Abstract

A detailed comparison between a low-finesse Fabry–Perot cavity and a typical two-beam interferometer is developed and checked experimentally. The consequences of approximating the true Fabry–Perot function by the two-beam function are evaluated for commonly used signal-processing schemes in order to quantify the final error introduced in various fiber sensing schemes employing this configuration.

© 1992 Optical Society of America

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References

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  1. D. A. Jackson, J. D. C. Jones, “Fibre optic sensors,” Opt. Acta 33, 1469–1503 (1986).
    [Crossref]
  2. D. A. Jackson, “Monomode optical fibre interferometers for precision measurement,” J. Phys. E 18, 981–1001 (1985).
    [Crossref]
  3. A. D. Kersey, D. A. Jackson, M. Corke, “A simple fibre Fabry–Perot sensor,” Opt. Commun. 45, 71–75 (1983).
    [Crossref]
  4. A. T. Berkoff, A. D. Kersey, “Interferometric fibre displacement/strain sensor based on source coherence synthesis,” Electron. Lett. 26, 452–453 (1990).
    [Crossref]
  5. S. Venkatesh, W. V. Sorin, “Fibre-tip displacement sensor using sinusoidal FM-based technique,” Electron. Lett. 27, 1652–1654 (1991).
    [Crossref]
  6. O. B. Wright, “Stabilized dual-wavelength fiber-optic interferometer for vibration measurement,” Opt. Lett. 16, 56–58 (1991).
    [Crossref] [PubMed]
  7. K. A. Murphy, M. F. Gunther, A. M. Vengsarkar, R. O. Claus, “Quadrature phase-shifted, extrinsic Fabry–Perot optical fiber sensors,” Opt. Lett. 16, 273–275 (1991).
    [Crossref] [PubMed]
  8. J. L. Santos, D. A. Jackson, “Passive demodulation of miniature fiber-optic-based interferometric sensors using a time multiplexing technique,” Opt. Lett. 16, 1210–1212 (1991).
    [Crossref] [PubMed]
  9. A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
    [Crossref]
  10. A. D. Kersey, M. Corke, D. A. Jackson, “A linearised polarimetric optical sensor using a ‘heterodyne type’ signal recovery scheme,” Electron. Lett. 20, 209–211 (1984).
    [Crossref]
  11. S. A. Al-Chalabi, B. Culshaw, D. Davies, “Partially coherent sources in interferometric sensors,” in Proceedings of the First International Conference on Optical Fibre Sensors, IEEE Conf. Publ. 221 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 132–135.
  12. F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Coherence multiplexing of remote fibre Fabry–Perot sensing systems,” Opt. Commun. 65, 319–321 (1988).
    [Crossref]

1991 (4)

1990 (1)

A. T. Berkoff, A. D. Kersey, “Interferometric fibre displacement/strain sensor based on source coherence synthesis,” Electron. Lett. 26, 452–453 (1990).
[Crossref]

1988 (1)

F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Coherence multiplexing of remote fibre Fabry–Perot sensing systems,” Opt. Commun. 65, 319–321 (1988).
[Crossref]

1986 (1)

D. A. Jackson, J. D. C. Jones, “Fibre optic sensors,” Opt. Acta 33, 1469–1503 (1986).
[Crossref]

1985 (1)

D. A. Jackson, “Monomode optical fibre interferometers for precision measurement,” J. Phys. E 18, 981–1001 (1985).
[Crossref]

1984 (1)

A. D. Kersey, M. Corke, D. A. Jackson, “A linearised polarimetric optical sensor using a ‘heterodyne type’ signal recovery scheme,” Electron. Lett. 20, 209–211 (1984).
[Crossref]

1983 (1)

A. D. Kersey, D. A. Jackson, M. Corke, “A simple fibre Fabry–Perot sensor,” Opt. Commun. 45, 71–75 (1983).
[Crossref]

1982 (1)

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[Crossref]

Al-Chalabi, S. A.

S. A. Al-Chalabi, B. Culshaw, D. Davies, “Partially coherent sources in interferometric sensors,” in Proceedings of the First International Conference on Optical Fibre Sensors, IEEE Conf. Publ. 221 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 132–135.

Berkoff, A. T.

A. T. Berkoff, A. D. Kersey, “Interferometric fibre displacement/strain sensor based on source coherence synthesis,” Electron. Lett. 26, 452–453 (1990).
[Crossref]

Claus, R. O.

Corke, M.

A. D. Kersey, M. Corke, D. A. Jackson, “A linearised polarimetric optical sensor using a ‘heterodyne type’ signal recovery scheme,” Electron. Lett. 20, 209–211 (1984).
[Crossref]

A. D. Kersey, D. A. Jackson, M. Corke, “A simple fibre Fabry–Perot sensor,” Opt. Commun. 45, 71–75 (1983).
[Crossref]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[Crossref]

Culshaw, B.

S. A. Al-Chalabi, B. Culshaw, D. Davies, “Partially coherent sources in interferometric sensors,” in Proceedings of the First International Conference on Optical Fibre Sensors, IEEE Conf. Publ. 221 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 132–135.

Davies, D.

S. A. Al-Chalabi, B. Culshaw, D. Davies, “Partially coherent sources in interferometric sensors,” in Proceedings of the First International Conference on Optical Fibre Sensors, IEEE Conf. Publ. 221 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 132–135.

Farahi, F.

F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Coherence multiplexing of remote fibre Fabry–Perot sensing systems,” Opt. Commun. 65, 319–321 (1988).
[Crossref]

Gunther, M. F.

Jackson, D. A.

J. L. Santos, D. A. Jackson, “Passive demodulation of miniature fiber-optic-based interferometric sensors using a time multiplexing technique,” Opt. Lett. 16, 1210–1212 (1991).
[Crossref] [PubMed]

F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Coherence multiplexing of remote fibre Fabry–Perot sensing systems,” Opt. Commun. 65, 319–321 (1988).
[Crossref]

D. A. Jackson, J. D. C. Jones, “Fibre optic sensors,” Opt. Acta 33, 1469–1503 (1986).
[Crossref]

D. A. Jackson, “Monomode optical fibre interferometers for precision measurement,” J. Phys. E 18, 981–1001 (1985).
[Crossref]

A. D. Kersey, M. Corke, D. A. Jackson, “A linearised polarimetric optical sensor using a ‘heterodyne type’ signal recovery scheme,” Electron. Lett. 20, 209–211 (1984).
[Crossref]

A. D. Kersey, D. A. Jackson, M. Corke, “A simple fibre Fabry–Perot sensor,” Opt. Commun. 45, 71–75 (1983).
[Crossref]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[Crossref]

Jones, J. D. C.

F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Coherence multiplexing of remote fibre Fabry–Perot sensing systems,” Opt. Commun. 65, 319–321 (1988).
[Crossref]

D. A. Jackson, J. D. C. Jones, “Fibre optic sensors,” Opt. Acta 33, 1469–1503 (1986).
[Crossref]

Kersey, A. D.

A. T. Berkoff, A. D. Kersey, “Interferometric fibre displacement/strain sensor based on source coherence synthesis,” Electron. Lett. 26, 452–453 (1990).
[Crossref]

A. D. Kersey, M. Corke, D. A. Jackson, “A linearised polarimetric optical sensor using a ‘heterodyne type’ signal recovery scheme,” Electron. Lett. 20, 209–211 (1984).
[Crossref]

A. D. Kersey, D. A. Jackson, M. Corke, “A simple fibre Fabry–Perot sensor,” Opt. Commun. 45, 71–75 (1983).
[Crossref]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[Crossref]

Murphy, K. A.

Newson, T. P.

F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Coherence multiplexing of remote fibre Fabry–Perot sensing systems,” Opt. Commun. 65, 319–321 (1988).
[Crossref]

Santos, J. L.

Sorin, W. V.

S. Venkatesh, W. V. Sorin, “Fibre-tip displacement sensor using sinusoidal FM-based technique,” Electron. Lett. 27, 1652–1654 (1991).
[Crossref]

Vengsarkar, A. M.

Venkatesh, S.

S. Venkatesh, W. V. Sorin, “Fibre-tip displacement sensor using sinusoidal FM-based technique,” Electron. Lett. 27, 1652–1654 (1991).
[Crossref]

Wright, O. B.

Electron. Lett. (4)

A. T. Berkoff, A. D. Kersey, “Interferometric fibre displacement/strain sensor based on source coherence synthesis,” Electron. Lett. 26, 452–453 (1990).
[Crossref]

S. Venkatesh, W. V. Sorin, “Fibre-tip displacement sensor using sinusoidal FM-based technique,” Electron. Lett. 27, 1652–1654 (1991).
[Crossref]

A. D. Kersey, D. A. Jackson, M. Corke, “Passive compensation scheme suitable for use in the single-mode fibre interferometer,” Electron. Lett. 18, 392–393 (1982).
[Crossref]

A. D. Kersey, M. Corke, D. A. Jackson, “A linearised polarimetric optical sensor using a ‘heterodyne type’ signal recovery scheme,” Electron. Lett. 20, 209–211 (1984).
[Crossref]

J. Phys. E (1)

D. A. Jackson, “Monomode optical fibre interferometers for precision measurement,” J. Phys. E 18, 981–1001 (1985).
[Crossref]

Opt. Acta (1)

D. A. Jackson, J. D. C. Jones, “Fibre optic sensors,” Opt. Acta 33, 1469–1503 (1986).
[Crossref]

Opt. Commun. (2)

A. D. Kersey, D. A. Jackson, M. Corke, “A simple fibre Fabry–Perot sensor,” Opt. Commun. 45, 71–75 (1983).
[Crossref]

F. Farahi, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Coherence multiplexing of remote fibre Fabry–Perot sensing systems,” Opt. Commun. 65, 319–321 (1988).
[Crossref]

Opt. Lett. (3)

Other (1)

S. A. Al-Chalabi, B. Culshaw, D. Davies, “Partially coherent sources in interferometric sensors,” in Proceedings of the First International Conference on Optical Fibre Sensors, IEEE Conf. Publ. 221 (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 132–135.

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Figures (7)

Fig. 1
Fig. 1

(a) Transfer function in reflection of a Fabry–Perot cavity for two values of R (the two-beam limit is also represented), (b) relative error between Eq. (3) and approximation (4) as a function of R for ϕ = 2(m + 1/2)π, (c) same as (b) but for ϕ = (m + 1/2)π. TB, two beam; FP, Fabry–Perot.

Fig. 2
Fig. 2

(a) Fabry–Perot transfer functions for R = 0.035 and the corresponding two-beam case, (b) relative error between the two functions.

Fig. 3
Fig. 3

Experimental arrangement; PZT, piezoelectric cylinder.

Fig. 4
Fig. 4

Top, signal applied to the PZT; bottom, interferometer output; (b) experimental points and theoretical curve obtained from expression (3).

Fig. 5
Fig. 5

Scale error (relative to the two-beam limit) that was introduced by the Fabry–Perot transfer function and the square-and-add processing scheme outlined in Subsection 4.B.1.

Fig. 6
Fig. 6

Scale error (relative to the two-beam limit) that was introduced by the Fabry–Perot transfer function and the phase-shift processing scheme outlined in Subsection 4.B.2.

Fig. 7
Fig. 7

(a) Beams generated in the cavity until the fourth order (they are separated laterally only for clarity), (b) fringe visibility of the resulting two-beam function.

Equations (23)

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I r ( FP ) = I o [ 1 - ( 1 - R ) 2 1 + R 2 - 2 R cos ϕ ] = 2 R I o 1 - cos ϕ 1 + R 2 - 2 R cos ϕ ,
ϕ = 4 π L n λ 0 ,
I r ( FP ) = 1 - cos ϕ 1 + R 2 - 2 R cos ϕ .
I r ( FP ) 1 - cos ϕ ,
I r ( FP ) 1 = 1 - cos ϕ 1 + R 2 - 2 R cos ϕ ,
I r ( FP ) 2 = 1 - cos ( ϕ + π / 2 ) 1 + R 2 - 2 R cos ( ϕ + π / 2 ) = 1 + sin ϕ 1 + R 2 + 2 R sin ϕ .
I r ( FP ) 1 = 1 - [ cos ϕ 0 J 0 ( ϕ s ) - 2 sin ϕ 0 J 1 ( ϕ s ) sin ( ω s t ) + ] 1 + R 2 - 2 R cos ϕ ,
I r ( FP ) 2 = 1 + [ sin ϕ o J 0 ( ϕ s ) - 2 cos ϕ o J 1 ( ϕ s ) sin ( ω s t ) - ] 1 + R 2 + 2 R sin ϕ .
V FP 1 ϕ s sin ϕ o sin ( ω s t ) 1 + R 2 - 2 R cos ϕ o ,
V FP 2 ϕ s cos ϕ o sin ( ω s t ) 1 + R 2 + 2 R sin ϕ o .
V out ( V FP 1 2 + V FP 2 2 ) 1 / 2 ;
V out ϕ s sin ( ω s t ) F FP ,
F FP = [ ( sin ϕ o 1 + R 2 - 2 R cos ϕ o ) 2 + ( cos ϕ o 1 + R 2 + 2 R sin ϕ o ) 2 ] 1 / 2 [ 1 + 4 R ( sin 3 ϕ o - cos 3 ϕ o ) 1 + 4 R ( sin ϕ o - cos ϕ o ) ] 1 / 2 ,
V FP 1 ϕ s sin ϕ o cos ( ω s t ) 1 + R 2 - 2 R cos ϕ o ,
V FP 2 ϕ s cos ϕ o sin ( ω s t ) 1 + R 2 + 2 R sin ϕ o .
H 1 sin ( ω t + α 1 ) + H 2 sin ( ω t + α 2 ) = H sin ( ω t + α ) ,
H = [ H 1 2 + H 2 2 + 2 H 1 H 2 cos δ ] 1 / 2 , δ = α 2 - α 1 ; tan α = H 1 sin α 1 + H 2 sin α 2 H 1 cos α 1 + H 2 cos α 2 ,
V out ϕ s sin ( ω s t + α ) F FP .
F FP { 1 + 4 R [ sin 3 ϕ o + R cos 4 ϕ o - cos 3 ϕ o ( 1 + 4 R sin 3 ϕ o ) 1 / 2 ] } 1 / 2 ( 1 - 2 R cos ϕ o ) ( 1 + 2 R sin ϕ o ) ,
α = arctan ( C sin ϕ o C cos ϕ o + B ) , C ( 1 + 4 R sin 3 ϕ o ) 1 / 2 ;             B = - 2 R cos 2 ϕ o .
I 1 = I 0 R , I 2 = I 0 ( 1 - R ) 2 R , I 3 = I 0 ( 1 - R ) 2 R 3 , · · I m = I m - 1 R 2 ,             m = 3 , 4 , .
I out = 1 2 ( i I i + I 1 I 2 cos ( ϕ + π ) + m 3 I m I m - 1 cos ϕ ) = I t ( 1 + V cos ϕ ) ,
I t = 1 2 i I i = I o R 1 + R , V = 2 1 I t ( - I 1 I 2 + m 3 I m I m - 1 ) = 1 2 ( R - 1 ) .

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