Abstract

The path imbalance (PI) of the two-arm fiber-optic interferometric sensor is a substantial parameter; a precise value of millimeters is required. Currently the precision reflectometry and the millimeter optical time-domain reflectometry are used to measure the tiny optical path difference, but the performances of these measurements are limited from the length and the resolution of the PI. We propose a new method accomplished by interferometer to accurately measure millimeters to within a few decimeters of the PI.

© 2008 Optical Society of America

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References

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  1. V. Handerek, “Single mode optical fiber sensors,” in Optical Fiber Sensor Technology, K. T. V. Grattan and B. T. Meggitt, eds. (Chapman & Hall, 1995), pp. 197-222.
    [CrossRef]
  2. A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
    [CrossRef]
  3. A. Dandridge, “Zero path-length difference fiber-optic interferometers,” J. Lightwave Technol. LT-1, 514-516 (1983).
    [CrossRef]
  4. A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength shift detection,” Electron. Lett. 28, 236-238 (1992).
    [CrossRef]
  5. W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
    [CrossRef]
  6. Y. L. Yu, C. C. Liu, S. K. Liu, J. T. Zhang “Method for the measurement of the long difference between two arms of unbalance all-fiber interferometer,” J. Natural Science Heilongjiang Univ. 22, 216-218 (2005).
  7. 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]
  8. A. D. Kersey, A. Dandridge, and A. B. Tveten, “Time-division multiplexing of interferometric fiber sensors using passive phase-generated carrier interrogation,” Opt. Lett. 12, 775-777 (1987).
    [CrossRef] [PubMed]
  9. 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]
  10. M. Li and M. Zhang, “Optical path difference measurement of fiber interferometer,” Acta Photonica Sin. 28, 740-743 (1999).
  11. A. D. Kersey, M. J. Marrone, and M. A. Davis, “Polarisation insensitive fibre optic Michelson interferometer,” Electron. Lett. 27, 518-520 (1991).
    [CrossRef]
  12. M. Martinelli, “A universal compensator for polarisation change induced by birefringence on a retracing beam,” Opt. Commun. 72, 341-344 (1989).
    [CrossRef]

2005

Y. L. Yu, C. C. Liu, S. K. Liu, J. T. Zhang “Method for the measurement of the long difference between two arms of unbalance all-fiber interferometer,” J. Natural Science Heilongjiang Univ. 22, 216-218 (2005).

2000

1999

M. Li and M. Zhang, “Optical path difference measurement of fiber interferometer,” Acta Photonica Sin. 28, 740-743 (1999).

1996

W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
[CrossRef]

1992

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength shift detection,” Electron. Lett. 28, 236-238 (1992).
[CrossRef]

1991

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

1989

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

1987

1983

A. Dandridge, “Zero path-length difference fiber-optic interferometers,” J. Lightwave Technol. LT-1, 514-516 (1983).
[CrossRef]

1982

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]

1981

A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
[CrossRef]

Berkoff, T. A.

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength shift detection,” Electron. Lett. 28, 236-238 (1992).
[CrossRef]

Dandridge, A.

A. D. Kersey, A. Dandridge, and A. B. Tveten, “Time-division multiplexing of interferometric fiber sensors using passive phase-generated carrier interrogation,” Opt. Lett. 12, 775-777 (1987).
[CrossRef] [PubMed]

A. Dandridge, “Zero path-length difference fiber-optic interferometers,” J. Lightwave Technol. LT-1, 514-516 (1983).
[CrossRef]

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]

A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
[CrossRef]

Davis, M. A.

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

Giallorenzi, T. G.

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]

A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
[CrossRef]

Grattan, K. T. V.

W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
[CrossRef]

Handerek, V.

V. Handerek, “Single mode optical fiber sensors,” in Optical Fiber Sensor Technology, K. T. V. Grattan and B. T. Meggitt, eds. (Chapman & Hall, 1995), pp. 197-222.
[CrossRef]

Huang, S. C.

Huang, S. L.

W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
[CrossRef]

Hung, S. C.

Jackson, D. A.

A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
[CrossRef]

Kersey, A. D.

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength shift detection,” Electron. Lett. 28, 236-238 (1992).
[CrossRef]

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

A. D. Kersey, A. Dandridge, and A. B. Tveten, “Time-division multiplexing of interferometric fiber sensors using passive phase-generated carrier interrogation,” Opt. Lett. 12, 775-777 (1987).
[CrossRef] [PubMed]

Li, M.

M. Li and M. Zhang, “Optical path difference measurement of fiber interferometer,” Acta Photonica Sin. 28, 740-743 (1999).

Lin, W. W.

Liu, C. C.

Y. L. Yu, C. C. Liu, S. K. Liu, J. T. Zhang “Method for the measurement of the long difference between two arms of unbalance all-fiber interferometer,” J. Natural Science Heilongjiang Univ. 22, 216-218 (2005).

Liu, S. K.

Y. L. Yu, C. C. Liu, S. K. Liu, J. T. Zhang “Method for the measurement of the long difference between two arms of unbalance all-fiber interferometer,” J. Natural Science Heilongjiang Univ. 22, 216-218 (2005).

Marrone, M. J.

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

Martinelli, M.

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

Miles, R. O.

A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
[CrossRef]

Morey, W. W.

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength shift detection,” Electron. Lett. 28, 236-238 (1992).
[CrossRef]

Ning, T. N.

W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
[CrossRef]

Palmer, A. W.

W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
[CrossRef]

Shi, W. J.

W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
[CrossRef]

Tsay, J. S.

Tveten, A. B.

A. D. Kersey, A. Dandridge, and A. B. Tveten, “Time-division multiplexing of interferometric fiber sensors using passive phase-generated carrier interrogation,” Opt. Lett. 12, 775-777 (1987).
[CrossRef] [PubMed]

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]

A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
[CrossRef]

Yu, Y. L.

Y. L. Yu, C. C. Liu, S. K. Liu, J. T. Zhang “Method for the measurement of the long difference between two arms of unbalance all-fiber interferometer,” J. Natural Science Heilongjiang Univ. 22, 216-218 (2005).

Zhang, J. T.

Y. L. Yu, C. C. Liu, S. K. Liu, J. T. Zhang “Method for the measurement of the long difference between two arms of unbalance all-fiber interferometer,” J. Natural Science Heilongjiang Univ. 22, 216-218 (2005).

Zhang, M.

M. Li and M. Zhang, “Optical path difference measurement of fiber interferometer,” Acta Photonica Sin. 28, 740-743 (1999).

Acta Photonica Sin.

M. Li and M. Zhang, “Optical path difference measurement of fiber interferometer,” Acta Photonica Sin. 28, 740-743 (1999).

Appl. Phys. Lett.

A. Dandridge, A. B. Tveten, R. O. Miles, D. A. Jackson, and T. G. Giallorenzi, “Single-mode diode laser phase noise,”Appl. Phys. Lett. 38, 77-79 (1981).
[CrossRef]

Electron. Lett.

A. D. Kersey, T. A. Berkoff, and W. W. Morey, “High-resolution fibre-grating based strain sensor with interferometric wavelength shift detection,” Electron. Lett. 28, 236-238 (1992).
[CrossRef]

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

IEEE J. Quantum Electron.

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.

J. Natural Science Heilongjiang Univ.

Y. L. Yu, C. C. Liu, S. K. Liu, J. T. Zhang “Method for the measurement of the long difference between two arms of unbalance all-fiber interferometer,” J. Natural Science Heilongjiang Univ. 22, 216-218 (2005).

Opt. Commun.

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

Opt. Lett.

Proc. SPIE

W. J. Shi, T. N. Ning, K. T. V. Grattan, A. W. Palmer, and S. L. Huang “Novel wavelength measurement scheme using a stabilized interferometer system,” Proc. SPIE 2895, 64-67(1996).
[CrossRef]

Other

V. Handerek, “Single mode optical fiber sensors,” in Optical Fiber Sensor Technology, K. T. V. Grattan and B. T. Meggitt, eds. (Chapman & Hall, 1995), pp. 197-222.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Curves of the first kind Bessel function ( n = 1 4 ) as a function of phase Δ φ 0 ( 0 6 rads ) .

Fig. 2
Fig. 2

Curve of 20 log [ J 2 ( Δ φ 0 ) / J 4 ( Δ φ 0 ) ] as a function of the amplitude of modulation phase signal Δ φ 0 ( 0 5.135 rads ) .

Fig. 3
Fig. 3

PI measurement system with PIFOMIS.

Fig. 4
Fig. 4

Components of 1 and 3 kHz spectra of the output signal are equal for measuring the low-frequency response of the PZT phase modulator.

Fig. 5
Fig. 5

Input signal of the PZT phase modulator is a triangle wave with an amplitude of 5 V , and the period is 100 s .

Fig. 6
Fig. 6

Waveform of the output interference signal in a period of 100 ms with six extreme values for carrier phase signal Δ φ ( t ) = 4.12 rads .

Fig. 7
Fig. 7

Harmonic spectra of the output interference signal; the values of the second and fourth harmonic spectra are maximum for sin φ T ( t ) = 0 .

Fig. 8
Fig. 8

Harmonic spectra of the output interference signal; the values of first and third harmonic spectra are maximum for cos φ T ( t ) = 0 .

Fig. 9
Fig. 9

Waveform of the output interference signal in a period of 100 ms with ten extreme values for carrier phase signal Δ φ ( t ) = 8.4 rads .

Tables (2)

Tables Icon

Table 1 Measurement Results

Tables Icon

Table 2 Measurement Results

Equations (28)

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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 ,
I ( t ) = b ( 1 + a sin ω c t ) { 1 + k cos [ φ ( t ) + Δ φ sin ω c t ] } ,
I ( t ) = b ( 1 + a sin ω c t ) { 1 + k [ 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 ) } .
A ( ω c ) = b a 2   bk J 1 ( Δ φ 0 ) sin φ ( t ) + [ bak J 0 ( Δ φ 0 ) bak J 2 ( Δ φ 0 ) ] cos φ ( t ) ,
A ( 2 ω c ) = [ 2   bk J 2 ( Δ φ 0 ) ] cos φ ( t ) + [ bak J 1 ( Δ φ 0 ) bak J 3 ( Δ φ 0 ) ] sin φ ( t ) ,
A ( 3 ω c ) = [ bak J 2 ( Δ φ 0 ) bak J 4 ( Δ φ 0 ) ] cos φ ( t ) [ 2   bk J 3 ( Δ φ 0 ) ] sin φ ( t ) ,
A ( 4 ω c ) = [ 2   bk J 4 ( Δ φ 0 ) ] cos φ ( t ) + [ bak J 3 ( Δ φ 0 ) bak J 5 ( Δ φ 0 ) ] sin φ ( t ) .
A ( ω c ) = b a 2   bk J 1 ( Δ φ 0 ) sin φ ( t ) ,
A ( 2 ω c ) = [ bak J 1 ( Δ φ 0 ) bak J 3 ( Δ φ 0 ) ] sin φ ( t ) ,
A ( 3 ω c ) = [ 2   bk J 3 ( Δ φ 0 ) ] sin φ ( t ) ,
A ( 4 ω c ) = [ bak J 3 ( Δ φ 0 ) bak J 5 ( Δ φ 0 ) ] sin φ ( t ) .
A ( ω c ) A ( 3 ω c ) = b a 2   bk J 1 ( Δ φ 0 ) sin φ ( t ) [ 2   bk J 3 ( Δ φ 0 ) ] sin φ ( t ) .
A ( ω c ) = [ bak J 0 ( Δ φ 0 ) bak J 2 ( Δ φ 0 ) ] cos φ ( t ) ,
A ( 2 ω c ) = [ 2   bk J 2 ( Δ φ 0 ) ] cos φ ( t ) ,
A ( 3 ω c ) = [ bak J 2 ( Δ φ 0 ) bak J 4 ( Δ φ 0 ) ] cos φ ( t ) ,
A ( 4 ω c ) = [ 2   bk J 4 ( Δ φ 0 ) ] cos φ ( t ) .
Δ L D = ( Δ φ D / Δ φ R ) Δ L R .
Δ L D = Δ φ D h Δ φ D Δ L R .
I ( t ) = b ( 1 + a sin ω c t ) { 1 + k cos [ φ ( t ) + φ en sin ω en t + Δ φ sin ω c t ] } .
I ( t ) = b ( 1 + a sin ω c t ) { 1 + k [ J 0 ( Δ φ 0 ) + 2 n = 1 J 2 n ( Δ φ 0 ) cos 2 ( n ω c t ) ] cos [ φ ( t ) + φ en sin ω en t ] [ 2 n = 0 J 2 n + 1 ( Δ φ 0 ) sin ( ( 2 n + 1 ) ω c t ) ] sin [ φ ( t ) + φ en sin ω en t ] } .
A 2 ω c ( t ) = [ 2   bk J 2 ( Δ φ 0 ) ] cos [ φ ( t ) + φ en sin ω en t ] + [ bak J 1 ( Δ φ 0 ) bak J 3 ( Δ φ 0 ) ] sin [ φ ( t ) + φ en sin ω en t ] ,
A 4 ω c ( t ) = [ 2   bk J 4 ( Δ φ 0 ) ] cos [ φ ( t ) + φ en sin ω en t ] + [ bak J 3 ( Δ φ 0 ) bak J 5 ( Δ φ 0 ) ] sin [ φ ( t ) + φ en sin ω en t ] .
A ( 2 ω c ) = [ 2   bk J 2 ( Δ φ 0 ) ] J 0 ( φ en ) cos φ ( t ) ,
A ( 4 ω c ) = [ 2   bk J 4 ( Δ φ 0 ) ] J 0 ( φ en ) cos φ ( t ) .
A ( 2 ω c ) = [ 2   bk J 2 ( Δ φ 0 + φ en ) ] cos φ ( t ) ,
A ( 4 ω c ) = [ 2   bk J 4 ( Δ φ 0 + φ en ) ] cos φ ( t ) .
Δ φ 0 , mean = Δ φ 0 , 1 + Δ φ 0 , 2 + Δ φ 0 , 3 + Δ φ 0 , 4 + Δ φ 0 , 5 5 ,
S = ( Δ φ 0 , 1 Δ φ 0 , mean ) 2 + ( Δ φ 0 , 2 Δ φ 0 , mean ) 2 + . + ( Δ φ 0 , 5 Δ φ 0 , mean ) 2 5 .

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