Abstract

An intensity-based fiber-optic sensor for measuring axial and angular displacement has been designed and tested in a controlled laboratory environment. In addition, a mathematical model allowing the simultaneous calculation of the three desired parameters needed to characterize the tilt and the position of a surface under investigation is described. Preliminary tests show good agreement between the theory and the experimental results and show the sensor’s potential for application in the manufacturing industry for position and vibration control. The sensor shows significant improvement in angular range over previously reported methods. An axial displacement range of 2 mm, with an accuracy of 40 μm, and an angular displacement range of 40 mrad, with an accuracy of 0.5 mrad, are demonstrated. Suggestions for further improvement of the range and the sensitivity of the sensor are also described.

© 1998 Optical Society of America

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References

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  1. D. Su, D. R. Hall, J. D. C. Jones, “Workpiece position sensing by means of a fiber optical beam delivery system,” Opt. Eng. 32, 1823–1825 (1993).
    [CrossRef]
  2. E. Bois, S. J. Huard, G. Boisde, “Loss compensated fiber-optic displacement sensor including a lens,” Appl. Opt. 28, 419–420 (1989).
    [CrossRef] [PubMed]
  3. C. Wu, “Fiber optic angular displacement sensor,” Rev. Sci. Instrum. 66, 3672–3675 (1995).
    [CrossRef]
  4. R. C. Spooncer, C. Butler, B. E. Jones, “Optical fiber displacement sensors for process and manufacturing applications,” Opt. Eng. 31, 1632–1637 (1992).
    [CrossRef]
  5. A. B. Stanbridge, D. J. Ewins, “Measurement of translational and angular vibration using a scanning laser Doppler vibrometer,” in First International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE2358, 37–47 (1994).
    [CrossRef]
  6. J. L. Remo, “Solid state optic vibration/displacement sensors,” Opt. Eng. 35, 2798–2803 (1996).
    [CrossRef]
  7. H. Wang, “Collimated beam fiber optic position sensor: effects of sample rotations on modulation functions,” Opt. Eng. 36, 8–14 (1997).
    [CrossRef]
  8. D. Sagrario, “Design and characterization of an axial and angular displacement fiber optic sensor,” M.S. thesis (University of Maryland, College Park, Md., 1997).
  9. Z. Zhao, W. S. Lau, A. C. K. Choi, Y. Y. Shan, “Modulation functions of the reflective optical fiber sensor for specular and diffuse reflection,” Opt. Eng. 33, 2986–2991 (1994).
    [CrossRef]

1997 (1)

H. Wang, “Collimated beam fiber optic position sensor: effects of sample rotations on modulation functions,” Opt. Eng. 36, 8–14 (1997).
[CrossRef]

1996 (1)

J. L. Remo, “Solid state optic vibration/displacement sensors,” Opt. Eng. 35, 2798–2803 (1996).
[CrossRef]

1995 (1)

C. Wu, “Fiber optic angular displacement sensor,” Rev. Sci. Instrum. 66, 3672–3675 (1995).
[CrossRef]

1994 (1)

Z. Zhao, W. S. Lau, A. C. K. Choi, Y. Y. Shan, “Modulation functions of the reflective optical fiber sensor for specular and diffuse reflection,” Opt. Eng. 33, 2986–2991 (1994).
[CrossRef]

1993 (1)

D. Su, D. R. Hall, J. D. C. Jones, “Workpiece position sensing by means of a fiber optical beam delivery system,” Opt. Eng. 32, 1823–1825 (1993).
[CrossRef]

1992 (1)

R. C. Spooncer, C. Butler, B. E. Jones, “Optical fiber displacement sensors for process and manufacturing applications,” Opt. Eng. 31, 1632–1637 (1992).
[CrossRef]

1989 (1)

Bois, E.

Boisde, G.

Butler, C.

R. C. Spooncer, C. Butler, B. E. Jones, “Optical fiber displacement sensors for process and manufacturing applications,” Opt. Eng. 31, 1632–1637 (1992).
[CrossRef]

Choi, A. C. K.

Z. Zhao, W. S. Lau, A. C. K. Choi, Y. Y. Shan, “Modulation functions of the reflective optical fiber sensor for specular and diffuse reflection,” Opt. Eng. 33, 2986–2991 (1994).
[CrossRef]

Ewins, D. J.

A. B. Stanbridge, D. J. Ewins, “Measurement of translational and angular vibration using a scanning laser Doppler vibrometer,” in First International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE2358, 37–47 (1994).
[CrossRef]

Hall, D. R.

D. Su, D. R. Hall, J. D. C. Jones, “Workpiece position sensing by means of a fiber optical beam delivery system,” Opt. Eng. 32, 1823–1825 (1993).
[CrossRef]

Huard, S. J.

Jones, B. E.

R. C. Spooncer, C. Butler, B. E. Jones, “Optical fiber displacement sensors for process and manufacturing applications,” Opt. Eng. 31, 1632–1637 (1992).
[CrossRef]

Jones, J. D. C.

D. Su, D. R. Hall, J. D. C. Jones, “Workpiece position sensing by means of a fiber optical beam delivery system,” Opt. Eng. 32, 1823–1825 (1993).
[CrossRef]

Lau, W. S.

Z. Zhao, W. S. Lau, A. C. K. Choi, Y. Y. Shan, “Modulation functions of the reflective optical fiber sensor for specular and diffuse reflection,” Opt. Eng. 33, 2986–2991 (1994).
[CrossRef]

Remo, J. L.

J. L. Remo, “Solid state optic vibration/displacement sensors,” Opt. Eng. 35, 2798–2803 (1996).
[CrossRef]

Sagrario, D.

D. Sagrario, “Design and characterization of an axial and angular displacement fiber optic sensor,” M.S. thesis (University of Maryland, College Park, Md., 1997).

Shan, Y. Y.

Z. Zhao, W. S. Lau, A. C. K. Choi, Y. Y. Shan, “Modulation functions of the reflective optical fiber sensor for specular and diffuse reflection,” Opt. Eng. 33, 2986–2991 (1994).
[CrossRef]

Spooncer, R. C.

R. C. Spooncer, C. Butler, B. E. Jones, “Optical fiber displacement sensors for process and manufacturing applications,” Opt. Eng. 31, 1632–1637 (1992).
[CrossRef]

Stanbridge, A. B.

A. B. Stanbridge, D. J. Ewins, “Measurement of translational and angular vibration using a scanning laser Doppler vibrometer,” in First International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE2358, 37–47 (1994).
[CrossRef]

Su, D.

D. Su, D. R. Hall, J. D. C. Jones, “Workpiece position sensing by means of a fiber optical beam delivery system,” Opt. Eng. 32, 1823–1825 (1993).
[CrossRef]

Wang, H.

H. Wang, “Collimated beam fiber optic position sensor: effects of sample rotations on modulation functions,” Opt. Eng. 36, 8–14 (1997).
[CrossRef]

Wu, C.

C. Wu, “Fiber optic angular displacement sensor,” Rev. Sci. Instrum. 66, 3672–3675 (1995).
[CrossRef]

Zhao, Z.

Z. Zhao, W. S. Lau, A. C. K. Choi, Y. Y. Shan, “Modulation functions of the reflective optical fiber sensor for specular and diffuse reflection,” Opt. Eng. 33, 2986–2991 (1994).
[CrossRef]

Appl. Opt. (1)

Opt. Eng. (5)

R. C. Spooncer, C. Butler, B. E. Jones, “Optical fiber displacement sensors for process and manufacturing applications,” Opt. Eng. 31, 1632–1637 (1992).
[CrossRef]

J. L. Remo, “Solid state optic vibration/displacement sensors,” Opt. Eng. 35, 2798–2803 (1996).
[CrossRef]

H. Wang, “Collimated beam fiber optic position sensor: effects of sample rotations on modulation functions,” Opt. Eng. 36, 8–14 (1997).
[CrossRef]

D. Su, D. R. Hall, J. D. C. Jones, “Workpiece position sensing by means of a fiber optical beam delivery system,” Opt. Eng. 32, 1823–1825 (1993).
[CrossRef]

Z. Zhao, W. S. Lau, A. C. K. Choi, Y. Y. Shan, “Modulation functions of the reflective optical fiber sensor for specular and diffuse reflection,” Opt. Eng. 33, 2986–2991 (1994).
[CrossRef]

Rev. Sci. Instrum. (1)

C. Wu, “Fiber optic angular displacement sensor,” Rev. Sci. Instrum. 66, 3672–3675 (1995).
[CrossRef]

Other (2)

A. B. Stanbridge, D. J. Ewins, “Measurement of translational and angular vibration using a scanning laser Doppler vibrometer,” in First International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, E. P. Tomasini, ed., Proc. SPIE2358, 37–47 (1994).
[CrossRef]

D. Sagrario, “Design and characterization of an axial and angular displacement fiber optic sensor,” M.S. thesis (University of Maryland, College Park, Md., 1997).

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Figures (10)

Fig. 1
Fig. 1

(a) Possible displacement of a flat surface. (b) Gaussian intensity profile and projection on screen. (c) Spatial description of sensor head.

Fig. 2
Fig. 2

Optical fiber holder and microscope image of sensor head fiber geometry.

Fig. 3
Fig. 3

Experimental setup for calibration of the axial–angular displacement fiber-optic sensor.

Fig. 4
Fig. 4

Relation between collected light power and axial displacement for the four receiving fibers.

Fig. 5
Fig. 5

Angular displacement as a function of power at z = 3.715 mm (change in α).

Fig. 6
Fig. 6

Angular displacement as a function of power at z = 4.604 mm (change in α).

Fig. 7
Fig. 7

(a) Theoretical versus experimental values for the angular displacement α about the vertical axis for the bottom fiber at z = 4.604 mm. (b) Theoretical versus experimental values for the angular displacement α about the vertical axis for the left fiber at z = 4.604 mm. (c) Theoretical versus experimental values for the angular displacement α about the vertical axis for the right fiber at z = 4.604 mm. (d) Theoretical versus experimental values for the angular displacement α about the vertical axis for the top fiber at z = 4.604 mm.

Fig. 8
Fig. 8

Actual versus computed values for the angle of rotation α about the vertical axis: z = 4.604 mm, β = 0 rad.

Fig. 9
Fig. 9

Calculated values of angular displacement β corresponding to z = 4.604 mm.

Fig. 10
Fig. 10

Calculated values of axial displacement corresponding to z = 4.604 mm.

Tables (2)

Tables Icon

Table 1 Collecting Fiber Coordinates with Respect to the Emitting Fiber

Tables Icon

Table 2 Fitting Parameters for Eq. (8) Derived from Experimental Results (z = 3.715 mm) shown in Fig. 5

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

I r ,   z = I 0 ω 0 ω z 2 exp - 2   r 2 ω z 2 ,
ω z = ω 0 1 + λ z π ω 0 2 2 1 / 2 ,
power   =   intensity   ×   area ,
P i x ,   y ,   z = C i 1 I 0 ω 0 ω z 2 × exp - 2 C i 2 a i - x 2 + b i - y 2 ω z 2 π r c 2 ,
x = z   tan 2 α ,     y = z   tan 2 β ,
x = 2 α z ,     y = 2 β z   for   small   α   and   β .
ω z = ω 0 z 0   z   for   z     z 0
1 2 C i 2 ω 0 z 0 2 ln z + ln P i - ln I 0 z 0 2 C i 1 π r c 2 + 4 α 2 + β 2 z 2 - 4 a α + b β z + a 2 + b 2 = 0 .

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