Abstract

A new scheme of three-frequency differential detection with a sideband locking technique is firstly proposed to suppress backscattering noise for improving the accuracy of resonator fiber optic gyroscope (RFOG). In the system we proposed, one light path is divided into three paths and sinusoidal wave modulations of different frequencies are respectively applied to generate the sideband. The first-order sidebands of the three channels of light in the cavity are locked to the adjacent three resonance peaks by sideband locking technique. The carrier and the remaining sidebands of the three channels of light are moved to a position away from the resonance peak, thereby achieving the purpose of being suppressed by the cavity itself. As a result, the frequency difference between the CW light and the other two CCW lights reaches one free spectral range (FSR), eliminating the expected backscattering noise. The experimental results demonstrate that the RFOG has a bias stability 0.9°/h based on the Allan deviation, and the corresponding angular random walk (ARW) 0.016°/√h, which validate that our scheme can effectively suppress backscattering noise to promote performance of RFOG in practical applications.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  18. K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator micro optic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18(1), 66–72 (2000).
    [Crossref]
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    [Crossref]
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    [Crossref]
  21. D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281(4), 580–586 (2008).
    [Crossref]
  22. M. Harumoto and K. Hotate, “Resonator fibre-optic gyro using digital serrodyne modulation – fundamental experiments and evaluation of the limitations,” Opt. Laser Technol. 29(2), xii (1997).
    [Crossref]
  23. J. Wang, L. Feng, Y. Tang, and Y. Zhi, “Resonator integrated optic gyro employing trapezoidal phase modulation technique,” Opt. Lett. 40(2), 155–158 (2015).
    [Crossref]
  24. L. Feng, J. Wang, Y. Zhi, Y. Tang, Q. Wang, H. Li, and W. Wang, “Transmissive resonator optic gyro based on silica waveguide ring resonator,” Opt. Express 22(22), 27565–27575 (2014).
    [Crossref]
  25. Q. Wang, L. Feng, H. Li, X. Wang, Y. Jia, and D. Liu, “Enhanced differential detection technique for the resonator integrated optic gyro,” Opt. Lett. 43(12), 2941–2944 (2018).
    [Crossref]
  26. K. Hotate, K. Takiguchi, and A. Hirose, “Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 2(1), 75–77 (1990).
    [Crossref]
  27. K. Suzuki, K. Takiguchi, and K. Hotate, “Reduction of backscattering induced noise by ternary phase shift keying in resonator micro-optic gyro integrated on silica planar lightwave circuit,” Electron. Lett. 35(13), 1076–1077 (1999).
    [Crossref]
  28. K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 121 (1999).
    [Crossref]
  29. T. J. Kaiser, D. Cardarelli, and J. G. Walsh, “Experimental developments in the RFOG,” Proc. SPIE 1367, 121–126 (1991).
    [Crossref]
  30. N. Liu, Y. Niu, L. Feng, H. Jiao, and X. Wang, “Suppression of backscattering-induced noise by sideband locking based on high and low modulation frequencies in ROG,” Appl. Opt. 57(26), 7455–7461 (2018).
    [Crossref]

2018 (3)

2017 (1)

2016 (2)

2015 (4)

Y. Zhi, L. Feng, J. Wang, and Y. Tang, “Reduction of backscattering noise in a resonator integrated optic gyro by double triangular phase modulation,” Appl. Opt. 54(1), 114 (2015).
[Crossref]

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

L. Feng, H. Jiao, and W. Song, “Research on polarization noise of hollow-core photonic crystal fiber resonator optic gyroscope,” Proc. SPIE 9679, 967919 (2015).
[Crossref]

J. Wang, L. Feng, Y. Tang, and Y. Zhi, “Resonator integrated optic gyro employing trapezoidal phase modulation technique,” Opt. Lett. 40(2), 155–158 (2015).
[Crossref]

2014 (2)

L. Feng, J. Wang, Y. Zhi, Y. Tang, Q. Wang, H. Li, and W. Wang, “Transmissive resonator optic gyro based on silica waveguide ring resonator,” Opt. Express 22(22), 27565–27575 (2014).
[Crossref]

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent Advances in Miniaturized Optical Gyroscopes,” JEOS:RP 9(1), 14013 (2014).
[Crossref]

2013 (2)

2012 (2)

H. Ma, X. Lu, L. Yao, X. Yu, and Z. Jin, “Full investigation of the resonant frequency servo loop for resonator fiber-optic gyro,” Appl. Opt. 51(21), 5178–5185 (2012).
[Crossref]

L. K. Strandjord, T. Qiu, J. Wu, T. Ohnstein, and G. A. Sanders, “Resonator fiber optic gyro progress including observation of navigation grade angle random walk,” Proc. SPIE 8421, 842109 (2012).
[Crossref]

2011 (1)

2008 (1)

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281(4), 580–586 (2008).
[Crossref]

2006 (1)

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45(8), 080506 (2006).
[Crossref]

2000 (1)

1999 (2)

K. Suzuki, K. Takiguchi, and K. Hotate, “Reduction of backscattering induced noise by ternary phase shift keying in resonator micro-optic gyro integrated on silica planar lightwave circuit,” Electron. Lett. 35(13), 1076–1077 (1999).
[Crossref]

K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 121 (1999).
[Crossref]

1997 (1)

M. Harumoto and K. Hotate, “Resonator fibre-optic gyro using digital serrodyne modulation – fundamental experiments and evaluation of the limitations,” Opt. Laser Technol. 29(2), xii (1997).
[Crossref]

1993 (1)

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization-rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1993).
[Crossref]

1991 (1)

T. J. Kaiser, D. Cardarelli, and J. G. Walsh, “Experimental developments in the RFOG,” Proc. SPIE 1367, 121–126 (1991).
[Crossref]

1990 (2)

K. Hotate, K. Takiguchi, and A. Hirose, “Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 2(1), 75–77 (1990).
[Crossref]

M. Takahashi, S. Tai, and K. Kyuma, “Effect of reflections on the drift characteristics of a fiber-optic passive ring-resonator gyroscope,” J. Lightwave Technol. 8(5), 811–816 (1990).
[Crossref]

1983 (1)

1981 (2)

Arditty, H. J.

Armenise, M. N.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent Advances in Miniaturized Optical Gyroscopes,” JEOS:RP 9(1), 14013 (2014).
[Crossref]

Cardarelli, D.

T. J. Kaiser, D. Cardarelli, and J. G. Walsh, “Experimental developments in the RFOG,” Proc. SPIE 1367, 121–126 (1991).
[Crossref]

Ciminelli, C.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent Advances in Miniaturized Optical Gyroscopes,” JEOS:RP 9(1), 14013 (2014).
[Crossref]

Dell’Olio, F.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent Advances in Miniaturized Optical Gyroscopes,” JEOS:RP 9(1), 14013 (2014).
[Crossref]

Ding, C.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45(8), 080506 (2006).
[Crossref]

Ezekiel, S.

Feng, L.

Q. Wang, L. Feng, H. Li, X. Wang, Y. Jia, and D. Liu, “Enhanced differential detection technique for the resonator integrated optic gyro,” Opt. Lett. 43(12), 2941–2944 (2018).
[Crossref]

H. Jiao, L. Feng, N. Liu, and Z. Yang, “Improvement of long-term stability of hollow-core photonic-crystal fiber optic gyro based on single-polarization resonator,” Opt. Express 26(7), 8645–8655 (2018).
[Crossref]

N. Liu, Y. Niu, L. Feng, H. Jiao, and X. Wang, “Suppression of backscattering-induced noise by sideband locking based on high and low modulation frequencies in ROG,” Appl. Opt. 57(26), 7455–7461 (2018).
[Crossref]

J. Wang, L. Feng, Q. Wang, X. Wang, and H. Jiao, “Reduction of angle random walk by in-phase triangular phase modulation technique for resonator integrated optic gyro,” Opt. Express 24(5), 5463–5468 (2016).
[Crossref]

J. Wang, L. Feng, Q. Wang, H. Jiao, and X. Wang, “Suppression of backreflection error in resonator integrated optic gyro by the phase difference traversal method,” Opt. Lett. 41(7), 1586–1589 (2016).
[Crossref]

L. Feng, H. Jiao, and W. Song, “Research on polarization noise of hollow-core photonic crystal fiber resonator optic gyroscope,” Proc. SPIE 9679, 967919 (2015).
[Crossref]

J. Wang, L. Feng, Y. Tang, and Y. Zhi, “Resonator integrated optic gyro employing trapezoidal phase modulation technique,” Opt. Lett. 40(2), 155–158 (2015).
[Crossref]

Y. Zhi, L. Feng, J. Wang, and Y. Tang, “Reduction of backscattering noise in a resonator integrated optic gyro by double triangular phase modulation,” Appl. Opt. 54(1), 114 (2015).
[Crossref]

L. Feng, J. Wang, Y. Zhi, Y. Tang, Q. Wang, H. Li, and W. Wang, “Transmissive resonator optic gyro based on silica waveguide ring resonator,” Opt. Express 22(22), 27565–27575 (2014).
[Crossref]

L. Feng, M. Lei, H. Liu, Y. Zhi, and J. Wang, “Suppression of backreflection noise in a resonator integrated optic gyro by hybrid phase-modulation technology,” Appl. Opt. 52(8), 1668–1675 (2013).
[Crossref]

Harumoto, M.

M. Harumoto and K. Hotate, “Resonator fibre-optic gyro using digital serrodyne modulation – fundamental experiments and evaluation of the limitations,” Opt. Laser Technol. 29(2), xii (1997).
[Crossref]

Hayashi, G.

K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 121 (1999).
[Crossref]

He, Z.

Hirose, A.

K. Hotate, K. Takiguchi, and A. Hirose, “Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 2(1), 75–77 (1990).
[Crossref]

Ho, W.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

Hotate, K.

H. Ma, Z. He, and K. Hotate, “Reduction of Backscattering Induced Noise by Carrier Suppression in Waveguide-Type Optical Ring Resonator Gyro,” J. Lightwave Technol. 29(1), 85–90 (2011).
[Crossref]

K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator micro optic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18(1), 66–72 (2000).
[Crossref]

K. Suzuki, K. Takiguchi, and K. Hotate, “Reduction of backscattering induced noise by ternary phase shift keying in resonator micro-optic gyro integrated on silica planar lightwave circuit,” Electron. Lett. 35(13), 1076–1077 (1999).
[Crossref]

K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 121 (1999).
[Crossref]

M. Harumoto and K. Hotate, “Resonator fibre-optic gyro using digital serrodyne modulation – fundamental experiments and evaluation of the limitations,” Opt. Laser Technol. 29(2), xii (1997).
[Crossref]

K. Hotate, K. Takiguchi, and A. Hirose, “Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 2(1), 75–77 (1990).
[Crossref]

Jia, Y.

Jiao, H.

Jin, Z.

Kaiser, T. J.

T. J. Kaiser, D. Cardarelli, and J. G. Walsh, “Experimental developments in the RFOG,” Proc. SPIE 1367, 121–126 (1991).
[Crossref]

Kyuma, K.

M. Takahashi, S. Tai, and K. Kyuma, “Effect of reflections on the drift characteristics of a fiber-optic passive ring-resonator gyroscope,” J. Lightwave Technol. 8(5), 811–816 (1990).
[Crossref]

Lefevre, H. C.

Lei, M.

Li, H.

Liu, D.

Liu, H.

Liu, N.

Lu, X.

Ma, H.

Nakazawa, N.

Niu, Y.

Ohnstein, T.

L. K. Strandjord, T. Qiu, J. Wu, T. Ohnstein, and G. A. Sanders, “Resonator fiber optic gyro progress including observation of navigation grade angle random walk,” Proc. SPIE 8421, 842109 (2012).
[Crossref]

Prentiss, M. G.

Qiu, T.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

L. K. Strandjord, T. Qiu, J. Wu, T. Ohnstein, and G. A. Sanders, “Resonator fiber optic gyro progress including observation of navigation grade angle random walk,” Proc. SPIE 8421, 842109 (2012).
[Crossref]

Sanders, G. A.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

L. K. Strandjord, T. Qiu, J. Wu, T. Ohnstein, and G. A. Sanders, “Resonator fiber optic gyro progress including observation of navigation grade angle random walk,” Proc. SPIE 8421, 842109 (2012).
[Crossref]

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization-rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1993).
[Crossref]

G. A. Sanders, M. G. Prentiss, and S. Ezekiel, “Passive ring resonator method for sensitive inertial rotation measurements in geophysics and relativity,” Opt. Lett. 6(11), 569–571 (1981).
[Crossref]

Smiciklas, M.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

Song, W.

L. Feng, H. Jiao, and W. Song, “Research on polarization noise of hollow-core photonic crystal fiber resonator optic gyroscope,” Proc. SPIE 9679, 967919 (2015).
[Crossref]

Strandjord, L. K.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

L. K. Strandjord, T. Qiu, J. Wu, T. Ohnstein, and G. A. Sanders, “Resonator fiber optic gyro progress including observation of navigation grade angle random walk,” Proc. SPIE 8421, 842109 (2012).
[Crossref]

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization-rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1993).
[Crossref]

Suzuki, K.

K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator micro optic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18(1), 66–72 (2000).
[Crossref]

K. Suzuki, K. Takiguchi, and K. Hotate, “Reduction of backscattering induced noise by ternary phase shift keying in resonator micro-optic gyro integrated on silica planar lightwave circuit,” Electron. Lett. 35(13), 1076–1077 (1999).
[Crossref]

Tai, S.

M. Takahashi, S. Tai, and K. Kyuma, “Effect of reflections on the drift characteristics of a fiber-optic passive ring-resonator gyroscope,” J. Lightwave Technol. 8(5), 811–816 (1990).
[Crossref]

Takahashi, M.

M. Takahashi, S. Tai, and K. Kyuma, “Effect of reflections on the drift characteristics of a fiber-optic passive ring-resonator gyroscope,” J. Lightwave Technol. 8(5), 811–816 (1990).
[Crossref]

Takiguchi, K.

K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator micro optic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18(1), 66–72 (2000).
[Crossref]

K. Suzuki, K. Takiguchi, and K. Hotate, “Reduction of backscattering induced noise by ternary phase shift keying in resonator micro-optic gyro integrated on silica planar lightwave circuit,” Electron. Lett. 35(13), 1076–1077 (1999).
[Crossref]

K. Hotate, K. Takiguchi, and A. Hirose, “Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 2(1), 75–77 (1990).
[Crossref]

Tang, Y.

Tatoli, T.

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent Advances in Miniaturized Optical Gyroscopes,” JEOS:RP 9(1), 14013 (2014).
[Crossref]

Walsh, J. G.

T. J. Kaiser, D. Cardarelli, and J. G. Walsh, “Experimental developments in the RFOG,” Proc. SPIE 1367, 121–126 (1991).
[Crossref]

Wang, J.

Wang, L.

Wang, Q.

Wang, W.

Wang, X.

Wu, J.

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

L. K. Strandjord, T. Qiu, J. Wu, T. Ohnstein, and G. A. Sanders, “Resonator fiber optic gyro progress including observation of navigation grade angle random walk,” Proc. SPIE 8421, 842109 (2012).
[Crossref]

Yang, Z.

Yao, L.

Ying, D.

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281(4), 580–586 (2008).
[Crossref]

Yu, X.

Zhang, J.

Zhang, X.

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45(8), 080506 (2006).
[Crossref]

Zhi, Y.

Appl. Opt. (4)

Electron. Lett. (1)

K. Suzuki, K. Takiguchi, and K. Hotate, “Reduction of backscattering induced noise by ternary phase shift keying in resonator micro-optic gyro integrated on silica planar lightwave circuit,” Electron. Lett. 35(13), 1076–1077 (1999).
[Crossref]

IEEE Photonics Technol. Lett. (1)

K. Hotate, K. Takiguchi, and A. Hirose, “Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro,” IEEE Photonics Technol. Lett. 2(1), 75–77 (1990).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. (1)

JEOS:RP (1)

F. Dell’Olio, T. Tatoli, C. Ciminelli, and M. N. Armenise, “Recent Advances in Miniaturized Optical Gyroscopes,” JEOS:RP 9(1), 14013 (2014).
[Crossref]

Opt. Commun. (1)

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281(4), 580–586 (2008).
[Crossref]

Opt. Eng. (1)

H. Ma, X. Zhang, Z. Jin, and C. Ding, “Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique,” Opt. Eng. 45(8), 080506 (2006).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

M. Harumoto and K. Hotate, “Resonator fibre-optic gyro using digital serrodyne modulation – fundamental experiments and evaluation of the limitations,” Opt. Laser Technol. 29(2), xii (1997).
[Crossref]

Opt. Lett. (5)

Proc. SPIE (6)

L. Feng, H. Jiao, and W. Song, “Research on polarization noise of hollow-core photonic crystal fiber resonator optic gyroscope,” Proc. SPIE 9679, 967919 (2015).
[Crossref]

L. K. Strandjord and G. A. Sanders, “Performance improvements of a polarization-rotating resonator fiber optic gyroscope,” Proc. SPIE 1795, 94–104 (1993).
[Crossref]

L. K. Strandjord, T. Qiu, J. Wu, T. Ohnstein, and G. A. Sanders, “Resonator fiber optic gyro progress including observation of navigation grade angle random walk,” Proc. SPIE 8421, 842109 (2012).
[Crossref]

J. Wu, M. Smiciklas, L. K. Strandjord, T. Qiu, W. Ho, and G. A. Sanders, “Resonator fiber optic gyro with high backscatter-error suppression using two independent phase-locked lasers,” Proc. SPIE 9634, 96341O (2015).
[Crossref]

K. Hotate and G. Hayashi, “Resonator fiber optic gyro using digital serrodyne modulation-method to reduce the noise induced by the backscattering and closed-loop operation using digital signal processing,” Proc. SPIE 3746, 121 (1999).
[Crossref]

T. J. Kaiser, D. Cardarelli, and J. G. Walsh, “Experimental developments in the RFOG,” Proc. SPIE 1367, 121–126 (1991).
[Crossref]

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Figures (11)

Fig. 1.
Fig. 1. Illustration of RFOG system and the spectra of CW and CCW.
Fig. 2.
Fig. 2. Schematic diagram of three-frequency differential gyro. (laser, tunable narrow-linewidth fiber laser; PD, photodetector; PM, phase modulator; C1, C2, couplers; Demod, demodulation module; SBL, sideband locking; RTL, resonance-tracking loop; DDS, direct digital synthesis; err. @ Ω1L, Ω2L, Ω3L, PDH error signals at Ω1L, Ω2L, Ω3L; ADC, analog-to-digital converter; DAC, digital-to-analog converter; FPGA, field-programmable gate array.)
Fig. 3.
Fig. 3. Modulation structures for traditional and tunable modulation/demodulation locking. (a) Pound Drever Hall (PDH); (b) Sideband locking (SBL). (For SBL only the upper half of the modulation structure is shown. The solid curve represents |F(ω)|2 and the dashed curve represents ∠F(ω), where F(ω) is the amplitude transmission coefficient of the cavity. For the frequency-tunable cases, the arrow labeled tune indicates the frequency spacing that is adjusted to tune the carrier, denoted by a thick line.)
Fig. 4.
Fig. 4. Demodulation of cos(Ω1L) term when β1=2.405, β1´=2.405, Ω1H = 1.3 MHz, Ω1L=100 KHz.
Fig. 5.
Fig. 5. Illustration of carrier suppression by locking the sideband to the cavity resonance. (The sidebands for CW (blue) locking and CCW (red) locking. Illustrated are three resonances separated by one FSR of 10 MHz.)
Fig. 6.
Fig. 6. Spectrum diagram of three-frequency lights under CW rotation. (Gyro resonance modes for CW (blue) and CCW (red) lights. Illustrated are three resonances separated by one FSR of 10 MHz, and a rotation induced frequency shift of the counter-propagating modes determines.)
Fig. 7.
Fig. 7. Measurement of the cavity SPR.
Fig. 8.
Fig. 8. PD signals of CW and CCW and their demodulations by low frequency. (the intensity output detected by PD1 for CW (green) light; the intensity output detected by PD2 for CCW (orange) light; the demodulation (blue) of the cosine term of Ω1L; the demodulation (red) of the cosine term of Ω2L; the demodulation (red) of the cosine term of Ω3L.)
Fig. 9.
Fig. 9. Scheme of locking the first-order sideband to cavity resonance. (a) the swept signal for driving laser PZT; (b) the intensity output detected by PD; (c) the demodulation of the cosine term of 2Ω1L;(d) the demodulation of the cosine term of Ω1H; (e) the demodulation of the cosine term of Ω1L.
Fig. 10.
Fig. 10. Allan deviation of gyroscope output. (a) Allan deviation of three-frequency differential RFOG based on the sideband locking output; (b) Allan deviation of double closed-loop RFOG output.
Fig. 11.
Fig. 11. PSDs of the gyro outputs in case of the DCL and case of the TFDSBL.

Equations (19)

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E CWT  =  E CW F CW ( ω C W ) +  R b E CCW F CCW ( ω C C W )
I CW = E CWT E CWT  =  | E CW | 2 H s g  +  R b | E CCW | 2 H b c  +    R b | E CW E CCW | H c h = I CW0  +  N 1  +  N 2
E CW _ M = E 0 e i ( ω C W t + β sin Ω C W t ) = E 0 n = + J n ( β ) e i ( ω C W t + n Ω C W t )
R b E CCW _ M = R b E 0 n = + J n ( β ) e i ( ω C C W t + n Ω C C W t )
I CW _ M = I CW0 _ M + N 1 _ M + N 2 _ M
I CW0 _ M = E 0 2 n = + H s g _ 0 | J n | 2  + 2 E 0 2 k = 1 + n = + H s g _ k | J n k J n | cos ( k Ω C W t )
N 1 _ M = R b E 0 2 n = + H b c _ 0 | J n | 2  + 2 R b E 0 2 k = 1 + n = + H b c _ k | J n k J n | cos ( k Ω C C W t )
N 2 _ M = 2 R b E 0 2 n = + n = + H c h _ n n J n ( β ) J n ( β ) cos [ ( n Ω C W n Ω C C W ) t + ( ω C W ω C C W ) t ]
I CW0 _ M = E 0 2 n = + H s g _ 1 | J n 1 J n |
N 1 _ M = 0
N 2 _ M = R b E 0 2 H c h _ 10 J 1 ( β ) J 0 ( β ) cos [ Ω C W t + ( ω C W ω C C W ) t ] cos Ω C W t
E in = E 0 e i ( ω t + β 1 sin Ω 1 H t  +  β 1 sin Ω 1 L t )
E in E 0 × { J 0 ( β 1 ) [ J 0 ( β 1 ) e i ω t + J 1 ( β 1 ) e i ( ω + Ω 1 L ) t J 1 ( β 1 ) e i ( ω Ω 1 L ) t ]  +  J 1 ( β 1 ) [ J 0 ( β 1 ) e i ( ω + Ω 1 H ) t + J 1 ( β 1 ) e i ( ω + Ω 1 H  +  Ω 1 L ) t J 1 ( β 1 ) e i ( ω + Ω 1 H Ω 1 L ) t ] J 1 ( β 1 ) [ J 0 ( β 1 ) e i ( ω Ω 1 H ) t + J 1 ( β 1 ) e i ( ω Ω 1 H  +  Ω 1 L ) t J 1 ( β 1 ) e i ( ω Ω 1 H Ω 1 L ) t ] }
P Ω 1 L = 2 J 0 ( β 1 ) J 1 ( β 1 ) P 0 × { J 0 ( β 1 ) 2 { Re [ T ( ω ) ] cos Ω 1 L t  +  Im [ T ( ω ) ] sin Ω 1 L t }  +  J 1 ( β 1 ) 2 { Re [ T ( ω  +  Ω 1 H ) ] cos Ω 1 L t  +  Im [ T ( ω  +  Ω 1 H ) ] sin Ω 1 L t }  +  J 1 ( β 1 ) 2 { Re [ T ( ω Ω 1 H ) ] cos Ω 1 L t  +  Im [ T ( ω Ω 1 H ) ] sin Ω 1 L t } }
f P M 2 + f P M 3 = 2 F S R
f P M 2 + f P M 1 = F S R  +  Δ f
f P M 3 f P M 1 = F S R Δ f
f P M 2 + 2 f P M 1 f P M 3 = 2 Δ f
Ω  =  ( f P M 2 + 2 f P M 1 f P M 3 ) n λ 2 D

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