Abstract

Electrical crosstalk in an interferometric fiber-optic gyroscope (IFOG) is regarded as the most significant factor influencing dead bands. Here, we present a six-state modulation (SSM) technique to reduce crosstalk. Compared to conventional four-state modulation (FSM) or square-wave modulation (SWM), the SSM reduces the correlation between modulation voltage and demodulation reference by separating their fundamental frequencies, and thus reduces the bias error induced by crosstalk. The measured dead band of a 1500-m IFOG is approximately 0.02 °/h using FSM and approximately 0.08 °/h using SWM, whereas there is no evidence of dead band using SSM. The IFOG using SSM also exhibits better angular random walk (ARW) and bias instability performance compared to the same IFOG using FSM or SWM. These results verify the crosstalk reduction effect of SSM. In theory, by using the relative intensity noise (RIN) suppressing technique with the optimal modulation depth of 2π/3, the SSM can eliminate the crosstalk, which offers the potential for a high-performance IFOG with low noise, high sensitivity, wide dynamic range, and no dead band.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. H. C. Lefèvre, The Fiber-Optic Gyroscope (Artech House, 2014).
  2. G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
    [Crossref]
  3. I. R. Edu, R. Obreja, and T. L. Grigorie, “Current technologies and trends in the development of gyros used in navigation applications-a review,” in Proceedings of the 5th WSEAS International Conference on Communications and Information Technology, (World Scientific and Engineering Academy and Society, 2011), pp. 63–68.
  4. G. A. Pavlath, “Closed-loop fiber optic gyros,” in Fiber Optic Gyros:20th Anniversary Conference, (International Society for Optics and Photonics, 1996), pp. 46–60.
    [Crossref]
  5. O. Çelikel and S. E. San, “Design details and characterization of all digital closed-loop interferometric fiber optic gyroscope with superluminescent light emitting diode,” Opt. Rev. 16(1), 35–43 (2009).
    [Crossref]
  6. A. M. Kurbatov, “New methods to improve the performance of open and closed loop fiber-optic gyros,” Gyroscopy Navigation 6(3), 207–217 (2015).
    [Crossref]
  7. A. M. Kurbatov and R. A. Kurbatov, “Methods of improving the accuracy of fiber-optic gyros,” Gyroscopy Navigation 3(2), 132–143 (2012).
    [Crossref]
  8. F. Sun, L. Wang, G. Wang, and G. Liu, “Study on the drift of modulated phase in interference fiber optic gyroscope,” J. Comput. (Taipei) 5, 394–400 (2010).
  9. K.-H. Chong, W.-S. Choi, and K.-T. Chong, “Analysis of dead zone sources in a closed-loop fiber optic gyroscope,” Appl. Opt. 55(1), 165–170 (2016).
    [Crossref] [PubMed]
  10. H. Gu, Y. Huan, A. Wang, and J. Luan, “Real-time dynamic simulation of angular velocity and suppression of dead zone in IFOG,” Opt. Rev. 22(1), 39–45 (2015).
    [Crossref]
  11. D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
    [Crossref]
  12. P. A. Ward, “Interferometric fiber optic gyroscope with off-frequency modulation signals,” 7,817,284. U.S. Patent. 2010 Oct 19.
  13. J. Jing, T. Hai-Ting, P. Xiong, and S. Ning-Fang, “Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro,” Chin. Phys. B 19(3), 030701 (2010).
    [Crossref]
  14. J. G. Mark, D. A. Tazartes, and A. Cordova, “Method and apparatus for overcoming cross-coupling in a fiber optic gyroscope employing overmodulation,” 5,682,241. U.S. Patent. 1997 Oct 28.
  15. G. Spahlinger, “Fiber optic Sagnac interferometer with digital phase ramp resetting via correlation-free demodulator control,” 5,123,741. U.S. Patent. 1992 Jun 23.
  16. G. Spahlinger, M. W. Kemmler, M. Ruf, M. A. Ribes, and S. Zimmermann, “Error compensation via signal correlation in high-precision closed-loop fiber optic gyros,” in SPIE’s 1996 International Symposium on Optical Science, Engineering, and Instrumentation, (International Society for Optics and Photonics, 1996), pp. 218–227.
    [Crossref]
  17. C.-J. Chen, “Interferometric Fiber Optic Gyroscope Dead Band Suppression,” Appl. Phys. Express 1, 072501 (2008).
    [Crossref]
  18. G. Sanders, R. Dankwort, L. Strandjord, and R. Bergh, “Fiber optic gyroscope with deadband error reduction,” 5,999,304. U.S. Patent. 1999 Dec 7.
  19. P. Lo and R. A. Kovacs, “Fiber optic gyroscope with reduced non-linearity at low angular rates,” 5,684,591. U.S. Patent. 1997 Nov 4.
  20. D. A. Tazartes and G. A. Pavlath, “Automatic gain control for fiber optic gyroscope deterministic control loops,” 7,859,678. U.S. Patent. 2010 Dec 28.
  21. J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11(5), 159–161 (1967).
    [Crossref]
  22. F. Guattari, S. Chouvin, C. Moluçon, and H. Lefèvre, “A simple optical technique to compensate for excess RIN in a fiber-optic gyroscope,” in 2014 DGON Inertial Sensors and Systems, (Institute of Systems Optimization, 2014), pp. 1–14.
  23. C.-J. Chen and C. H. Lange, “System and method for reducing fiber optic gyroscope color noise,” 7,167,250. U.S. Patent. 2007 Jan 23.
  24. J. Chamoun and M. J. F. Digonnet, “Pseudo-random-bit-sequence phase modulation for reduced errors in a fiber optic gyroscope,” Opt. Lett. 41(24), 5664–5667 (2016).
    [Crossref] [PubMed]
  25. J. Chamoun and M. J. F. Digonnet, “Aircraft-navigation-grade laser-driven FOG with Gaussian-noise phase modulation,” Opt. Lett. 42(8), 1600–1603 (2017).
    [Crossref] [PubMed]

2017 (1)

2016 (3)

2015 (2)

H. Gu, Y. Huan, A. Wang, and J. Luan, “Real-time dynamic simulation of angular velocity and suppression of dead zone in IFOG,” Opt. Rev. 22(1), 39–45 (2015).
[Crossref]

A. M. Kurbatov, “New methods to improve the performance of open and closed loop fiber-optic gyros,” Gyroscopy Navigation 6(3), 207–217 (2015).
[Crossref]

2012 (1)

A. M. Kurbatov and R. A. Kurbatov, “Methods of improving the accuracy of fiber-optic gyros,” Gyroscopy Navigation 3(2), 132–143 (2012).
[Crossref]

2011 (1)

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

2010 (2)

J. Jing, T. Hai-Ting, P. Xiong, and S. Ning-Fang, “Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro,” Chin. Phys. B 19(3), 030701 (2010).
[Crossref]

F. Sun, L. Wang, G. Wang, and G. Liu, “Study on the drift of modulated phase in interference fiber optic gyroscope,” J. Comput. (Taipei) 5, 394–400 (2010).

2009 (1)

O. Çelikel and S. E. San, “Design details and characterization of all digital closed-loop interferometric fiber optic gyroscope with superluminescent light emitting diode,” Opt. Rev. 16(1), 35–43 (2009).
[Crossref]

2008 (1)

C.-J. Chen, “Interferometric Fiber Optic Gyroscope Dead Band Suppression,” Appl. Phys. Express 1, 072501 (2008).
[Crossref]

1967 (1)

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11(5), 159–161 (1967).
[Crossref]

Aleinik, A. S.

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

Arrizon, A.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Çelikel, O.

O. Çelikel and S. E. San, “Design details and characterization of all digital closed-loop interferometric fiber optic gyroscope with superluminescent light emitting diode,” Opt. Rev. 16(1), 35–43 (2009).
[Crossref]

Chamoun, J.

Chen, C.-J.

C.-J. Chen, “Interferometric Fiber Optic Gyroscope Dead Band Suppression,” Appl. Phys. Express 1, 072501 (2008).
[Crossref]

Chen, D.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11(5), 159–161 (1967).
[Crossref]

Choi, W.-S.

Chong, K.-H.

Chong, K.-T.

Deineka, G. B.

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

Digonnet, M. J. F.

Egorov, D. A.

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

Gu, H.

H. Gu, Y. Huan, A. Wang, and J. Luan, “Real-time dynamic simulation of angular velocity and suppression of dead zone in IFOG,” Opt. Rev. 22(1), 39–45 (2015).
[Crossref]

Hai-Ting, T.

J. Jing, T. Hai-Ting, P. Xiong, and S. Ning-Fang, “Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro,” Chin. Phys. B 19(3), 030701 (2010).
[Crossref]

Ho, W.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Huan, Y.

H. Gu, Y. Huan, A. Wang, and J. Luan, “Real-time dynamic simulation of angular velocity and suppression of dead zone in IFOG,” Opt. Rev. 22(1), 39–45 (2015).
[Crossref]

Jing, J.

J. Jing, T. Hai-Ting, P. Xiong, and S. Ning-Fang, “Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro,” Chin. Phys. B 19(3), 030701 (2010).
[Crossref]

Kurbatov, A. M.

A. M. Kurbatov, “New methods to improve the performance of open and closed loop fiber-optic gyros,” Gyroscopy Navigation 6(3), 207–217 (2015).
[Crossref]

A. M. Kurbatov and R. A. Kurbatov, “Methods of improving the accuracy of fiber-optic gyros,” Gyroscopy Navigation 3(2), 132–143 (2012).
[Crossref]

Kurbatov, R. A.

A. M. Kurbatov and R. A. Kurbatov, “Methods of improving the accuracy of fiber-optic gyros,” Gyroscopy Navigation 3(2), 132–143 (2012).
[Crossref]

Liu, G.

F. Sun, L. Wang, G. Wang, and G. Liu, “Study on the drift of modulated phase in interference fiber optic gyroscope,” J. Comput. (Taipei) 5, 394–400 (2010).

Luan, J.

H. Gu, Y. Huan, A. Wang, and J. Luan, “Real-time dynamic simulation of angular velocity and suppression of dead zone in IFOG,” Opt. Rev. 22(1), 39–45 (2015).
[Crossref]

Mead, D.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Mosor, S.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Ning-Fang, S.

J. Jing, T. Hai-Ting, P. Xiong, and S. Ning-Fang, “Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro,” Chin. Phys. B 19(3), 030701 (2010).
[Crossref]

Olekhnovich, R. O.

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

Otto, G. N.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11(5), 159–161 (1967).
[Crossref]

Qiu, T.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Salit, M.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

San, S. E.

O. Çelikel and S. E. San, “Design details and characterization of all digital closed-loop interferometric fiber optic gyroscope with superluminescent light emitting diode,” Opt. Rev. 16(1), 35–43 (2009).
[Crossref]

Sanders, G. A.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Sanders, S. J.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Smiciklas, M.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Strandjord, L. K.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Strigalev, V. E.

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

Sun, F.

F. Sun, L. Wang, G. Wang, and G. Liu, “Study on the drift of modulated phase in interference fiber optic gyroscope,” J. Comput. (Taipei) 5, 394–400 (2010).

Untilov, A. A.

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

Wang, A.

H. Gu, Y. Huan, A. Wang, and J. Luan, “Real-time dynamic simulation of angular velocity and suppression of dead zone in IFOG,” Opt. Rev. 22(1), 39–45 (2015).
[Crossref]

Wang, G.

F. Sun, L. Wang, G. Wang, and G. Liu, “Study on the drift of modulated phase in interference fiber optic gyroscope,” J. Comput. (Taipei) 5, 394–400 (2010).

Wang, L.

F. Sun, L. Wang, G. Wang, and G. Liu, “Study on the drift of modulated phase in interference fiber optic gyroscope,” J. Comput. (Taipei) 5, 394–400 (2010).

Wu, J.

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Xiong, P.

J. Jing, T. Hai-Ting, P. Xiong, and S. Ning-Fang, “Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro,” Chin. Phys. B 19(3), 030701 (2010).
[Crossref]

Zook, J. D.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11(5), 159–161 (1967).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Express (1)

C.-J. Chen, “Interferometric Fiber Optic Gyroscope Dead Band Suppression,” Appl. Phys. Express 1, 072501 (2008).
[Crossref]

Appl. Phys. Lett. (1)

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11(5), 159–161 (1967).
[Crossref]

Chin. Phys. B (1)

J. Jing, T. Hai-Ting, P. Xiong, and S. Ning-Fang, “Electrical crosstalk-coupling measurement and analysis for digital closed loop fibre optic gyro,” Chin. Phys. B 19(3), 030701 (2010).
[Crossref]

Gyroscopy Navigation (3)

A. M. Kurbatov, “New methods to improve the performance of open and closed loop fiber-optic gyros,” Gyroscopy Navigation 6(3), 207–217 (2015).
[Crossref]

A. M. Kurbatov and R. A. Kurbatov, “Methods of improving the accuracy of fiber-optic gyros,” Gyroscopy Navigation 3(2), 132–143 (2012).
[Crossref]

D. A. Egorov, R. O. Olekhnovich, A. A. Untilov, A. S. Aleinik, G. B. Deineka, and V. E. Strigalev, “Study on dead zones of fiber-optic gyros,” Gyroscopy Navigation 2(4), 197–207 (2011).
[Crossref]

J. Comput. (Taipei) (1)

F. Sun, L. Wang, G. Wang, and G. Liu, “Study on the drift of modulated phase in interference fiber optic gyroscope,” J. Comput. (Taipei) 5, 394–400 (2010).

Opt. Lett. (2)

Opt. Rev. (2)

H. Gu, Y. Huan, A. Wang, and J. Luan, “Real-time dynamic simulation of angular velocity and suppression of dead zone in IFOG,” Opt. Rev. 22(1), 39–45 (2015).
[Crossref]

O. Çelikel and S. E. San, “Design details and characterization of all digital closed-loop interferometric fiber optic gyroscope with superluminescent light emitting diode,” Opt. Rev. 16(1), 35–43 (2009).
[Crossref]

Proc. SPIE (1)

G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, S. Mosor, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyro development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
[Crossref]

Other (12)

I. R. Edu, R. Obreja, and T. L. Grigorie, “Current technologies and trends in the development of gyros used in navigation applications-a review,” in Proceedings of the 5th WSEAS International Conference on Communications and Information Technology, (World Scientific and Engineering Academy and Society, 2011), pp. 63–68.

G. A. Pavlath, “Closed-loop fiber optic gyros,” in Fiber Optic Gyros:20th Anniversary Conference, (International Society for Optics and Photonics, 1996), pp. 46–60.
[Crossref]

H. C. Lefèvre, The Fiber-Optic Gyroscope (Artech House, 2014).

J. G. Mark, D. A. Tazartes, and A. Cordova, “Method and apparatus for overcoming cross-coupling in a fiber optic gyroscope employing overmodulation,” 5,682,241. U.S. Patent. 1997 Oct 28.

G. Spahlinger, “Fiber optic Sagnac interferometer with digital phase ramp resetting via correlation-free demodulator control,” 5,123,741. U.S. Patent. 1992 Jun 23.

G. Spahlinger, M. W. Kemmler, M. Ruf, M. A. Ribes, and S. Zimmermann, “Error compensation via signal correlation in high-precision closed-loop fiber optic gyros,” in SPIE’s 1996 International Symposium on Optical Science, Engineering, and Instrumentation, (International Society for Optics and Photonics, 1996), pp. 218–227.
[Crossref]

G. Sanders, R. Dankwort, L. Strandjord, and R. Bergh, “Fiber optic gyroscope with deadband error reduction,” 5,999,304. U.S. Patent. 1999 Dec 7.

P. Lo and R. A. Kovacs, “Fiber optic gyroscope with reduced non-linearity at low angular rates,” 5,684,591. U.S. Patent. 1997 Nov 4.

D. A. Tazartes and G. A. Pavlath, “Automatic gain control for fiber optic gyroscope deterministic control loops,” 7,859,678. U.S. Patent. 2010 Dec 28.

P. A. Ward, “Interferometric fiber optic gyroscope with off-frequency modulation signals,” 7,817,284. U.S. Patent. 2010 Oct 19.

F. Guattari, S. Chouvin, C. Moluçon, and H. Lefèvre, “A simple optical technique to compensate for excess RIN in a fiber-optic gyroscope,” in 2014 DGON Inertial Sensors and Systems, (Institute of Systems Optimization, 2014), pp. 1–14.

C.-J. Chen and C. H. Lange, “System and method for reducing fiber optic gyroscope color noise,” 7,167,250. U.S. Patent. 2007 Jan 23.

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Figures (12)

Fig. 1
Fig. 1 Schematic of a double closed-loop IFOG showing the electrical cross-coupling path.
Fig. 2
Fig. 2 Transfer function plot of an IFOG from phase shift to photodetector response (ignoring the transient spikes at each modulation state transition) with square-wave modulation (SWM) when subjected to (a) rotation rate and (b) increased phase modulator gain. The modulation depth is denoted by φm, and the Sagnac phase shift is denoted by φs. The corresponding demodulation reference is illustrated below each photodetector response. The phase shift undergoes a phase ramp reset at the fourth time interval τ, where τ is the transit time of light through fiber coil.
Fig. 3
Fig. 3 Transfer function plot of an IFOG with the first four-state modulation (FSM) scheme, where the four sequential states are −2π + φm, φm, 2π-φm, and -φm, when subjected to (a) rotation rate and (b) increased phase modulator gain.
Fig. 4
Fig. 4 Transfer function plot of an IFOG with the second FSM scheme, where the four sequential states are φm, −2π + φm, -φm, and 2π-φm, when subjected to (a) rotation rate and (b) increased phase modulator gain.
Fig. 5
Fig. 5 Generation of the bias modulation ∆Φb(t) by the difference between the modulated phase Φb(t) and Φb(t-τ) with the (a) SWM and (b) FSM. The corresponding demodulation sequence D(t) is illustrated below for the purpose of cross-correlation calculation.
Fig. 6
Fig. 6 Transfer function plot of an IFOG with six-state modulation A (SSMA), the six sequential states of which are φm, −2π + φm, φm, -φm, 2π-φm, and -φm, when subjected to (a) rotation rate and (b) increased phase modulator gain.
Fig. 7
Fig. 7 Transfer function plot of an IFOG with six-state modulation B (SSMB), the six sequential states of which are φm, 2π-φm, φm, -φm, −2π + φm, and -φm, when subjected to (a) rotation rate and (b) increased phase modulator gain.
Fig. 8
Fig. 8 Generation of the bias modulation ∆Φb(t) by the difference between the modulated phase Φb(t) and Φb(t-τ) with the (a) SSMA and (b) SSMB. The corresponding demodulation sequence D(t) is illustrated below for the purpose of cross-correlation calculation.
Fig. 9
Fig. 9 Normalized absolute value of the crosstalk-induced bias errors versus modulation depth for different modulation schemes, with the optimal modulation depths highlighted.
Fig. 10
Fig. 10 Normalized bias errors induced by crosstalk versus phase shift of the coupling transfer function for different modulation schemes with different modulation depths.
Fig. 11
Fig. 11 Measured Allan deviation of the IFOG outputs for different modulation schemes with different modulation depths: (a) π/2, (b) 2π/3, (c) 7π/8.
Fig. 12
Fig. 12 Dead band measurement results of the IFOG for different modulation schemes: [(a), (d), (g)] the SWM, [(b), (e), (h)] FSM, and [(c), (f), (i)] SSMB, with different modulation depths: [(a), (b), (c)] π/2, [(d), (e), (f)] 2π/3, and [(g), (h), (i)] 7π/8. The standard deviation, σe, of each IFOG output from the ideal rate is presented at bottom right of each plot.

Tables (1)

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Table 1 Evaluated ARW and bias instability of the IFOG according to the Allan deviation in Fig. 11

Equations (17)

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Δ Φ b (t)= Φ b (t) Φ b (tτ),
Φ b (t)= K pm V b (t),
R ^ ed (k)= 1 N n=0 N1 E[n] D[nk],
φ e = G eq R ^ ed (0),
E SWM [n]= K c φ m / K pm {1,1,1,1,1,1,0,0,0,0,0,0,}
D SWM [n]={1,1,1,1,1,1,1,1,1,1,1,1,}.
φ eSWM = G eq N n=0 N1 E SWM [n] D SWM [n]= G eq K c 2 K pm φ m = K e φ m ,
φ eFSM = G eq N n=0 N1 E FSM [n] D FSM [n]= K e (π φ m ),
E FSM [n]= K c / K pm { φ m π, φ m π, φ m π, φ m , φ m , φ m ,π,π,π,0,0,0,}
D FSM [n]={1,1,1,1,1,1,1,1,1,1,1,1,}
φ eSSMA = G eq N n=0 N1 E SSMA [n] D SSMA [n]= K e ( 2 3 π φ m ),
E SSMA [n]= K c / K pm { φ m , φ m , φ m π, φ m π, φ m , φ m ,0,0,π,π,0,0,}
D SSMA [n]={1,1,1,1,1,1,+1,+1,+1,+1,+1,+1,}
φ eSSMB = G eq N n=0 N1 E SSMB [n] D SSMB [n]= K e ( 2 3 π φ m ),
E SSMB [n]= K c / K pm { φ m , φ m ,π,π, φ m , φ m ,0,0, φ m π, φ m π,0,0,}
D SSMB [n]={1,1,+1,+1,1,1,+1,+1,1,1,+1,+1,}
| φ eSSMA |= 1 3 | φ eFSM | when φ m =π/2 ,

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