Abstract

The use of a highly elliptical core two-mode fiber for simultaneous measurement of pressure (radial pressure or hydrostatic pressure) and temperature is presented. The sources of errors are discussed. Expressions are developed to calculate the cross sensitivities. From the numerical examples, some useful conclusions are given.

© 1996 Optical Society of America

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References

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  1. A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
    [CrossRef]
  2. S.-Y. Huang, J. N. Blake, B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990).
    [CrossRef]
  3. C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1984), Chap. 2.

1994 (1)

A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
[CrossRef]

1990 (1)

S.-Y. Huang, J. N. Blake, B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990).
[CrossRef]

Blake, J. N.

S.-Y. Huang, J. N. Blake, B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990).
[CrossRef]

Clausx, R. O.

A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
[CrossRef]

Craig Michie, W.

A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
[CrossRef]

Culshaw, B.

A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
[CrossRef]

Gerald, C. F.

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1984), Chap. 2.

Huang, S.-Y.

S.-Y. Huang, J. N. Blake, B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990).
[CrossRef]

Jankovic, L.

A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
[CrossRef]

Kim, B. Y.

S.-Y. Huang, J. N. Blake, B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990).
[CrossRef]

Vengsarkar, A. M.

A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
[CrossRef]

Wheatley, P. O.

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1984), Chap. 2.

J. Lightwave Technol. (2)

A. M. Vengsarkar, W. Craig Michie, L. Jankovic, B. Culshaw, R. O. Clausx, “Fiber-optic dual-technique sensor for simultaneous measurement of strain and temperature,” J. Lightwave Technol. 12, 170–177 (1994).
[CrossRef]

S.-Y. Huang, J. N. Blake, B. Y. Kim, “Perturbation effects on mode propagation in highly elliptical core two-mode fibers,” J. Lightwave Technol. 8, 23–33 (1990).
[CrossRef]

Other (1)

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, Mass., 1984), Chap. 2.

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Equations (38)

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Δ ϕ i = Δ β i L ,             i = x , y ,
Δ ϕ i Λ i , P Δ P + Λ i , T Δ T + Λ i , P T Δ P Δ T             i = x , y ,
Λ i , P = ( Δ β i ) P L + Δ β i L P             i = x , y ,
Λ i , T = ( Δ β i ) T L + Δ β i L T             i = x , y
Λ i , P T = P [ ( Δ β i ) T L + Δ β i L T ] = Λ i , T P             i = x , y
Δ ϕ i Λ i , P Δ P + Λ i , T Δ T ,
L δ P r = 2 ν L E ,
δ ( Δ β i ) δ P r = [ 1.077 Δ β i + 0.336 λ ( Δ β i ) λ ] 1 E ,
Λ i , P r = δ ( Δ ϕ i ) δ P r = [ 1.417 Δ β i + 0.336 λ ( Δ β i ) λ ] L E             i = x , y ,
δ L δ P h = - ( 1 - ν ) L E ,
δ ( Δ β i ) δ P h = [ - 0.336 Δ β i - 0.099 λ ( Δ β i ) λ ] 1 E ,
Λ i , P h = δ ( Δ ϕ i ) δ P h = [ - 0.464 Δ β i - 0.099 λ ( Δ β i ) λ ] L E             i = x , y ,
Λ i , T = δ ( Δ ϕ i ) δ T = - λ ( Δ β i ) λ L ( α + ζ )             i = x , y ,
Δ Φ = Λ Δ ξ ,
Λ = [ Λ λ 1 x , P Λ λ 1 x , T Λ λ 2 x , P Λ λ 2 x , T ] , Δ Φ = [ Δ λ 1 ϕ x Δ λ 2 ϕ x ] , Δ ξ = [ Δ P Δ T ] .
Δ λ 1 ϕ x Λ λ 1 x , P Δ P + Λ λ 1 x , T Δ T + Λ λ 1 x , P T Δ P Δ T , Δ λ 2 ϕ x Λ λ 2 x , P Δ P + Λ λ 2 x , T Δ T + Λ λ 2 x , P T Δ P Δ T ,
cond ( Λ ) = Λ Λ - 1 ,
δ ( Δ ξ ) Δ ξ cond ( Λ ) δ Λ Λ 1 - cond ( Λ ) δ Λ Λ ,
δ ( Δ ξ ) Δ ξ cond ( Λ ) δ ( Δ Φ ) Δ Φ .
Λ ~ [ 0.64 0.1 0.55 0.12 ]             λ = 580 nm λ = 600 nm .
Λ ~ [ - 0.20 0.1 - 0.18 0.12 ]             λ = 580 nm λ = 600 nm .
Λ i , P r T = P r [ - λ ( Δ β i ) λ L ( α + ζ ) ] = - λ 2 ( Δ β i ) λ P r L ( α + ζ ) - λ ( Δ β i ) λ ( α + ζ ) 2 ν E L = - λ ( α + ζ ) L ( λ { [ 1.077 Δ β i + 0.336 λ ( Δ β i ) λ ] 1 E } + 2 ν E ( Δ β i ) λ ) = - λ ( α + ζ ) L E [ - 1.077 ( Δ β i ) λ + 0.336 ( Δ β i ) λ + 0.336 λ 2 ( Δ β i ) λ 2 + 2 ν ( Δ β i ) λ ]             i = x , y = - λ ( α + ζ ) L E [ 1.753 ( Δ β i ) λ + 0.336 λ 2 ( Δ β i ) λ 2 ] .
Λ i , P h T = λ ( α + ζ ) L E [ 0.593 ( Δ β i ) λ + 0.099 λ 2 ( Δ β i ) λ 2 ] .
0.64 δ ( Δ P r ) + 0.1 δ ( Δ T ) - Λ x , P r T λ = 580 nm Δ P r Δ T = 0 , 0.55 δ ( Δ P r ) + 0.12 δ ( Δ T ) - Λ x , P r T λ = 600 nm Δ P r Δ T = 0.
Λ x , P r T λ = 580 nm ~ 6.94 × 10 - 6 rad / MPa ° C , Λ x , P r T λ = 600 nm ~ 1 × 10 - 5 rad / MPa ° C ,
δ ( Δ P r ) ~ 7.67 × 10 - 6 Δ P r Δ T , δ ( Δ T ) ~ 1.19 × 10 - 4 Δ P r Δ T ,
δ ( Δ P r ) / Δ P r ~ 7.67 × 10 - 4 Δ T % , δ ( Δ T ) / Δ T ~ 1.19 × 10 - 2 Δ P r % .
Λ x , P h T λ = 580 nm ~ - 2.17 × 10 - 6 rad / MPa ° C ,             Λ x , P h T λ = 600 nm ~ - 3.12 × 10 - 6 rad / MPa ° C ,
δ ( Δ P h ) ~ 8.57 × 10 - 6 Δ P h Δ T , δ ( Δ T ) ~ 3.89 × 10 - 5 Δ P h Δ T ,
δ ( Δ P h ) / Δ P h ~ 8.57 × 10 - 4 Δ T % , δ ( Δ T ) / Δ T ~ 3.89 × 10 - 3 Δ P h % .
[ δ ( Δ P r ) / Δ P r ] max ~ 0.0767 % , [ δ ( Δ T ) / Δ T ] max ~ 1.19 % ,
[ δ ( Δ P h ) / Δ P h ] max ~ 0.0857 % , [ δ ( Δ T ) / Δ T ] max ~ 0.389 % .
Λ x , P r T Λ x , T 1.753 E = 2.5 × 10 - 5 / MPa = constant .
δ ( Δ T ) / Δ T = 2.5 × 10 - 3 Δ P % .
[ δ ( Δ T ) / Δ T ] max ~ 0.25 % .
Λ x , P h T Λ x , T - 0.593 E - 8.47 × 10 - 6 / MPa = constant ,
δ ( Δ P h ) / Δ P h 0 , δ ( Δ T ) / Δ T ~ 8.47 × 10 - 4 Δ P h % .
[ δ ( Δ T ) / Δ T ] max ~ 0.0847 % .

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