Abstract

Using the overlap integral method and the Gaussian approximation for the single-mode fiber-optic field, the working principle of one- and two-dimensional differential fiber-optic displacement sensors for submillimeter measurements is demonstrated. The sensors consist of one emitting fiber and two or three receiving fibers, respectively, for the one- and two-dimensional sensors. Sensor responses are intrinsically linear over a wide range of travels. Moreover, for the two-dimensional sensor, each axis of displacement can be measured independently. Sensor responses are simulated experimentally using a highly precise robot. Linearity, travel, and sensitivity are characterized for the different gap distance between the emitting and receiving fibers. A design chart that includes nonlinearity error, travel, sensitivity, and gap is finally proposed.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [PubMed]
  3. L. Yuan, “Automatic-compensated two-dimensional fiber-optic sensor,” Opt. Fiber Technol. 4, 490-498 (1998).
    [CrossRef]
  4. J.-M. Lopez-Higuera, M. A. Morante, and A. Cobo, “Simple low-frequency optical fiber accelerometer with large rotating machine monitoring applications,” J. Lightwave Technol. 15, 1120-1130 (1997).
    [CrossRef]
  5. C. Doyle and G. F. Fernando, “Two-axis optical fiber accelerometer,” J. Mater. Sci. Lett. 19, 959-961 (2000).
    [CrossRef]
  6. S. J. Lee and D. W. Cho, “Development of a micro-opto-mechanical accelerometer based on intensity modulation,” Microsyst. Technol. 10, 147-154 (2004).
    [CrossRef]
  7. P. B. Tarsa, D. M. Brzozowski, P. Rabinowitz, and K. K. Lehmann, “Cavity ringdown strain gauge,” Opt. Lett. 29, 1339-1341 (2004).
    [CrossRef] [PubMed]
  8. C. Li, Y.-M. Zhang, H. Liu, S. Wu, and C.-W. Huanga, “Distributed fiber-optic bi-directional strain-displacement sensor modulated by fiber bending loss,” Sens. Actuators, A 111, 236-239 (2004).
    [CrossRef]
  9. Y. C. Yang, W. Hwang, H. C. Park, and K.S.Han, “Vibration sensing and impact location detection using optical fiber vibration sensor,” Key Eng. Mater. 183-187, 661-666 (2000).
    [CrossRef]
  10. E.-G. Neumann, Single-Mode Fibers I: Fundamentals (Springer-Verlag, 1988).
  11. Y. St-Amant, “Alignement automatisé de fibres optiques amorces monomodes,” Ph.D. dissertation (Mechanical Engineering Department Université Laval, Québec, Canada, 2004).
  12. J. A. Buck, Fundamentals of Optical Fibers, (Wiley , 1995).
  13. C. Doyle and G. F. Fernando, “Biaxial fiber-optic accelerometers,” Proc. SPIE 3986, 389-396 (2000).
    [CrossRef]

2004

S. J. Lee and D. W. Cho, “Development of a micro-opto-mechanical accelerometer based on intensity modulation,” Microsyst. Technol. 10, 147-154 (2004).
[CrossRef]

C. Li, Y.-M. Zhang, H. Liu, S. Wu, and C.-W. Huanga, “Distributed fiber-optic bi-directional strain-displacement sensor modulated by fiber bending loss,” Sens. Actuators, A 111, 236-239 (2004).
[CrossRef]

P. B. Tarsa, D. M. Brzozowski, P. Rabinowitz, and K. K. Lehmann, “Cavity ringdown strain gauge,” Opt. Lett. 29, 1339-1341 (2004).
[CrossRef] [PubMed]

2000

C. Doyle and G. F. Fernando, “Two-axis optical fiber accelerometer,” J. Mater. Sci. Lett. 19, 959-961 (2000).
[CrossRef]

Y. C. Yang, W. Hwang, H. C. Park, and K.S.Han, “Vibration sensing and impact location detection using optical fiber vibration sensor,” Key Eng. Mater. 183-187, 661-666 (2000).
[CrossRef]

C. Doyle and G. F. Fernando, “Biaxial fiber-optic accelerometers,” Proc. SPIE 3986, 389-396 (2000).
[CrossRef]

1998

L. Yuan, “Automatic-compensated two-dimensional fiber-optic sensor,” Opt. Fiber Technol. 4, 490-498 (1998).
[CrossRef]

1997

J.-M. Lopez-Higuera, M. A. Morante, and A. Cobo, “Simple low-frequency optical fiber accelerometer with large rotating machine monitoring applications,” J. Lightwave Technol. 15, 1120-1130 (1997).
[CrossRef]

1985

Appl. Opt.

J. Lightwave Technol.

J.-M. Lopez-Higuera, M. A. Morante, and A. Cobo, “Simple low-frequency optical fiber accelerometer with large rotating machine monitoring applications,” J. Lightwave Technol. 15, 1120-1130 (1997).
[CrossRef]

J. Mater. Sci. Lett.

C. Doyle and G. F. Fernando, “Two-axis optical fiber accelerometer,” J. Mater. Sci. Lett. 19, 959-961 (2000).
[CrossRef]

Key Eng. Mater.

Y. C. Yang, W. Hwang, H. C. Park, and K.S.Han, “Vibration sensing and impact location detection using optical fiber vibration sensor,” Key Eng. Mater. 183-187, 661-666 (2000).
[CrossRef]

Microsyst. Technol.

S. J. Lee and D. W. Cho, “Development of a micro-opto-mechanical accelerometer based on intensity modulation,” Microsyst. Technol. 10, 147-154 (2004).
[CrossRef]

Opt. Fiber Technol.

L. Yuan, “Automatic-compensated two-dimensional fiber-optic sensor,” Opt. Fiber Technol. 4, 490-498 (1998).
[CrossRef]

Opt. Lett.

Proc. SPIE

C. Doyle and G. F. Fernando, “Biaxial fiber-optic accelerometers,” Proc. SPIE 3986, 389-396 (2000).
[CrossRef]

Sens. Actuators, A

C. Li, Y.-M. Zhang, H. Liu, S. Wu, and C.-W. Huanga, “Distributed fiber-optic bi-directional strain-displacement sensor modulated by fiber bending loss,” Sens. Actuators, A 111, 236-239 (2004).
[CrossRef]

Other

E.-G. Neumann, Single-Mode Fibers I: Fundamentals (Springer-Verlag, 1988).

Y. St-Amant, “Alignement automatisé de fibres optiques amorces monomodes,” Ph.D. dissertation (Mechanical Engineering Department Université Laval, Québec, Canada, 2004).

J. A. Buck, Fundamentals of Optical Fibers, (Wiley , 1995).

Y. Lu, C. Butler, C. McKenzie, and J. K. Zhang, “A compact two dimensional optical fibre displacement sensor,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology, Quality Measurements: The Indispensable Bridge between Theory and Reality (IEEE1996), pp. 921-926.
[PubMed]

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Figures (11)

Fig. 1
Fig. 1

Working principle of (a) one-dimensional and (b) two- dimensional differential fiber-optic sensor.

Fig. 2
Fig. 2

Geometrical parameters of the optical coupling between two fibers.

Fig. 3
Fig. 3

Dimensionless sensitivity as a function of the dimensionless gap for a one-dimensional displacement sensor.

Fig. 4
Fig. 4

Experimental setup.

Fig. 5
Fig. 5

Optical power distribution for a gap z equal to (a)  250 μm and (b)  10 mm . Optical power difference distribution using an offset distance δ equal to 125 μm for (c)  z = 250 μm and (d)  z = 10 mm . Optical power difference distribution divided by the offset distance for offset values δ equal to 10 μm (dashed curve) and 125 μm (continuous curve), respectively, for (e)  z = 250 μm and (f)  z = 10 μm .

Fig. 6
Fig. 6

Sensitivity of the sensor as a function of the gap distance for a nonlinearity error of 0.5%, 1%, and 2%.

Fig. 7
Fig. 7

Comparison between the theoretical and experimental values of the sensitivity divided by the offset distance between the receiving fibers : theoretical value (continuous curve), experimental values using an offset distance equals to 125 μm (dotted curve) and 10 μm (dashed curve).

Fig. 8
Fig. 8

Sensor travel as a function of the gap distance for 0.5%, 1%, and 2% nonlinearity error (dashed curve) and the proposed design guidelines (continuous curve).

Fig. 9
Fig. 9

Design chart of the proposed sensor.

Fig. 10
Fig. 10

Thirteen one-dimensional scans performed to validate the two-dimensional sensor.

Fig. 11
Fig. 11

(a) Optical power transverse distributions of the 13 one-dimensional scans illustrated in Fig. 10, and (b) optical power difference distributions of (a).

Equations (21)

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P dB = 10 log ( 4 σ G 2 + ( σ + 1 ) 2 ) 10 P ln 10 [ ( σ + 1 ) ( F x 2 + F y 2 ) G 2 + ( σ + 1 ) 2 ] ,
σ = ( w 02 w 01 ) 2 , p = 2 ( π n w 01 λ ) 2 , F x = x z R 1 , F y = y z R 1 , G = z z R 1 , z R 1 = π n w 01 2 λ ,
P dB = A ( x 2 + y 2 ) + B ,
A = 10 p ln 10 [ ( σ + 1 ) G 2 + ( σ + 1 ) 2 ] 1 z R 1 2 ,
B = 10 log ( 4 σ G 2 + ( σ + 1 ) 2 ) .
P 1 dB = A ( x 1 ) 2 + B ,
P 2 dB = A ( x 2 ) 2 + B ,
B = 10 log ( 4 σ G 2 + ( σ + 1 ) 2 ) 10 p ln 10 [ ( σ + 1 ) G 2 + ( σ + 1 ) 2 ] ( y z R 1 ) 2 .
Δ P dB = P 2 dB P 1 dB = A [ ( x 2 ) 2 ( x 1 ) 2 ] .
Δ P dB = ( 2 A δ ) x c ,
S = ( 2 A δ ) .
S = 20 ln 10 [ ( σ + 1 ) G 2 + ( σ + 1 ) 2 ] δ w 01 2 .
S w 01 2 δ = 20 ln 10 [ ( σ + 1 ) G 2 + ( σ + 1 ) 2 ] .
S δ = 20 ln 10 [ ( σ + 1 ) G 2 + ( σ + 1 ) 2 ] 1 w 01 2 .
P 1 dB = A [ ( x 1 ) 2 + ( y 1 ) 2 ] + B ,
P 2 dB = A [ ( x 2 ) 2 + ( y 1 ) 2 ] + B ,
P 3 dB = A [ ( x 2 ) 2 + ( y 3 ) 2 ] + B .
Δ P x dB = P 2 dB P 1 dB = A [ ( x 2 ) 2 ( x 1 ) 2 ] ,
Δ P y dB = P 3 dB P 1 dB = A [ ( y 3 ) 2 ( y 1 ) 2 ] .
Δ P x dB = ( 2 A δ ) x c ,
Δ P y dB = ( 2 A δ ) y c ,

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