Abstract

A strain-distribution sensing technique based on the measurement of the phase spectrum of the reflected light from a fiber-optic Bragg grating is described. When a grating is subject to a strain gradient, the grating will experience a chirp and therefore the resonant wavelength will vary along the grating, causing wavelength-dependent penetration depth. Because the group delay for each wavelength component is related to its penetration depth and the resonant wavelength is determined by strain, a measured phase spectrum can then indicate the local strain as a function of location within the grating. This phase-based Bragg grating sensing technique offers a powerful new means for studying some important effects over a few millimeters or centimeters in smart structures.

© 1996 Optical Society of America

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  1. R. M. Measures, “Smart composite structures with embedded sensors,” Compos. Eng. 2, 597–618 (1992).
  2. A. T. Alavie, R. Maaskant, R. M. Measures, “Bragg grating laser sensing system for smart structures,” presented at the Eighth CIMTEC-World Ceramics Congress and Forum on New Materials, Florence, Italy, 29 June–4 July 1994.
  3. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
  4. W. W. Morey, G. Meltz, W. H. Glenn, “Fibre optic Bragg grating sensors,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 98–107 (1989).
  5. S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).
  6. A. D. Kersey, A. Dandridge, M. A. Davis, “Low-crosstalk code-division multiplexed interferometric array,” Electron. Lett. 28, 351–352 (1992).
  7. S. Huang, M. M. Ohn, M. LeBlanc, R. Lee, R. M. Measures, “Fiber optic intragrating distributed strain sensor,” in Distributed and Multiplexed Fiber Optic Sensors IV, A. D. Kersey, J. P. Oakin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2294, (1994).
  8. S. Huang, M. LeBlanc, M. M. Ohn, R. M. Measures, “Bragg integrating structural sensing,”Appl. Opt. 34, 5003–5009 (1995).
  9. H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1975).
  10. V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).
  11. B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).
  12. J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).
  13. F. Ouellette, “Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides,” Opt. Lett. 12, 847–849 (1987).
  14. K. O. Hill, “Aperiodic distributed-parameter waveguides for integrated optics,”Appl. Opt. 13, 1853–1856 (1974).
  15. M. LeBlanc, R. M. Measures, “Micromechanical considerations for embedded single ended sensors,” in Smart Structures and Materials 1993: Smart Sensing, Processing, and Instrumentation, R. O. Claus, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1918, 215–227 (1993).
  16. M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

1995 (2)

S. Huang, M. LeBlanc, M. M. Ohn, R. M. Measures, “Bragg integrating structural sensing,”Appl. Opt. 34, 5003–5009 (1995).

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

1993 (3)

V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

1992 (2)

A. D. Kersey, A. Dandridge, M. A. Davis, “Low-crosstalk code-division multiplexed interferometric array,” Electron. Lett. 28, 351–352 (1992).

R. M. Measures, “Smart composite structures with embedded sensors,” Compos. Eng. 2, 597–618 (1992).

1987 (1)

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).

1975 (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1975).

1974 (1)

Alavie, A. T.

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

A. T. Alavie, R. Maaskant, R. M. Measures, “Bragg grating laser sensing system for smart structures,” presented at the Eighth CIMTEC-World Ceramics Congress and Forum on New Materials, Florence, Italy, 29 June–4 July 1994.

Albert, J.

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).

Bilodeau, F.

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).

Coroy, T.

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

Dandridge, A.

A. D. Kersey, A. Dandridge, M. A. Davis, “Low-crosstalk code-division multiplexed interferometric array,” Electron. Lett. 28, 351–352 (1992).

Davis, M. A.

A. D. Kersey, A. Dandridge, M. A. Davis, “Low-crosstalk code-division multiplexed interferometric array,” Electron. Lett. 28, 351–352 (1992).

Erickson, L. E.

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).

Glenn, W. H.

W. W. Morey, G. Meltz, W. H. Glenn, “Fibre optic Bragg grating sensors,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 98–107 (1989).

Hill, K. O.

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).

K. O. Hill, “Aperiodic distributed-parameter waveguides for integrated optics,”Appl. Opt. 13, 1853–1856 (1974).

Huang, S.

S. Huang, M. LeBlanc, M. M. Ohn, R. M. Measures, “Bragg integrating structural sensing,”Appl. Opt. 34, 5003–5009 (1995).

S. Huang, M. M. Ohn, M. LeBlanc, R. Lee, R. M. Measures, “Fiber optic intragrating distributed strain sensor,” in Distributed and Multiplexed Fiber Optic Sensors IV, A. D. Kersey, J. P. Oakin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2294, (1994).

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Johnson, D. C.

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).

Karr, S.

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).

Kersey, A. D.

A. D. Kersey, A. Dandridge, M. A. Davis, “Low-crosstalk code-division multiplexed interferometric array,” Electron. Lett. 28, 351–352 (1992).

Kogelnik, H.

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1975).

LeBlanc, M.

S. Huang, M. LeBlanc, M. M. Ohn, R. M. Measures, “Bragg integrating structural sensing,”Appl. Opt. 34, 5003–5009 (1995).

S. Huang, M. M. Ohn, M. LeBlanc, R. Lee, R. M. Measures, “Fiber optic intragrating distributed strain sensor,” in Distributed and Multiplexed Fiber Optic Sensors IV, A. D. Kersey, J. P. Oakin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2294, (1994).

M. LeBlanc, R. M. Measures, “Micromechanical considerations for embedded single ended sensors,” in Smart Structures and Materials 1993: Smart Sensing, Processing, and Instrumentation, R. O. Claus, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1918, 215–227 (1993).

Lee, R.

S. Huang, M. M. Ohn, M. LeBlanc, R. Lee, R. M. Measures, “Fiber optic intragrating distributed strain sensor,” in Distributed and Multiplexed Fiber Optic Sensors IV, A. D. Kersey, J. P. Oakin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2294, (1994).

Liu, K.

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

Maaskant, R.

A. T. Alavie, R. Maaskant, R. M. Measures, “Bragg grating laser sensing system for smart structures,” presented at the Eighth CIMTEC-World Ceramics Congress and Forum on New Materials, Florence, Italy, 29 June–4 July 1994.

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Malo, B.

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).

Measures, R.

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Measures, R. M.

S. Huang, M. LeBlanc, M. M. Ohn, R. M. Measures, “Bragg integrating structural sensing,”Appl. Opt. 34, 5003–5009 (1995).

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

R. M. Measures, “Smart composite structures with embedded sensors,” Compos. Eng. 2, 597–618 (1992).

A. T. Alavie, R. Maaskant, R. M. Measures, “Bragg grating laser sensing system for smart structures,” presented at the Eighth CIMTEC-World Ceramics Congress and Forum on New Materials, Florence, Italy, 29 June–4 July 1994.

S. Huang, M. M. Ohn, M. LeBlanc, R. Lee, R. M. Measures, “Fiber optic intragrating distributed strain sensor,” in Distributed and Multiplexed Fiber Optic Sensors IV, A. D. Kersey, J. P. Oakin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2294, (1994).

M. LeBlanc, R. M. Measures, “Micromechanical considerations for embedded single ended sensors,” in Smart Structures and Materials 1993: Smart Sensing, Processing, and Instrumentation, R. O. Claus, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1918, 215–227 (1993).

Melle, S. M.

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

Meltz, G.

W. W. Morey, G. Meltz, W. H. Glenn, “Fibre optic Bragg grating sensors,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 98–107 (1989).

Mizrahi, V.

V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).

Morey, W. W.

W. W. Morey, G. Meltz, W. H. Glenn, “Fibre optic Bragg grating sensors,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 98–107 (1989).

Ohn, M.

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Ohn, M. M.

S. Huang, M. LeBlanc, M. M. Ohn, R. M. Measures, “Bragg integrating structural sensing,”Appl. Opt. 34, 5003–5009 (1995).

S. Huang, M. M. Ohn, M. LeBlanc, R. Lee, R. M. Measures, “Fiber optic intragrating distributed strain sensor,” in Distributed and Multiplexed Fiber Optic Sensors IV, A. D. Kersey, J. P. Oakin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2294, (1994).

Ouellette, F.

Sahlgren, B.

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Sandgren, S.

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Sipe, J. E.

V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).

Storøy, H.

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Stubbe, R.

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

Thériault, S.

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).

Bell Syst. Tech. J. (1)

H. Kogelnik, “Filter response of nonuniform almost-periodic structures,” Bell Syst. Tech. J. 55, 109–126 (1975).

Compos. Eng. (1)

R. M. Measures, “Smart composite structures with embedded sensors,” Compos. Eng. 2, 597–618 (1992).

Electron. Lett. (3)

A. D. Kersey, A. Dandridge, M. A. Davis, “Low-crosstalk code-division multiplexed interferometric array,” Electron. Lett. 28, 351–352 (1992).

B. Malo, K. O. Hill, F. Bilodeau, D. C. Johnson, J. Albert, “Point-by-point fabrication of micro-Bragg gratings in photosensitive fiber using single excimer pulse refractive index modification techniques,” Electron. Lett. 29, 1668–1669 (1993).

J. Albert, K. O. Hill, B. Malo, S. Thériault, F. Bilodeau, D. C. Johnson, L. E. Erickson, “Apodisation of the spectral response of fiber Bragg gratings using a phase mask with variable diffraction efficiency,” Electron. Lett. 31, 222–223 (1995).

IEEE Photon. Technol. Lett. (1)

S. M. Melle, A. T. Alavie, S. Karr, T. Coroy, K. Liu, R. M. Measures, “A Bragg grating-tuned fibre laser strain sensor system,” IEEE Photon. Technol. Lett. 5, 263–266 (1993).

J. Lightwave Technol. (1)

V. Mizrahi, J. E. Sipe, “Optical properties of photosensitive fiber phase gratings,” J. Lightwave Technol. 11, 1513–1517 (1993).

Opt. Lett. (1)

Other (5)

M. LeBlanc, R. M. Measures, “Micromechanical considerations for embedded single ended sensors,” in Smart Structures and Materials 1993: Smart Sensing, Processing, and Instrumentation, R. O. Claus, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1918, 215–227 (1993).

M. Ohn, S. Sandgren, S. Huang, R. Maaskant, R. Stubbe, B. Sahlgren, R. Measures, H. Storøy, “Phase based Bragg intra-grating sensing of strain gradients,” in Smart Structures and Materials 1995: Smart Sensing, Processing, and Instrumentation, W. B. Spillman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2444, 127–135 (1995).

S. Huang, M. M. Ohn, M. LeBlanc, R. Lee, R. M. Measures, “Fiber optic intragrating distributed strain sensor,” in Distributed and Multiplexed Fiber Optic Sensors IV, A. D. Kersey, J. P. Oakin, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2294, (1994).

A. T. Alavie, R. Maaskant, R. M. Measures, “Bragg grating laser sensing system for smart structures,” presented at the Eighth CIMTEC-World Ceramics Congress and Forum on New Materials, Florence, Italy, 29 June–4 July 1994.

W. W. Morey, G. Meltz, W. H. Glenn, “Fibre optic Bragg grating sensors,” in Fiber Optic and Laser Sensors VII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1169, 98–107 (1989).

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Figures (8)

Fig. 1
Fig. 1

Principle of the phase-based method: (a) measured phase spectrum, (b) phase-slope (group-delay) spectrum, (c) deduced penetration depth as a function of strain, (d) strain distribution along the grating.

Fig. 2
Fig. 2

Intensity spectra, phase spectra, and group-delay spectra for the gratings with (a) a constant Δn = 7 × 10−5 and (b) a Gaussian-distributed Δn(z) = 1.28 × 10−4 exp{−10[(zL G /2)/L G ]2} under a linearly varied strain field with g = 142.74 με/mm.

Fig. 3
Fig. 3

Recovered strain distributions based on the group-delay spectra in Figs. 2(a) and 2(b), respectively.

Fig. 4
Fig. 4

Recovered strain distributions with apodized gratings of (a) L G = 10.34 mm under g = 475.8 με/mm, (b) L G = 10.34 mm under g = 95.16 με/mm, and (c) L G = 20.68 mm under g = 95.16 με/mm.

Fig. 5
Fig. 5

Reflective intensity spectrum, phase spectrum, and group-delay spectrum for a grating with a Gaussian-distributed Δn(z) under a uniform strain field.

Fig. 6
Fig. 6

Axial strain distribution along a fiber that is embedded in an epoxy cylinder mounted on an aluminum beam with different loading applied to the beam. A 5-cm-long grating is located at the fiber end. (The gray area corresponds to the fiber part before the near end of the grating, and the point z = 5 mm corresponds to the fiber free end, i.e., the grating far end.)

Fig. 7
Fig. 7

(a) Group-delay spectrum obtained by the T-matrix method for the partially debonding case of ε1 = 0.75%. (b) Recovered strain distribution (solid curve) and the real strain field (dotted curve).

Fig. 8
Fig. 8

(a) Group-delay spectrum of a grating with a preset strain gradient under the strain field for the case of ε1 = 0.75%. (b) Recovered strain distribution. (c) Obtained net strain field (solid curve) and the real strain field (dotted curve).

Equations (10)

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λ ( Z ) = 2 n ¯ ( z ) Λ ( z ) = λ 0 + λ 0 { 1 n ¯ 0 2 [ p 12 v ( p 11 + p 12 ) ] } ε ( z ) ,
R ( λ ) = A 0 / B 0 2 , Ψ ( λ ) = arg ( A 0 / B 0 ) .
d Ψ d λ = 4 n ¯ c π λ c 2 ( λ ) ,
ε ( z ) = ε 1 + g z ,
λ ( z ) λ z = 0 = λ 0 { 1 n ¯ 0 2 [ p 12 v ( p 11 + p 12 ) ] } g z ,
z ( λ ) = λ λ z = 0 λ 0 { 1 n ¯ 0 2 [ p 12 v ( p 11 + p 12 ) ] } g .
d Ψ = 4 n ¯ 0 π ( λ λ z = 0 ) λ 0 3 { 1 n ¯ 0 2 [ p 12 v ( p 11 + p 12 ) ] } g ,
d 2 Ψ / d λ 2 = 4 n ¯ 0 π λ 0 3 { 1 n ¯ 0 2 [ p 12 v ( p 11 + p 12 ) ] } g .
l eff = ( Λ 0 / g eq ) 1 / 2 ,
g eq = { 1 1 / 2 n ¯ 0 2 [ p 12 v ( p 11 + p 12 ) ] } g .

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