Abstract

A method of extracting the strain profile along a fiber Bragg grating from the intensity reflection spectrum is described. The procedure is based on a filter synthesis theory that relates the aperiodicity of a grating with its reflection spectrum. To illustrate the approach, we measured the strain profile near a hole in a plate and obtained a strain resolution of 80 μ∊. The spatial resolution depends on the strain gradient; i.e., the higher the gradient, the better the resolution. A resolution of 0.8 mm was achieved for a 5-mm grating with a gradient of 250 μ∊/mm.

© 1996 Optical Society of America

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References

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  1. S. Huang, M. Ohn, R. M. Measures, Appl. Opt. 35, 1135 (1996).
    [CrossRef] [PubMed]
  2. S. Huang, M. LeBlanc, M. Ohn, R. M. Measures, Appl. Opt. 34, 5003 (1995).
    [CrossRef] [PubMed]
  3. M. Matsuhara, K. O. Hill, A. Watanabe, J. Opt. Soc. Am. 65, 804 (1975).
    [CrossRef]
  4. C. D. Butter, G. B. Hocker, Appl. Opt. 17, 2867 (1978).
    [CrossRef] [PubMed]
  5. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
    [CrossRef]
  6. M. LeBlanc, S. Y. Huang, M. Ohn, R. M. Measures, Electron. Lett. 30, 2163 (1994).
    [CrossRef]
  7. S. A. Meguid, Engineering Fracture Mechanics (Elsevier, New York, 1989).
  8. K. O. Hill, Appl. Opt. 13, 1853 (1974).
    [CrossRef] [PubMed]

1996 (1)

1995 (1)

1994 (1)

M. LeBlanc, S. Y. Huang, M. Ohn, R. M. Measures, Electron. Lett. 30, 2163 (1994).
[CrossRef]

1993 (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

1978 (1)

1975 (1)

1974 (1)

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Butter, C. D.

Hill, K. O.

Hocker, G. B.

Huang, S.

Huang, S. Y.

M. LeBlanc, S. Y. Huang, M. Ohn, R. M. Measures, Electron. Lett. 30, 2163 (1994).
[CrossRef]

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

LeBlanc, M.

S. Huang, M. LeBlanc, M. Ohn, R. M. Measures, Appl. Opt. 34, 5003 (1995).
[CrossRef] [PubMed]

M. LeBlanc, S. Y. Huang, M. Ohn, R. M. Measures, Electron. Lett. 30, 2163 (1994).
[CrossRef]

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Matsuhara, M.

Measures, R. M.

Meguid, S. A.

S. A. Meguid, Engineering Fracture Mechanics (Elsevier, New York, 1989).

Ohn, M.

Watanabe, A.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, J. Albert, Appl. Phys. Lett. 62, 1035 (1993).
[CrossRef]

Electron. Lett. (1)

M. LeBlanc, S. Y. Huang, M. Ohn, R. M. Measures, Electron. Lett. 30, 2163 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (1)

S. A. Meguid, Engineering Fracture Mechanics (Elsevier, New York, 1989).

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Figures (3)

Fig. 1
Fig. 1

Schematic description of the location of the Bragg grating in proximity to a circular hole in an aluminum plate. The plate dimension is 270 mm × 51 mm × 3.18 mm, and the hole is in its geometric center.

Fig. 2
Fig. 2

Reflection spectra with the plate unloaded ( = 0 μ∊) and loaded = 1150 μ∊).

Fig. 3
Fig. 3

Calculated strain profiles for the spectra of Fig. 2. For the case = 1150 μ∊, the region 0.82 ≤ z ≤ 4.17 mm is not affected by the grating ends (solid curve). The finite length of the grating affects the entire measured profile for = 0 μ∊ (dotted curve).

Equations (3)

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λ ( z ) = 2 n ( z ) Λ ( z ) = 2 n 0 Λ 0 [ 1 + opt ( z ) ] .
λ ( z = 0 ) λ ( z ) ln [ 1 - R ( λ ) ] d λ = π 2 2 0 z Δ n 2 ( z ) n 2 ( z ) d ( z ) .
L eff = [ Λ 0 | d d z opt ( z ) | z = z i ] 1 / 2 .

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