Abstract

In general applications, the output signals of the fiber-optic interferometric sensor (FOIS) need some demodulation techniques to linearly demodulate the sensing phase signal. The common signal demodulation circuit of the FOIS is passive homodyne demodulation using phase-generated carrier [(PGC) demodulation]. Preliminary analysis of the research demonstrates that a variation in the output demodulated signal is related to the length of the fiber, and the output demodulated signal will approach zero at some certain lengths of the fiber. To improve the performance of the FOIS, it is necessary to develop the modified PGC demodulation to compensate for the propagation delay of the fiber.

© 2007 Optical Society of America

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References

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  1. V. Handerek, in Optical Fiber Sensor Technology, K. T. V. Grattan and B. T. Meggitt, eds. (Chapman & Hall, 1995), pp. 197-222.
    [CrossRef] [PubMed]
  2. D. A. Jackson, R. Priest, A. Dandridge, and A. B. Tveten, "Elimination of drift in a single-mode optical fiber interferometer using a piezo-electrically stretched coiled fiber," Appl. Opt. 19, 2926-2920 (1980).
    [CrossRef] [PubMed]
  3. A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, "Homodyne demodulation scheme for fiber optic sensors using phase generated carrier," IEEE J. Quantum Electron. QE-18, 1647-1653 (1982).
    [CrossRef]
  4. K. P. Koo, A. Dandridge, A. B. Tveten, and A. Dandridge, "Passive stabilization scheme for fiber interferometry using (3 × 3) fiber directional couplers," Appl. Phys. Lett. 41, 616-618 (1982).
    [CrossRef] [PubMed]
  5. C. B. Cameron, R. M. Keolian, and S. L. Garrett, "A symmetric analogue demodulator for optical fiber interferometric in sensor," in Proceedings of the 34th Midwest Symposium on Circuits and Systems (IEEE, 1991).
  6. A. D. Kersey, A. Dandridge, and A. B. Tveten, "Multiplexing of interferometric fiber sensors using time division addressing and phase generated carrier demodulation," Opt. Lett. 12, 775-777 (1987).
    [CrossRef] [PubMed]
  7. S. C. Huang, W. W. Lin, M. H. Chen, S. C. Hung, and H. L. Chao, "Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors," J. Lightwave Technol. 14, 1488-1500 (1996).
    [CrossRef]
  8. W. W. Lin, S. C. Huang, J. S. Tsay, and S. C. Hung, "System design and optimization of optically amplified WDM/TDM hybrid polarization-insensitive fiber-optic Michelson interferometric sensor," J. Lightwave Technol. 18, 348-359 (2000).
    [CrossRef]
  9. S. C. Huang, W. W. Lin, M. T. Tsai, and M. H. Chen, "Fiber optic in-line distributed sensor for detection and localization of the pipeline leaks," Sens. Actuators A 135, 570-579 (2007).
    [CrossRef] [PubMed]
  10. S.-C. Huang, W.-W. Lin, and M.-H. Chen, "Cross-talk analysis of time-division multiplexing of polarization-insensitive fiber-optic Michelson interferometric sensors with a 3 × 3 directional coupler," Appl. Opt. 36, 921-933 (1997).
    [CrossRef] [PubMed]
  11. I. J. Bush, D. R. Sherman, and J. A. Bostick, "TDM interferometer demodulation technique with 5 million samples per second capability," Proc. SPIE 1797, 242-248 (1992).
    [CrossRef]
  12. I. J. Bush, A. Cekorich, and C. Kirkendall, "Multi-channel interferometric demodulator," Proc. SPIE 3180, 19-29 (1997).
    [CrossRef] [PubMed]
  13. C. McGarrity and D. A. Jackson, "Improvement on phase generated carrier technique for passive demodulation of miniature interferometric sensor," Opt. Commun. 109, 246-248 (1994).
    [CrossRef]
  14. A. D. Kersey, M. J. Marrone, and M. A. Davis, "Polarisation insensitive fibre optic Michelson interferometer," Electron. Lett. 27, 518-520 (1991).
    [CrossRef] [PubMed]
  15. M. Martinelli, "A universal compensator for polarisation change induced by birefringence on a retracing beam," Opt. Commun. 72, 341-344 (1989).
    [CrossRef] [PubMed]

2007 (1)

S. C. Huang, W. W. Lin, M. T. Tsai, and M. H. Chen, "Fiber optic in-line distributed sensor for detection and localization of the pipeline leaks," Sens. Actuators A 135, 570-579 (2007).
[CrossRef] [PubMed]

2000 (1)

1997 (2)

1996 (1)

S. C. Huang, W. W. Lin, M. H. Chen, S. C. Hung, and H. L. Chao, "Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors," J. Lightwave Technol. 14, 1488-1500 (1996).
[CrossRef]

1994 (1)

C. McGarrity and D. A. Jackson, "Improvement on phase generated carrier technique for passive demodulation of miniature interferometric sensor," Opt. Commun. 109, 246-248 (1994).
[CrossRef]

1992 (1)

I. J. Bush, D. R. Sherman, and J. A. Bostick, "TDM interferometer demodulation technique with 5 million samples per second capability," Proc. SPIE 1797, 242-248 (1992).
[CrossRef]

1991 (1)

A. D. Kersey, M. J. Marrone, and M. A. Davis, "Polarisation insensitive fibre optic Michelson interferometer," Electron. Lett. 27, 518-520 (1991).
[CrossRef] [PubMed]

1989 (1)

M. Martinelli, "A universal compensator for polarisation change induced by birefringence on a retracing beam," Opt. Commun. 72, 341-344 (1989).
[CrossRef] [PubMed]

1987 (1)

1982 (2)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, "Homodyne demodulation scheme for fiber optic sensors using phase generated carrier," IEEE J. Quantum Electron. QE-18, 1647-1653 (1982).
[CrossRef]

K. P. Koo, A. Dandridge, A. B. Tveten, and A. Dandridge, "Passive stabilization scheme for fiber interferometry using (3 × 3) fiber directional couplers," Appl. Phys. Lett. 41, 616-618 (1982).
[CrossRef] [PubMed]

1980 (1)

Appl. Opt. (2)

Appl. Phys. Lett. (1)

K. P. Koo, A. Dandridge, A. B. Tveten, and A. Dandridge, "Passive stabilization scheme for fiber interferometry using (3 × 3) fiber directional couplers," Appl. Phys. Lett. 41, 616-618 (1982).
[CrossRef] [PubMed]

Electron. Lett. (1)

A. D. Kersey, M. J. Marrone, and M. A. Davis, "Polarisation insensitive fibre optic Michelson interferometer," Electron. Lett. 27, 518-520 (1991).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

A. Dandridge, A. B. Tveten, and T. G. Giallorenzi, "Homodyne demodulation scheme for fiber optic sensors using phase generated carrier," IEEE J. Quantum Electron. QE-18, 1647-1653 (1982).
[CrossRef]

J. Lightwave Technol. (2)

S. C. Huang, W. W. Lin, M. H. Chen, S. C. Hung, and H. L. Chao, "Crosstalk analysis and system design of time-division multiplexing of polarization-insensitive fiber optic Michelson interferometric sensors," J. Lightwave Technol. 14, 1488-1500 (1996).
[CrossRef]

W. W. Lin, S. C. Huang, J. S. Tsay, and S. C. Hung, "System design and optimization of optically amplified WDM/TDM hybrid polarization-insensitive fiber-optic Michelson interferometric sensor," J. Lightwave Technol. 18, 348-359 (2000).
[CrossRef]

Opt. Commun. (2)

M. Martinelli, "A universal compensator for polarisation change induced by birefringence on a retracing beam," Opt. Commun. 72, 341-344 (1989).
[CrossRef] [PubMed]

C. McGarrity and D. A. Jackson, "Improvement on phase generated carrier technique for passive demodulation of miniature interferometric sensor," Opt. Commun. 109, 246-248 (1994).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

I. J. Bush, D. R. Sherman, and J. A. Bostick, "TDM interferometer demodulation technique with 5 million samples per second capability," Proc. SPIE 1797, 242-248 (1992).
[CrossRef]

I. J. Bush, A. Cekorich, and C. Kirkendall, "Multi-channel interferometric demodulator," Proc. SPIE 3180, 19-29 (1997).
[CrossRef] [PubMed]

Sens. Actuators (1)

S. C. Huang, W. W. Lin, M. T. Tsai, and M. H. Chen, "Fiber optic in-line distributed sensor for detection and localization of the pipeline leaks," Sens. Actuators A 135, 570-579 (2007).
[CrossRef] [PubMed]

Other (2)

V. Handerek, in Optical Fiber Sensor Technology, K. T. V. Grattan and B. T. Meggitt, eds. (Chapman & Hall, 1995), pp. 197-222.
[CrossRef] [PubMed]

C. B. Cameron, R. M. Keolian, and S. L. Garrett, "A symmetric analogue demodulator for optical fiber interferometric in sensor," in Proceedings of the 34th Midwest Symposium on Circuits and Systems (IEEE, 1991).

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Figures (12)

Fig. 1
Fig. 1

Schematic of the differentiate and cross-multiply sine–cosine interferometric phase-shift demodulator.

Fig. 2
Fig. 2

Schematic of the modified differentiate and cross-multiply sine–cosine interferometric phase-shift demodulator.

Fig. 3
Fig. 3

Configuration of the PIFOMIS and the arrangement of the leading fiber.

Fig. 4
Fig. 4

Frequency spectrums of the demodulated output simulation signal of the ordinary PGC demodulator.

Fig. 5
Fig. 5

Frequency spectrums of the demodulated output simulation signal of the modified PGC demodulator.

Fig. 6
Fig. 6

Waveforms of a fundamental square wave (upper trace), an instantaneous interference signal (middle trace) and a fundamental carrier signal (lower trace).

Fig. 7
Fig. 7

Waveforms of the simulation signal (upper trace) and the demodulated output simulation signal (lower trace) after compensation when the leading fiber has a length of 0 m.

Fig. 8
Fig. 8

Frequency spectrum of the demodulated output simulation signal after the phase compensation when the leading fiber is 0 m.

Fig. 9
Fig. 9

Frequency spectrum of the demodulated output simulation signal without compensation when the leading fiber is 0 m.

Fig. 10
Fig. 10

Waveforms of the simulation signal (upper trace) and the demodulated output simulation signal (lower trace) for which the compensated phase is still the optimum for 0 m leading fiber when the leading fiber has a length of 400 m.

Fig. 11
Fig. 11

Frequency spectrum of the demodulated output simulation signal for which the compensated phase is still the optimum for 0 m leading fiber when the leading fiber is 400 m.

Fig. 12
Fig. 12

Frequency spectrum of the demodulated output simulation signal for which the compensated phase is still the optimum for 0 m leading fiber when the leading fiber is 9600 m.

Tables (2)

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Table 1 Compensation Angles at Each Scale of 4-Bit Phase Compensator

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Table 2 V PP of the Demodulated Output Simulation Signals

Equations (32)

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Δ ϕ ( t ) = 2 π Δ L n c Δ i δ ν δ i   sin   ω c t = Δ ϕ 0   sin   ω c t ,
Δ ϕ 0 = 2 π Δ L n c Δ i δ ν δ i ,
I ( t ) = A + B   cos [ ϕ ( t ) + Δ ϕ 0   sin   ω c t ] .
I ( t ) = A + B { [ J 0 ( Δ ϕ 0 ) + 2 n = 1 J 2 n ( Δ ϕ 0 ) cos   2 ( n ω c t ) ] × cos   ϕ ( t ) [ 2 n = 0 J 2 n + 1 ( Δ ϕ 0 ) sin ( ( 2 n + 1 ) ω c t ) ] × sin   ϕ ( t ) } .
S 1 ( t ) = B J 1 ( Δ ϕ 0 ) sin   ϕ ( t ) ,
S 2 ( t ) = B J 2 ( Δ ϕ 0 ) cos   ϕ ( t ) .
X 1 ( t ) = B 2 J 1 ( Δ ϕ 0 ) J 2 ( Δ ϕ 0 ) ϕ ( t ) t sin 2 ϕ ( t ) ,
X 2 ( t ) = B 2 J 1 ( Δ ϕ 0 ) J 2 ( Δ ϕ 0 ) ϕ ( t ) t cos 2 ϕ ( t ) .
X ( t ) = X 1 ( t ) X 2 ( t ) = B 2 J 1 ( Δ ϕ 0 ) J 2 ( Δ ϕ 0 ) ϕ ( t ) t .
Y ( t ) = B 2 J 1 ( Δ ϕ 0 ) J 2 ( Δ ϕ 0 ) ϕ ( t ) ,
Δ t = n L c ,
I ( t ) = A + B { [ J 0 ( ϕ c ) + 2 n = 1 J 2 n ( Δ ϕ 0 ) cos   2 ( n ω c ( t + Δ t ) ) ] × cos   ϕ ( t ) [ 2 n = 0 J 2 n + 1 ( Δ ϕ 0 ) sin ( 2 n + 1 ) × ω c ( t + Δ t ) ] sin   ϕ ( t ) } .
S 1 ( t ) = B J 1 ( Δ ϕ 0 ) cos ( ω c Δ t ) sin   ϕ ( t ) ,
S 2 ( t ) = B J 2 ( Δ ϕ 0 ) cos ( 2 ω c Δ t ) cos   ϕ ( t ) .
Y ( t ) = B 2 J 1 ( Δ ϕ 0 ) J 2 ( Δ ϕ 0 ) cos ( ω c Δ t ) cos ( 2 ω c Δ t ) ϕ ( t ) .
F s q u , 1 st ( t ) = 1 , if   2 π ω c < t < 0 ,
F s q u , 1 st ( t ) = 1 , if   0 < t < 2 π ω c ,
F s q u , 1 st ( t ) = 4 π n = 0 1 ( 2 n + 1 )   sin ( 2 n + 1 ) ω c t .
F s q u , 2 nd ( t ) = 1 , if   π ω c < t < 0 ,
F s q u , 2 nd ( t ) = 1 , if   0 < t < π ω c ,
F s q u , 2 nd ( t ) = 4 π n = 0 1 ( 2 n + 1 )   sin ( 4 n + 2 ) ω c t .
F s q u , 2 nd ( t + π 4 ω c ) = 4 π n = 0 1 ( 2 n + 1 )   sin ( 4 n + 2 ) ω c ( t + π 4 ω c ) = 4 π n = 0 ( 1 ) n ( 2 n + 1 )   cos ( 4 n + 2 ) ω c t .
S 1 ( t ) = 4 B π   sin   ϕ ( t ) n = 0 1 2 n + 1 J 2 n + 1 ( Δ ϕ 0 ) × cos [ ( 2 n + 1 ) ω c Δ t ] = 4 B π F 1 ( Δ t ) sin   ϕ ( t ) ,
S 2 ( t ) = 4 B π   cos   ϕ ( t ) n = 0 ( 1 ) n 2 n + 1 J ( 4 n + 2 ) ( Δ ϕ 0 ) × cos [ ( 4 n + 2 ) ω c Δ t ] = 4 B π F 2 ( Δ t ) cos   ϕ ( t ) ,
F 1 ( Δ t ) = n = 0 1 2 n + 1 J 2 n + 1 ( Δ ϕ 0 ) cos [ ( 2 n + 1 ) ω c Δ t ] ,
F 2 ( Δ t ) = n = 0 ( 1 ) n 2 n + 1 J ( 4 n + 2 ) ( Δ ϕ 0 ) cos [ ( 4 n + 2 ) ω c Δ t ] .
F 1 ( Δ t ) max = F 1 ( 0 ) = n = 0 1 2 n + 1 J 2 n + 1 ( 2.37 ) ,
F 2 ( Δ t ) max = F 2 ( 0 ) = n = 0 ( 1 ) n 2 n + 1 J ( 4 n + 2 ) ( 2.37 ) ,
Y ( t ) = 16 π 2 B 2 F 1 ( Δ t ) F 2 ( Δ t ) ϕ ( t ) .
Y max ( t ) = 16 π 2 B 2 F 1 ( 0 ) F 2 ( 0 ) ϕ ( t ) .
ϕ d 1 = 2 π f c n ( 2 L ) c = 4 π f c n L c ,
ϕ d 2 = 2 π ( 2 f c ) n ( 2 L ) c = 8 π f c n L c .

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