Abstract

We describe a method for the compensation of gain unbalance in optical sensors with separate light paths that involve two separate detection and conditioning electronic devices. The method is based on the digital measurement of harmonics of the output intensities from each path by means of the fast Fourier transform algorithm. The quotient of the amplitude of harmonics allows us to calculate the unbalance between paths and to compensate for it. In particular, this method can be applied in electric power and current sensors that use Faraday and Pockels cells to measure current and voltage, respectively.

© 2003 Optical Society of America

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References

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  1. P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
    [CrossRef]
  2. N. C. Pistoni, M. Martinelli, “Vibration-insensitive fiber-optic current sensor,” Opt. Lett. 18, 314–316 (1993).
    [CrossRef] [PubMed]
  3. X. Fang, A. Wang, R. G. May, R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Techn. 12, 1882–1889 (1994).
    [CrossRef]
  4. P. Menke, T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Techn. 13, 1362–1370 (1995).
    [CrossRef]
  5. A. Papp, H. Harms, “Magnetooptical current transformer. I: Principles,” Appl. Opt. 19, 3729–3734 (1980).
    [CrossRef] [PubMed]
  6. A. M. Smith, “Optical fibres for current measurement applications,” Opt. and Laser Techn. , 12, 25–29 (1980).
    [CrossRef]
  7. A. J. Rogers, “Optical fiber current measurement,” in Optical Fiber Sensor Technology, K. T. V. Grattan, B. T. Meggitt, eds. (Chapman Hall, London, 1995), Chap. 13B.
    [CrossRef]
  8. B. C. B. Chu, Y. N. Ning, D. A. Jackson, “Faraday current sensor that uses a triangular-shaped bulk-optic sensing element,” Opt. Lett. 17, 1167–1169 (1992).
    [CrossRef] [PubMed]
  9. T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
    [CrossRef]
  10. M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
    [CrossRef]
  11. T. Ko, C. L. Tzeng, J. H. Wang, “Birefringence examination in a practical fiber-current-sensing system,” Appl. Opt. 33, 7693–7697 (1994).
    [CrossRef] [PubMed]
  12. Y. Li, C. Li, T. Yoshino, “Optical electric-power-sensing system using Faraday and Pockels cells,” Appl. Opt. 40, 5738–5741 (2001).
    [CrossRef]
  13. C. Li, X. Cui, T. Yoshino, “Measurement of AC electric power based on dual transverse Pockels effect,” IEEE Trans. Instrum. Meas. 50, 1375–1380 (2001).
    [CrossRef]
  14. A. E. Petersen, “Portable optical AC- and proposed DC-current sensor for high voltage applications,” IEEE Trans. Power Deliv. 10, 595–599 (1995).
    [CrossRef]
  15. M. Higaki, K. Fujii, S. Yamaguchi, “Optical dc current and voltage measurement by superposing ac magnetic or electric field,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed., SPIE Proc.3740, 509–512 (1999).
    [CrossRef]
  16. J. A. Ferrari, C. D. Perciante, A. Dubra, A. Arnaud, E. M. Frins, “AC current sensor with second-harmonic detection,” Appl. Opt. 39, 4638–4640 (2000).
    [CrossRef]

2001 (2)

C. Li, X. Cui, T. Yoshino, “Measurement of AC electric power based on dual transverse Pockels effect,” IEEE Trans. Instrum. Meas. 50, 1375–1380 (2001).
[CrossRef]

Y. Li, C. Li, T. Yoshino, “Optical electric-power-sensing system using Faraday and Pockels cells,” Appl. Opt. 40, 5738–5741 (2001).
[CrossRef]

2000 (1)

1999 (1)

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

1997 (2)

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
[CrossRef]

1995 (2)

A. E. Petersen, “Portable optical AC- and proposed DC-current sensor for high voltage applications,” IEEE Trans. Power Deliv. 10, 595–599 (1995).
[CrossRef]

P. Menke, T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Techn. 13, 1362–1370 (1995).
[CrossRef]

1994 (2)

T. Ko, C. L. Tzeng, J. H. Wang, “Birefringence examination in a practical fiber-current-sensing system,” Appl. Opt. 33, 7693–7697 (1994).
[CrossRef] [PubMed]

X. Fang, A. Wang, R. G. May, R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Techn. 12, 1882–1889 (1994).
[CrossRef]

1993 (1)

1992 (1)

1980 (2)

A. Papp, H. Harms, “Magnetooptical current transformer. I: Principles,” Appl. Opt. 19, 3729–3734 (1980).
[CrossRef] [PubMed]

A. M. Smith, “Optical fibres for current measurement applications,” Opt. and Laser Techn. , 12, 25–29 (1980).
[CrossRef]

Andronovic, I.

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

Arnaud, A.

Bosselmann, T.

P. Menke, T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Techn. 13, 1362–1370 (1995).
[CrossRef]

Chu, B. C. B.

Claus, R. O.

X. Fang, A. Wang, R. G. May, R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Techn. 12, 1882–1889 (1994).
[CrossRef]

Cruden, A.

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

Cui, X.

C. Li, X. Cui, T. Yoshino, “Measurement of AC electric power based on dual transverse Pockels effect,” IEEE Trans. Instrum. Meas. 50, 1375–1380 (2001).
[CrossRef]

Dubra, A.

Fang, X.

X. Fang, A. Wang, R. G. May, R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Techn. 12, 1882–1889 (1994).
[CrossRef]

Ferrari, J. A.

Frins, E. M.

Fujii, K.

M. Higaki, K. Fujii, S. Yamaguchi, “Optical dc current and voltage measurement by superposing ac magnetic or electric field,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed., SPIE Proc.3740, 509–512 (1999).
[CrossRef]

Fujimoto, T.

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

Harms, H.

Higaki, M.

M. Higaki, K. Fujii, S. Yamaguchi, “Optical dc current and voltage measurement by superposing ac magnetic or electric field,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed., SPIE Proc.3740, 509–512 (1999).
[CrossRef]

Ikuta, S.

M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
[CrossRef]

Jackson, D. A.

Kawashima, K.

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

Ko, T.

Li, C.

Y. Li, C. Li, T. Yoshino, “Optical electric-power-sensing system using Faraday and Pockels cells,” Appl. Opt. 40, 5738–5741 (2001).
[CrossRef]

C. Li, X. Cui, T. Yoshino, “Measurement of AC electric power based on dual transverse Pockels effect,” IEEE Trans. Instrum. Meas. 50, 1375–1380 (2001).
[CrossRef]

Li, Y.

Madden, W. I.

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

Martinelli, M.

May, R. G.

X. Fang, A. Wang, R. G. May, R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Techn. 12, 1882–1889 (1994).
[CrossRef]

McDonald, J. R.

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

Menke, P.

P. Menke, T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Techn. 13, 1362–1370 (1995).
[CrossRef]

Michie, W. C.

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

Mizutani, Y.

M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
[CrossRef]

Mori, E.

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

Nakagawa, H.

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

Niewczas, P.

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

Ning, Y. N.

Noda, H.

M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
[CrossRef]

Papp, A.

Perciante, C. D.

Petersen, A. E.

A. E. Petersen, “Portable optical AC- and proposed DC-current sensor for high voltage applications,” IEEE Trans. Power Deliv. 10, 595–599 (1995).
[CrossRef]

Pistoni, N. C.

Rogers, A. J.

A. J. Rogers, “Optical fiber current measurement,” in Optical Fiber Sensor Technology, K. T. V. Grattan, B. T. Meggitt, eds. (Chapman Hall, London, 1995), Chap. 13B.
[CrossRef]

Shimizu, M.

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

Smith, A. M.

A. M. Smith, “Optical fibres for current measurement applications,” Opt. and Laser Techn. , 12, 25–29 (1980).
[CrossRef]

Sone, I.

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

Takahashy, M.

M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
[CrossRef]

Terai, K.

M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
[CrossRef]

Tzeng, C. L.

Wang, A.

X. Fang, A. Wang, R. G. May, R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Techn. 12, 1882–1889 (1994).
[CrossRef]

Wang, J. H.

Yamaguchi, S.

M. Higaki, K. Fujii, S. Yamaguchi, “Optical dc current and voltage measurement by superposing ac magnetic or electric field,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed., SPIE Proc.3740, 509–512 (1999).
[CrossRef]

Yoshino, T.

Y. Li, C. Li, T. Yoshino, “Optical electric-power-sensing system using Faraday and Pockels cells,” Appl. Opt. 40, 5738–5741 (2001).
[CrossRef]

C. Li, X. Cui, T. Yoshino, “Measurement of AC electric power based on dual transverse Pockels effect,” IEEE Trans. Instrum. Meas. 50, 1375–1380 (2001).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Instrum. Meas. (1)

C. Li, X. Cui, T. Yoshino, “Measurement of AC electric power based on dual transverse Pockels effect,” IEEE Trans. Instrum. Meas. 50, 1375–1380 (2001).
[CrossRef]

IEEE Trans. Power Deliv. (3)

A. E. Petersen, “Portable optical AC- and proposed DC-current sensor for high voltage applications,” IEEE Trans. Power Deliv. 10, 595–599 (1995).
[CrossRef]

T. Fujimoto, M. Shimizu, H. Nakagawa, I. Sone, K. Kawashima, E. Mori, “Development of an optical current transformer for adjustable speed pumped storage systems,” IEEE Trans. Power Deliv. 12, 45–50 (1997).
[CrossRef]

M. Takahashy, H. Noda, K. Terai, S. Ikuta, Y. Mizutani, “Optical current transformer for gas insulated switchgear using silica optical fiber,” IEEE Trans. Power Deliv. 12, 1422–1427 (1997).
[CrossRef]

J. Lightwave Techn. (2)

X. Fang, A. Wang, R. G. May, R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Techn. 12, 1882–1889 (1994).
[CrossRef]

P. Menke, T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Techn. 13, 1362–1370 (1995).
[CrossRef]

Opt. and Laser Techn. (1)

A. M. Smith, “Optical fibres for current measurement applications,” Opt. and Laser Techn. , 12, 25–29 (1980).
[CrossRef]

Opt. Eng. (1)

P. Niewczas, A. Cruden, W. C. Michie, W. I. Madden, J. R. McDonald, I. Andronovic, “Vibration compensation technique for an optical current transducer,” Opt. Eng. 38, 1708–1714 (1999).
[CrossRef]

Opt. Lett. (2)

Other (2)

A. J. Rogers, “Optical fiber current measurement,” in Optical Fiber Sensor Technology, K. T. V. Grattan, B. T. Meggitt, eds. (Chapman Hall, London, 1995), Chap. 13B.
[CrossRef]

M. Higaki, K. Fujii, S. Yamaguchi, “Optical dc current and voltage measurement by superposing ac magnetic or electric field,” in Optical Engineering for Sensing and Nanotechnology (ICOSN ’99), I. Yamaguchi, ed., SPIE Proc.3740, 509–512 (1999).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Layout of a sensor involving bidirectional light propagation through the sensor head.

Fig. 2
Fig. 2

Classic polarimetric scheme that uses light traveling in one direction where the measured light intensities are associated with two orthogonal linear polarization states.

Fig. 3
Fig. 3

Output signal versus applied electric current. The filled circles and the open circles indicate the values of current amplitude obtained from Eq. (12) by using the fundamental frequency of 50 Hz and the first harmonic of 100 Hz for calculating the unbalance factor, respectively. The open triangles indicate the values obtained without gain compensation [i.e., from Eq. (2)].

Fig. 4
Fig. 4

Effect of variable gain unbalance. The continuous curves show the recovered signals obtained using the compensation method, and the dashed curves show the signal obtained without gain compensation: (a) 10% gain unbalance, (b) 15% gain unbalance, (c) 20% unbalance.

Equations (16)

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

I1t=I01+Δt,
I2t=I01-Δt,
Δt=I1t-I2tI1t+I2t.
I1t=I0G11+Δt,
I2t=I0G21-Δt,
Δt=I1t/I1-I2t/I2I1t/I1+I2t/I2,
Δt=12I1t-I1I1-I2t-I2I2.
Δt=0.
Δt=rI1t-I2trI1t+I2t.
Δt=n=0 An cosnωt+Φn,
I1t=I0G11+n=0 An cosnωt+Φn,
I2t=I0G21-n=0 An cosnωt+Φn.
Ĩ1nω=I0G1An,
Ĩ2nω=-I0G2An.
r=G2/G1=|Ĩ2nω/Ĩ1nω|.
Δt=|Ĩ2nω/Ĩ1nω|I1t-I2t|Ĩ2nω/Ĩ1nω|I1t+I2t.

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