Abstract

Experimental and theoretical results are presented on a simple compact fiber-optic sensor that uses a mirror placed on the end of a mass-loaded cantilevered elastic beam. Deflections of the beam due to acceleration are read out with multimode optical fibers and with a quarter-pitch GRIN rod lens. Two output fibers are used in a balanced-detection scheme. In the audio-frequency range, the minimum detectable acceleration is 2.4 × 10−6 Grms, and the maximum measurable acceleration is 39 Grms. The device is also sensitive to dc accelerations. However, during dc sensing, a fiber bending noise is found. This noise decreases the dynamic range of the accelerometer.

© 1984 Optical Society of America

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References

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  1. D. H. McMahon, A. R. Nelson, W. B. Spillman, IEEE Spectrum 18, 24 (1981).
  2. S. K. Yao, C. K. Asawa, IEEE J. Sel. Areas Commun. SAC-1, 562 (1983).
  3. W. B. Spillman, D. H. McMahon, in Proceedings, First International Conference on Optical Fiber Sensors, London (26Apr.1983), pp. 160–163.
  4. G. A. Rines, Appl. Opt. 20, 3453 (1981).
    [CrossRef] [PubMed]
  5. C. J. Schneider, U.S. Patent4,353,259 (12Oct.1982).
  6. D. H. McMahon, unpublished memorandum (1982).
  7. J. J. Tuma, Handbook of Physical Calculations (McGraw-Hill, New York, 1983).
  8. Selfoc Handbook (1982), available from NSG America, 136 Central Ave., Clark, N.J. 07066.
  9. R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1976).
  10. D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
    [CrossRef]
  11. D. Marcuse, J. Opt. Soc. Am. 66, 311 (1976).
    [CrossRef]
  12. K. S. Kaufman, R. Terras, R. F. Mathis, Jr. Opt. Soc. Am. 71, 1513 (1981).
    [CrossRef]

1983 (1)

S. K. Yao, C. K. Asawa, IEEE J. Sel. Areas Commun. SAC-1, 562 (1983).

1981 (3)

G. A. Rines, Appl. Opt. 20, 3453 (1981).
[CrossRef] [PubMed]

D. H. McMahon, A. R. Nelson, W. B. Spillman, IEEE Spectrum 18, 24 (1981).

K. S. Kaufman, R. Terras, R. F. Mathis, Jr. Opt. Soc. Am. 71, 1513 (1981).
[CrossRef]

1977 (1)

D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[CrossRef]

1976 (1)

Asawa, C. K.

S. K. Yao, C. K. Asawa, IEEE J. Sel. Areas Commun. SAC-1, 562 (1983).

Kaufman, K. S.

K. S. Kaufman, R. Terras, R. F. Mathis, Jr. Opt. Soc. Am. 71, 1513 (1981).
[CrossRef]

Kleinman, D. A.

D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[CrossRef]

Marcuse, D.

Mathis, R. F.

K. S. Kaufman, R. Terras, R. F. Mathis, Jr. Opt. Soc. Am. 71, 1513 (1981).
[CrossRef]

McMahon, D. H.

D. H. McMahon, A. R. Nelson, W. B. Spillman, IEEE Spectrum 18, 24 (1981).

W. B. Spillman, D. H. McMahon, in Proceedings, First International Conference on Optical Fiber Sensors, London (26Apr.1983), pp. 160–163.

D. H. McMahon, unpublished memorandum (1982).

Nelson, A. R.

D. H. McMahon, A. R. Nelson, W. B. Spillman, IEEE Spectrum 18, 24 (1981).

Nelson, D. F.

D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[CrossRef]

Rines, G. A.

Schneider, C. J.

C. J. Schneider, U.S. Patent4,353,259 (12Oct.1982).

Spillman, W. B.

D. H. McMahon, A. R. Nelson, W. B. Spillman, IEEE Spectrum 18, 24 (1981).

W. B. Spillman, D. H. McMahon, in Proceedings, First International Conference on Optical Fiber Sensors, London (26Apr.1983), pp. 160–163.

Terras, R.

K. S. Kaufman, R. Terras, R. F. Mathis, Jr. Opt. Soc. Am. 71, 1513 (1981).
[CrossRef]

Tuma, J. J.

J. J. Tuma, Handbook of Physical Calculations (McGraw-Hill, New York, 1983).

Wecht, K. W.

D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[CrossRef]

Yao, S. K.

S. K. Yao, C. K. Asawa, IEEE J. Sel. Areas Commun. SAC-1, 562 (1983).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. F. Nelson, D. A. Kleinman, K. W. Wecht, Appl. Phys. Lett. 30, 94 (1977).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

S. K. Yao, C. K. Asawa, IEEE J. Sel. Areas Commun. SAC-1, 562 (1983).

IEEE Spectrum (1)

D. H. McMahon, A. R. Nelson, W. B. Spillman, IEEE Spectrum 18, 24 (1981).

J. Opt. Soc. Am. (1)

Jr. Opt. Soc. Am. (1)

K. S. Kaufman, R. Terras, R. F. Mathis, Jr. Opt. Soc. Am. 71, 1513 (1981).
[CrossRef]

Other (6)

W. B. Spillman, D. H. McMahon, in Proceedings, First International Conference on Optical Fiber Sensors, London (26Apr.1983), pp. 160–163.

C. J. Schneider, U.S. Patent4,353,259 (12Oct.1982).

D. H. McMahon, unpublished memorandum (1982).

J. J. Tuma, Handbook of Physical Calculations (McGraw-Hill, New York, 1983).

Selfoc Handbook (1982), available from NSG America, 136 Central Ave., Clark, N.J. 07066.

R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Cleveland, 1976).

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Figures (7)

Fig. 1
Fig. 1

Perspective view of sensor structure.

Fig. 2
Fig. 2

Multimode fiber-optic accelerometer.

Fig. 3
Fig. 3

Side view of sensor (cross section) showing optical ray paths.

Fig. 4
Fig. 4

Close-packed linear array of three multimode fibers showing side-to-side motion of optical retro-image during acceleration.

Fig. 5
Fig. 5

Parameters to represent elastic beam bending.

Fig. 6
Fig. 6

Measured responsivity and noise of the Fig. 2 sensor.

Fig. 7
Fig. 7

Minimum detectable acceleration as a function of frequency for the Fig. 2 sensor.

Equations (27)

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δ ( x ) = F x 2 6 E I ( 3 L - x ) ,
δ = F L 3 3 E I .
θ ( x ) = d d x [ δ ( x ) ] = F 2 E I ( 2 L x - x 2 )
θ = F L 2 2 E I .
F = m a ,
ω r 2 = k / m ,
F = k δ .
a = δ ω r 2 .
θ = ( 2 δ ) / ( 3 L ) .
a max = 3 2 L ω r 2 θ max .
ω r 2 = ( 3 E I ) / ( m L 3 ) .
I = ( W H 3 ) / 12 ,
ω r 2 = ( E W H 3 ) / ( 4 m L 3 ) .
( Δ L ) / L ( Y / E ) .
1 R ( x ) = d θ d x = F ( L - x ) E I .
Y E = H 2 R min = H L m a dam 2 E I .
a dam = 2 L 2 ω r 2 3 H ( Y E ) .
θ max = ( d 4 Z ) ( n 0 π 2 ) .
a max = 3 L ω r 2 d n 0 π 16 Z .
Δ P P = ( h ν B η P ) 1 / 2 .
Δ P P = 7 × 10 - 10 ( B P ) 1 / 2 ,
a min / a max = ( Δ P P ) .
a min / a max = ( h c B η λ P ) 1 / 2 .
a min = ( h c B η λ P ) 1 / 2 ( 3 L ω r 2 d n 0 π 16 Z ) .
dynamic range ( dB ) = 20 log ( a max / a min ) .
R = ( ρ v a ) ( P 1 , a - P 1 , 0 ) .
R ρ v P 2 a max .

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