé, R. P.

Salgado, H. M.

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Arc-induced long-period fiber gratings," Fiber Integr. Opt. 24, 245-259 (2005).
[CrossRef]

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of temperature and strain based on arc-induced long-period fibre gratings," Electron. Lett. 41, 60-62 (2005).
[CrossRef]

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

Santos, J. L.

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of temperature and strain based on arc-induced long-period fibre gratings," Electron. Lett. 41, 60-62 (2005).
[CrossRef]

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Arc-induced long-period fiber gratings," Fiber Integr. Opt. 24, 245-259 (2005).
[CrossRef]

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

Semjonov, S. L.

Shu, X.

Sulimov, V.

Tam, H. Y.

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

Tao, X. M.

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

Vengsarkar, A. M.

Zhang, A. P.

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

Zhang, L.

Electron. Lett. (2)

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of temperature and strain based on arc-induced long-period fibre gratings," Electron. Lett. 41, 60-62 (2005).
[CrossRef]

G. Rego, F. Dürr, P. V. S. Marques, and H. G. Limberger, "Strong asymmetric stresses arc-induced in preannealed nitrogen-doped fibres," Electron. Lett. 42, 334-335 (2006).
[CrossRef]

Fiber Integr. Opt. (1)

G. Rego, P. S. Marques, H. M. Salgado, and J. L. Santos, "Arc-induced long-period fiber gratings," Fiber Integr. Opt. 24, 245-259 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

K. J. Han, Y. W. Lee, J. Kwon, S. Roh, J. Jung, and B. Lee, "Simultaneous measurement of strain and temperature incorporating a long-period fiber grating inscribed on a polarization-maintaining fiber," IEEE Photon. Technol. Lett. 16, 2114-2116 (2004).
[CrossRef]

B. O. Guan, A. P. Zhang, H. Y. Tam, H. L. W. Chan, C. L. Choy, X. M. Tao, and M. S. Demokan, "Step-changed long-period fiber gratings," IEEE Photon. Technol. Lett. 14, 657-659 (2002).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. A (1)

G. Humbert and A. Malki, "Electric-arc-induced gratings in nonhydrogenated fibers: fabrication and high-temperature characterizations," J. Opt. A 4, 194-198 (2002).
[CrossRef]

Opt. Commun. (1)

O. Ivanov, "Coupling of hybrid modes in strained and heated fibers," Opt. Commun. 239, 311-321 (2004).
[CrossRef]

Opt. Exp. (1)

Y.-G. Han, S. Lee, C.-S. Kim, J. Kang, U.-C. Paek, and Y. Chung, "Simultaneous measurement of temperature and strain using dual long-period fiber gratings with controlled temperature and strain sensitivities," Opt. Exp. 11, 476-481 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (2)

O. Frazão, G. Rego, F. M. Araújo, L. A. Ferreira, H. M. Salgado, and J. L. Santos, "Simultaneous measurement of strain and temperature based on polarization loss properties of arc-induced long period gratings," in Second European Workshop on Fiber Sensors,Proc. SPIE 5502, 168-171 (2004).
[CrossRef]

Y.-G. Han and S. B. Lee, "Effect of initial coupling strength on transmission characteristics of long-period fiber grating and its sensing application," in Optical Fiber Sensors,Proc. SPIE 5855, 675-678 (2005).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Temperature and (b) strain sensitivities of the fourth resonance of 540 μ m LPFGs as a function of electric current (corresponding pulling tension and arc duration are given near each point).

Fig. 2
Fig. 2

(a) Temperature and (b) strain sensitivities versus resonance wavelengths for gratings with several different periods. The numbers indicate orders of resonances in the spectrum.

Fig. 3
Fig. 3

(a) Measured spectra of the grating during the fabrication process: after writing the first section (dashed curve, S1) and after writing the second section (solid curve, S 1 + S 2 ). (b) Theoretical spectra of each of the two sections simulated separately (dashed and short dashed curves, S1 and S2), combined grating (solid curve, S 1 + S 2 ), and cascaded grating with cladding mode stripped between the two sections (dotted curve, S 1 + S T + S 2 ).

Fig. 4
Fig. 4

(a) Strain and (b) temperature responses of the sensor. Experimental data points are fitted by linear (for strain) and quadratic (for temperature) functions.

Fig. 5
Fig. 5

Sensor output for the calibration points.

Equations (6)

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

T = | t c o ( 1 ) t c o ( 2 ) exp ( i ψ ) + t c l ( 1 ) t c l ( 2 ) | 2 ,
( λ 1 λ 2 ) = ( λ 10 λ 20 ) + [ a 1 b 1 a 2 b 2 ] ( ε Δ T ) + [ 0 c 1 0 c 2 ] ( ε 2 Δ T 2 ) ,
( λ 10 λ 20 ) = ( 1547.251 1577.414 ) [ a 1 b 1 a 2 b 2 ] = 10 3 [ 0.377273 47.9454 0.010555 62.8258 ] ,
( c 1 c 2 ) = 10 6 ( 1.37254 1.29529 ) ,
Δ T = b [ 1 a 2 + ( b [ 1 a 2 ) 2 + 4 c [ 1 a 2 Δ λ [ 1 a 2 2 c [ 1 a 2 ,
ε = c [ 1 Δ λ 2 c [ 1 b 2 Δ T c [ 1 a 2 ,

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