Abstract

We demonstrate the working principle of a one-dimensional intensity-based fiber-optic displacement sensor. The sensor consists of one receiving fiber, which is moved laterally in the optical field emitted by an emitting fiber. It is shown numerically that the sensor response is highly linear (nonlinearity error of 0.1 to 2%) for a wide range of travel (2.24 to 860μm). The sensor response is also simulated experimentally using a highly precise robot, the results of which correspond very closely to numerical ones. Linearity, travel, and sensitivity are experimentally determined for different gaps between the emitting and the receiving fibers (10μm to 10mm). A design chart that includes the nonlinearity error (0.5% to 2%), the travel (2.78 to 860μm), the sensitivity (0.032 to 0.37dB/μm), and the gap distance (1 to 10mm) is finally proposed.

© 2009 Optical Society of America

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References

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  1. C. D. Kissinger, “Fiber optic proximity probe,” U.S. patent 3,327,584 (27 June 1967).
  2. R. O. Cook and C. W. Hamm, “Fiber optic lever displacement transducer,” Appl. Opt. 18, 3230-3241 (1979).
    [CrossRef] [PubMed]
  3. M. Johnson and G. Goodman, “One and two-dimensional, differential, reflective fiber displacement sensors,” Appl. Opt. 24, 2369-2372 (1985).
    [CrossRef] [PubMed]
  4. A. Shimamoto and K. Tanaka, “Geometrical analysis of an optical fiber bundle displacement sensor,” Appl. Opt. 35, 6767-6774 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
  6. G. A. Rines, “Fiber-optic accelerometer with hydrophone applications,” Appl. Opt. 20, 3453-3460 (1981).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. 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]
  9. J. Kalenik and R. Pajak, “A cantilever optical-fiber accelerometer,” Sens. Actuators A 68, 350-355 (1998).
    [CrossRef]
  10. C. Doyle and G. F. Fernando, “Two-axis optical fiber accelerometer,” J. Mater. Sci. Lett. 19, 959-961 (2000).
    [CrossRef]
  11. C. Doyle and G. F. Fernando, “Biaxial fiber-optic accelerometers,” Proc. SPIE 3986, 389-396 (2000).
    [CrossRef]
  12. Y. St-Amant, D. Gariépy, and D. Rancourt, “Intrinsic properties of the optical coupling between axisymmetric Gaussian beams,” Appl. Opt. 43, 5691-5704 (2004).
    [CrossRef] [PubMed]
  13. J. A. Buck, Fundamentals of Optical Fibers (Wiley, 1995).
  14. A. E. Siegman, Lasers (University Science, 1986).
  15. Y. St-Amant, D. Gariépy, and D. Rancourt, “Model-based far-field alignment algorithm for Gaussian beamlike single-mode optical devices,” Appl. Opt. 46, 2297-2306 (2007).
    [CrossRef] [PubMed]
  16. V. Trudel and Y. St-Amant, “One- and two-dimensional single-mode differential fiber-optic displacement sensor for submillimeter measurements,” Appl. Opt. 47, 1082-1089 (2008).
    [CrossRef] [PubMed]

2008 (1)

2007 (1)

2004 (2)

Y. St-Amant, D. Gariépy, and D. Rancourt, “Intrinsic properties of the optical coupling between axisymmetric Gaussian beams,” Appl. Opt. 43, 5691-5704 (2004).
[CrossRef] [PubMed]

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]

2000 (2)

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

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

1998 (1)

J. Kalenik and R. Pajak, “A cantilever optical-fiber accelerometer,” Sens. Actuators A 68, 350-355 (1998).
[CrossRef]

1997 (1)

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]

1996 (2)

A. Shimamoto and K. Tanaka, “Geometrical analysis of an optical fiber bundle displacement sensor,” Appl. Opt. 35, 6767-6774 (1996).
[CrossRef] [PubMed]

M. Morante, A. Cobo, J. M. Lopez-Higuera, and M. Lopez-Amo, “New approach using a bare fiber optic cantilever beam as a low-frequency acceleration measuring element,” Opt. Eng. 35, 1700-1706 (1996).
[CrossRef]

1985 (1)

1981 (1)

1979 (1)

Buck, J. A.

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

Cho, D. W.

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]

Cobo, A.

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]

M. Morante, A. Cobo, J. M. Lopez-Higuera, and M. Lopez-Amo, “New approach using a bare fiber optic cantilever beam as a low-frequency acceleration measuring element,” Opt. Eng. 35, 1700-1706 (1996).
[CrossRef]

Cook, R. O.

Doyle, C.

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

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

Fernando, G. F.

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

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

Gariépy, D.

Goodman, G.

Hamm, C. W.

Johnson, M.

Kalenik, J.

J. Kalenik and R. Pajak, “A cantilever optical-fiber accelerometer,” Sens. Actuators A 68, 350-355 (1998).
[CrossRef]

Kissinger, C. D.

C. D. Kissinger, “Fiber optic proximity probe,” U.S. patent 3,327,584 (27 June 1967).

Lee, S. J.

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]

Lopez-Amo, M.

M. Morante, A. Cobo, J. M. Lopez-Higuera, and M. Lopez-Amo, “New approach using a bare fiber optic cantilever beam as a low-frequency acceleration measuring element,” Opt. Eng. 35, 1700-1706 (1996).
[CrossRef]

Lopez-Higuera, J. M.

M. Morante, A. Cobo, J. M. Lopez-Higuera, and M. Lopez-Amo, “New approach using a bare fiber optic cantilever beam as a low-frequency acceleration measuring element,” Opt. Eng. 35, 1700-1706 (1996).
[CrossRef]

Lopez-Higuera, J.-M.

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]

Morante, M.

M. Morante, A. Cobo, J. M. Lopez-Higuera, and M. Lopez-Amo, “New approach using a bare fiber optic cantilever beam as a low-frequency acceleration measuring element,” Opt. Eng. 35, 1700-1706 (1996).
[CrossRef]

Morante, M. A.

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]

Pajak, R.

J. Kalenik and R. Pajak, “A cantilever optical-fiber accelerometer,” Sens. Actuators A 68, 350-355 (1998).
[CrossRef]

Rancourt, D.

Rines, G. A.

Shimamoto, A.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, 1986).

St-Amant, Y.

Tanaka, K.

Trudel, V.

Appl. Opt. (7)

J. Lightwave Technol. (1)

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. (1)

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

Microsyst. Technol. (1)

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. Eng. (1)

M. Morante, A. Cobo, J. M. Lopez-Higuera, and M. Lopez-Amo, “New approach using a bare fiber optic cantilever beam as a low-frequency acceleration measuring element,” Opt. Eng. 35, 1700-1706 (1996).
[CrossRef]

Proc. SPIE (1)

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

Sens. Actuators A (1)

J. Kalenik and R. Pajak, “A cantilever optical-fiber accelerometer,” Sens. Actuators A 68, 350-355 (1998).
[CrossRef]

Other (3)

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

A. E. Siegman, Lasers (University Science, 1986).

C. D. Kissinger, “Fiber optic proximity probe,” U.S. patent 3,327,584 (27 June 1967).

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Figures (11)

Fig. 1
Fig. 1

Working principle of the displacement sensor.

Fig. 2
Fig. 2

Fundamental propagation mode of a single-mode fiber (solid curve) and its Gaussian approximation (dashed curve).

Fig. 3
Fig. 3

Propagated optical fields and coupling efficiency.

Fig. 4
Fig. 4

Theoretical optical power distribution for gaps z d equal to (a)  50 μm , (b)  125 μm , (c)  500 μm , and (d)  10 mm .

Fig. 5
Fig. 5

Theoretical sensitivity of the sensor.

Fig. 6
Fig. 6

Experimental setup.

Fig. 7
Fig. 7

Experimental optical power distribution for gaps z d equal to (a)  10 μm , (b)  125 μm , (c)  500 μm , and (d)  10 mm .

Fig. 8
Fig. 8

Sensitivity of the sensor as a function of the gap distance.

Fig. 9
Fig. 9

Theoretical (solid curve) and experimental (solid circle) sensitivity comparison.

Fig. 10
Fig. 10

Sensor travel as a function of the gap distance for 0.1%, 0.5%, 1%, and 2% nonlinearity error (dashed curves) and the proposed design guidelines (solid curves).

Fig. 11
Fig. 11

Design chart.

Tables (2)

Tables Icon

Table 1 Numerical Parameters

Tables Icon

Table 2 Sensor Travel as a Function of the Gap Distance

Equations (8)

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x d = x 0 d + Δ .
Ψ ˜ ( r ) = { Ψ ˜ 0 J 0 ( u r a ) r a Ψ ˜ 0 J 0 ( u ) K 0 ( w ) K 0 ( w r a ) r > a ,
Ψ in ( r , θ ) = l = Ψ in , l ( r ) exp ( j l θ ) .
Ψ out ( r , θ , z ) = l = Ψ out , l ( r ) exp ( j l θ ) ,
Ψ out , l ( r , z ) = j l + 1 ( 2 π λ z ) 0 r exp ( j π λ z ( r 2 + r 2 ) ) J l ( 2 π r r λ z ) Ψ in , l ( r ) d r .
Ψ out ( r , z ) = ( 2 π j λ z ) 0 r exp ( j π λ z ( r 2 + r 2 ) ) J 0 ( 2 π r r λ z ) Ψ in , 0 ( r ) d r ,
η = P out P in = | y = x = Ψ 1 ( x , y , z ) Ψ 2 ( x , y , z ) d x d y y = x = Ψ 1 ( x , y , z ) Ψ 1 * ( x , y , z ) d x d y y = x = Ψ 2 ( x , y , z ) Ψ 2 * ( x , y , z ) d x d y | ,
η = | y = x = Ψ in ( x , y , z ) Ψ out ( x , y , z ) d x d y y = x = Ψ in ( x , y , z ) Ψ in * ( x , y , z ) d x d y y = x = Ψ out ( x , y , z ) Ψ out * ( x , y , z ) d x d y | .

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