Abstract

In this paper we propose a novel, improved, phase generated carrier (PGC) demodulation algorithm based on the PGC-differential-cross-multiplying approach (PGC-DCM). The influence of phase modulation amplitude variation and light intensity disturbance (LID) on traditional PGC demodulation algorithms is analyzed theoretically and experimentally. An experimental system for remote no-contact microvibration measurement is set up to confirm the stability of the improved PGC algorithm with LID. In the experiment, when the LID with a frequency of 50 Hz and the depth of 0.3 is applied, the signal-to-noise and distortion ratio (SINAD) of the improved PGC algorithm is 19 dB, higher than the SINAD of the PGC-DCM algorithm, which is 8.7 dB.

© 2012 Optical Society of America

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  1. T. Suzuki, O. Sasaki, K. Higuchi, and T. Maruyama, “Real time displacement measurement in sinusoidal phase modulating interferometry,” Appl. Opt. 28, 5270–5274 (1989).
    [CrossRef]
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    [CrossRef]
  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. 18, 1647–1653 (1982).
    [CrossRef]
  4. S. C. Huang, W. W. Lin, and M. H. Chen, “Phase sensitivity normalization in time division multiplexing of polarization-insensitive interferometric sensors using phase-generated carrier demodulation,” Opt. Eng. 35, 2634–2640 (1996).
    [CrossRef]
  5. C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
    [CrossRef]
  6. P. T. R. Christian and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
    [CrossRef]
  7. Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
    [CrossRef]
  8. L. W. Wang, M. Zhang, X. H. Mao, and Y. B. Liao, “The arctangent approach of digital PGC demodulation for optic interferometric sensors,” Proc. SPIE 6292, 62921E (2006).
  9. S. C. Huang and H. Lin, “Modified phase-generated carrier demodulation compensated for the propagation delay of the fiber,” Appl. Opt. 46, 7594–7603 (2007).
    [CrossRef]

2010

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

2009

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

2007

2006

L. W. Wang, M. Zhang, X. H. Mao, and Y. B. Liao, “The arctangent approach of digital PGC demodulation for optic interferometric sensors,” Proc. SPIE 6292, 62921E (2006).

2004

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37, R197–R216 (2004).
[CrossRef]

1996

S. C. Huang, W. W. Lin, and M. H. Chen, “Phase sensitivity normalization in time division multiplexing of polarization-insensitive interferometric sensors using phase-generated carrier demodulation,” Opt. Eng. 35, 2634–2640 (1996).
[CrossRef]

1994

P. T. R. Christian and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[CrossRef]

1989

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. 18, 1647–1653 (1982).
[CrossRef]

Chen, M. H.

S. C. Huang, W. W. Lin, and M. H. Chen, “Phase sensitivity normalization in time division multiplexing of polarization-insensitive interferometric sensors using phase-generated carrier demodulation,” Opt. Eng. 35, 2634–2640 (1996).
[CrossRef]

Christian, P. T. R.

P. T. R. Christian and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[CrossRef]

Chu, X. H.

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

Dandridge, A.

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37, R197–R216 (2004).
[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. 18, 1647–1653 (1982).
[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. 18, 1647–1653 (1982).
[CrossRef]

Higuchi, K.

Houston, B. H.

P. T. R. Christian and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[CrossRef]

Huang, L. J.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

Huang, S. C.

S. C. Huang and H. Lin, “Modified phase-generated carrier demodulation compensated for the propagation delay of the fiber,” Appl. Opt. 46, 7594–7603 (2007).
[CrossRef]

S. C. Huang, W. W. Lin, and M. H. Chen, “Phase sensitivity normalization in time division multiplexing of polarization-insensitive interferometric sensors using phase-generated carrier demodulation,” Opt. Eng. 35, 2634–2640 (1996).
[CrossRef]

Kirkendall, C. K.

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37, R197–R216 (2004).
[CrossRef]

Lai, S. R.

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

Liao, Y. B.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

L. W. Wang, M. Zhang, X. H. Mao, and Y. B. Liao, “The arctangent approach of digital PGC demodulation for optic interferometric sensors,” Proc. SPIE 6292, 62921E (2006).

Lin, H.

Lin, W. W.

S. C. Huang, W. W. Lin, and M. H. Chen, “Phase sensitivity normalization in time division multiplexing of polarization-insensitive interferometric sensors using phase-generated carrier demodulation,” Opt. Eng. 35, 2634–2640 (1996).
[CrossRef]

Mao, X. H.

L. W. Wang, M. Zhang, X. H. Mao, and Y. B. Liao, “The arctangent approach of digital PGC demodulation for optic interferometric sensors,” Proc. SPIE 6292, 62921E (2006).

Maruyama, T.

Sasaki, O.

Shi, Q. P.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

Suzuki, T.

Tian, C. D.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

Tian, Q.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

Tveten, A. B.

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

Wang, H. H.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

Wang, L. W.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

L. W. Wang, M. Zhang, X. H. Mao, and Y. B. Liao, “The arctangent approach of digital PGC demodulation for optic interferometric sensors,” Proc. SPIE 6292, 62921E (2006).

Zeng, X.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

Zhang, H. Y.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

Zhang, M.

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

L. W. Wang, M. Zhang, X. H. Mao, and Y. B. Liao, “The arctangent approach of digital PGC demodulation for optic interferometric sensors,” Proc. SPIE 6292, 62921E (2006).

Appl. Opt.

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. 18, 1647–1653 (1982).
[CrossRef]

J. Phys. D

C. K. Kirkendall and A. Dandridge, “Overview of high performance fiber-optic sensing,” J. Phys. D 37, R197–R216 (2004).
[CrossRef]

Opt. Eng.

S. C. Huang, W. W. Lin, and M. H. Chen, “Phase sensitivity normalization in time division multiplexing of polarization-insensitive interferometric sensors using phase-generated carrier demodulation,” Opt. Eng. 35, 2634–2640 (1996).
[CrossRef]

Q. P. Shi, Q. Tian, L. W. Wang, C. D. Tian, H. Y. Zhang, M. Zhang, Y. B. Liao, H. H. Wang, X. Zeng, and L. J. Huang, “Performance improvement of phase-generated carrier method by eliminating laser-intensity modulation for optical seismometer,” Opt. Eng. 49, 024402 (2010).
[CrossRef]

Proc. SPIE

L. W. Wang, M. Zhang, X. H. Mao, and Y. B. Liao, “The arctangent approach of digital PGC demodulation for optic interferometric sensors,” Proc. SPIE 6292, 62921E (2006).

C. D. Tian, L. W. Wang, M. Zhang, H. Y. Zhang, X. H. Chu, S. R. Lai, and Y. B. Liao, “Performance improvement of PGC method by using lookup table for optical seismometer,” Proc. SPIE 7503, 750348 (2009).
[CrossRef]

P. T. R. Christian and B. H. Houston, “Real-time analog and digital demodulator for interferometric fiber optic sensors,” Proc. SPIE 2191, 324–336 (1994).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the improved PGC demodulation algorithm.

Fig. 2.
Fig. 2.

Dependence of SINAD on the phase modulation amplitude C.

Fig. 3.
Fig. 3.

Dependence of SINAD on the light intensity disturbance depth m.

Fig. 4.
Fig. 4.

Experiment architecture. (IM, intensity modulator; BS, beam splitter; PZT, piezoelectric transducer.)

Fig. 5.
Fig. 5.

Experiment results.

Equations (26)

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I(t)=A+Bcos[Ccos(ω0t)+θ(t)],
θ(t)=Dcos(ωst)+φ(t),
L1(t)=BJ1(C)sinθ(t),
L2(t)=BJ2(C)cosθ(t),
L3(t)=BJ3(C)sinθ(t),
E(t)=L3(t)L1(t)=BJ3(C)sinθ(t)+BJ1(C)sinθ(t)=B[J3(C)+J1(C)]sinθ(t).
J1(C)+J3(C)=4CJ2(C).
E(t)=L1(t)L3(t)=4CBJ2(C)sinθ(t).
12B2J2(C)2[1+cos2θ(t)],
8C2B2J2(C)2[1cos2θ(t)].
cos2θ(t)=cos[2Dcos(ωst)+2φ(t)]=[J0(2D)+2k=1(1)kJ2k(2D)cos2kωst]cos2φ(t)2[k=0(1)kJ2k+1(2D)cos(2k+1)ωst]sin2φ(t).
B2J2(C)2{[k=1(1)kJ2k(2D)cos2kωst]cos2φ(t)[k=0(1)kJ2k+1(2D)cos(2k+1)ωst]sin2φ(t)}
16C2B2J2(C)2{[k=1(1)kJ2k(2D)cos2kωst]cos2φ(t)[k=0(1)kJ2k+1(2D)cos(2k+1)ωst]sin2φ(t)}.
c=16C2.
12B2J2(C)2[1cos2θ(t)].
b(t)=B2J2(C)2.
B2J1(C)J2(C)θ(t).
R(t)=J1(C)J2(C)θ(t).
S1(t)=arctan[vtanθ(t)],
S1(t)=arctan[vtanθ(t)]=arctan[tanθ(t)+(v1)tanθ(t)]=θ(t)+arctan[(v1)tanθ(t)vtan2θ(t)+1]=θ(t)+arctan[sin2θ(t)v+1v1cos2θ(t)]=θ(t)+fP[θ(t)],
fP[θ(t)]=arctan[sin2θ(t)v+1v1cos2θ(t)].
SNR=T[θ(t)]2dtT{fP[θ(t)]}2dt=T[θ(t)]2dtT{arctan[sin2θ(t)v+1v1cos2θ(t)]}2dt,
v=J1(C)J2(C),
S2(t)=B2J1(C)J2(C)θ(t).
S2(t)=B02[1+mcos(ωmt)]2J1(C)J2(C)θ(t)=[1+2mcos(ωmt)+m2[cos(ωmt)]2]B02J1(C)J2(C)θ(t)=(1+12m2)B02J1(C)J2(C)θ(t)+[2mcos(ωmt)+12m2cos(2ωmt)]B02J1(C)J2(C)θ(t).
SNR(m)=T[(1+12m2)B02J1(C)J2(C)θ(t)]2dtT{[2mcos(ωmt)+12m2cos(2ωmt)]B02J1(C)J2(C)θ(t)}2dt.

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