Abstract

In a dual-polarization interferometric fiber optic gyroscope (IFOG), polarization non-reciprocity (PN) errors are significant, which degrades the IFOG performance due to the polarization coupling between two orthogonal axes. A dual-polarization IFOG with reverse phase modulation is proposed in which PN phase error can be sufficiently suppressed. In our scheme using a 2-km polarization maintaining coil with open-loop configuration, angle random walk of 4.62×104°/h and a bias instability of 4.6 × 10−4 °/h is demonstrated in detecting the Earth’s rotation rate.

© 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. V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
    [Crossref]
  2. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
    [Crossref]
  3. K. U. Schreiber and J.-P. R. Wells, “Invited review article: Large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84(4), 041101 (2013).
    [Crossref] [PubMed]
  4. R. Bogue, “Recent developments in MEMS sensors: A review of applications, markets and technologies,” Sens. Rev. 33(4), 300–304 (2013).
    [Crossref]
  5. H. C. Lefèvre, The Fiber-Optic Gyroscope, 2nd ed. (Artech house, 2014).
  6. B. M. Barker and R. F. O’Connell, “Derivation of the equations of motion of a gyroscope from the quantum theory of gravitation,” Phys. Rev. D 2(8), 1428–1435 (1970).
    [Crossref]
  7. G. A. Sanders, S. J. Sanders, L. K. Strandjord, T. Qiu, J. Wu, M. Smiciklas, D. Mead, A. Arrizon, W. Ho, and M. Salit, “Fiber optic gyroscope development at Honeywell,” Proc. SPIE 9852, 985207 (2016).
    [Crossref]
  8. J. Napoli and R. Ward, “Two decades of KVH fiber optic gyro technology: From large, low performance FOGs to compact, precise FOGs and FOG-based inertial systems,” in DGON Intertial Sensors and Systems (ISS), (IEEE, 2016), pp. 1–19.
  9. R. A. Bergh, L. Arnesen, and C. Herdman, “Fiber optic gyro development at Fibernetics,” Proc. SPIE 9852, 98520E (2016).
  10. S. Mitani, T. Mizutani, and S. Sakai, “Current status of fiber optic gyro efforts for space applications in Japan,” Proc. SPIE 9852, 985208 (2016).
    [Crossref]
  11. V. Vali and R. W. Shorthill, “Fiber ring interferometer,” Appl. Opt. 15(5), 1099–1100 (1976).
    [Crossref] [PubMed]
  12. I. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. 17(1), 15–22 (1981).
    [Crossref]
  13. S. C. Rashleigh, W. K. Burns, R. P. Moeller, and R. Ulrich, “Polarization holding in birefringent single-mode fibers,” Opt. Lett. 7(1), 40–42 (1982).
    [Crossref] [PubMed]
  14. Z. Wang, Y. Yang, P. Lu, C. Liu, D. Zhao, C. Peng, Z. Zhang, and Z. Li, “Optically compensated polarization reciprocity in interferometric fiber-optic gyroscopes,” Opt. Express 22(5), 4908–4919 (2014).
    [Crossref] [PubMed]
  15. R. A. Bergh, H. C. Lefevre, and H. J. Shaw, “All-single-mode fiber-optic gyroscope,” Opt. Lett. 6(4), 198–200 (1981).
    [Crossref] [PubMed]
  16. Z. Wang, Dual-Polarization Two-Port Fiber-Optic Gyroscope (Springer, 2017).
    [Crossref]
  17. Y. Yang, Z. Wang, and Z. Li, “Optically compensated dual-polarization interferometric fiber-optic gyroscope,” Opt. Lett. 37(14), 2841–2843 (2012).
    [Crossref] [PubMed]
  18. Z. Wang, Y. Yang, P. Lu, R. Luo, Y. Li, D. Zhao, C. Peng, and Z. Li, “Dual-polarization interferometric fiber-optic gyroscope with an ultra-simple configuration,” Opt. Lett. 39(8), 2463–2466 (2014).
    [Crossref] [PubMed]
  19. F. Chen, Y. Li, R. Luo, F. Ben, D. He, C. Peng, and Z. Li, “Cost effective dual-polarization interferometric fiber optic gyroscope with ultra-simple configuration,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), p. JW2A.172.
  20. P. Lu, Z. Wang, Y. Yang, D. Zhao, S. Xiong, Y. Li, C. Peng, and Z. Li, “Multiple optical compensation in interferometric fiber-optic gyroscope for polarization nonreciprocal error suppression,” IEEE Photon. J. 6(5), 7200608 (2014).
  21. R. Luo, Y. Li, S. Deng, D. He, C. Peng, and Z. Li, “Compensation of thermal strain induced polarization nonreciprocity in dual-polarization fiber optic gyroscope,” Opt. Express 25(22), 26747–26759 (2017).
    [Crossref] [PubMed]
  22. R. Luo, Y. Li, S. Deng, C. Peng, and Z. Li, “Effective suppression of residual coherent phase error in a dual-polarization fiber optic gyroscope,” Opt. Lett. 43(4), 815–818 (2018).
    [Crossref] [PubMed]
  23. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
    [Crossref]
  24. B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightw. Technol. 4(9), 1334–1351 (1986).
    [Crossref]
  25. C. C. Cutler, S. A. Newton, and H. J. Shaw, “Limitation of rotation sensing by scattering,” Opt. Lett. 5(11), 488–490 (1980).
    [Crossref] [PubMed]
  26. H. C. Lefevre, R. A. Bergh, and H. J. Shaw, “All-fiber gyroscope with inertial-navigation short-term sensitivity,” Opt. Lett. 7(9), 454–456 (1982).
    [Crossref]
  27. S. L. A. Carrara, B. Y. Kim, and H. J. Shaw, “Bias drift reduction in polarization-maintaining fiber gyroscope,” Opt. Lett. 12(3), 214–216 (1987).
    [Crossref] [PubMed]
  28. J. N. Chamoun and M. J. F. Digonnet, “Noise and bias error due to polarization coupling in a fiber optic gyroscope,” J. Lightw. Technol. 33(13), 2839–2847 (2015).
    [Crossref]
  29. Y. Gronau and M. Tur, “Digital signal processing for an open-loop fiber-optic gyroscope,” Appl. Opt. 34(25), 5849–5853 (1995).
    [Crossref] [PubMed]
  30. A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
    [Crossref]
  31. E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.
  32. F. Bernauer, J. Wassermann, and H. Igel, “Rotational sensors—a comparison of different sensor types,” J. Seism. 16(4), 595–602 (2012).
    [Crossref]
  33. L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
    [Crossref]
  34. Z. Li and M. van der Baan, “Tutorial on rotational seismology and its applications in exploration geophysics seismology for exploration,” Geophysics 82(5), W17–W30 (2017).
    [Crossref]

2018 (2)

R. Luo, Y. Li, S. Deng, C. Peng, and Z. Li, “Effective suppression of residual coherent phase error in a dual-polarization fiber optic gyroscope,” Opt. Lett. 43(4), 815–818 (2018).
[Crossref] [PubMed]

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

2017 (3)

Z. Li and M. van der Baan, “Tutorial on rotational seismology and its applications in exploration geophysics seismology for exploration,” Geophysics 82(5), W17–W30 (2017).
[Crossref]

V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
[Crossref]

R. Luo, Y. Li, S. Deng, D. He, C. Peng, and Z. Li, “Compensation of thermal strain induced polarization nonreciprocity in dual-polarization fiber optic gyroscope,” Opt. Express 25(22), 26747–26759 (2017).
[Crossref] [PubMed]

2016 (4)

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

R. A. Bergh, L. Arnesen, and C. Herdman, “Fiber optic gyro development at Fibernetics,” Proc. SPIE 9852, 98520E (2016).

S. Mitani, T. Mizutani, and S. Sakai, “Current status of fiber optic gyro efforts for space applications in Japan,” Proc. SPIE 9852, 985208 (2016).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

2015 (1)

J. N. Chamoun and M. J. F. Digonnet, “Noise and bias error due to polarization coupling in a fiber optic gyroscope,” J. Lightw. Technol. 33(13), 2839–2847 (2015).
[Crossref]

2014 (3)

2013 (2)

K. U. Schreiber and J.-P. R. Wells, “Invited review article: Large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84(4), 041101 (2013).
[Crossref] [PubMed]

R. Bogue, “Recent developments in MEMS sensors: A review of applications, markets and technologies,” Sens. Rev. 33(4), 300–304 (2013).
[Crossref]

2012 (2)

Y. Yang, Z. Wang, and Z. Li, “Optically compensated dual-polarization interferometric fiber-optic gyroscope,” Opt. Lett. 37(14), 2841–2843 (2012).
[Crossref] [PubMed]

F. Bernauer, J. Wassermann, and H. Igel, “Rotational sensors—a comparison of different sensor types,” J. Seism. 16(4), 595–602 (2012).
[Crossref]

1995 (1)

1987 (1)

1986 (1)

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightw. Technol. 4(9), 1334–1351 (1986).
[Crossref]

1985 (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

1982 (2)

1981 (2)

1980 (1)

1976 (1)

1970 (1)

B. M. Barker and R. F. O’Connell, “Derivation of the equations of motion of a gyroscope from the quantum theory of gravitation,” Phys. Rev. D 2(8), 1428–1435 (1970).
[Crossref]

Arnesen, L.

R. A. Bergh, L. Arnesen, and C. Herdman, “Fiber optic gyro development at Fibernetics,” Proc. SPIE 9852, 98520E (2016).

Arrizon, A.

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

Barker, B. M.

B. M. Barker and R. F. O’Connell, “Derivation of the equations of motion of a gyroscope from the quantum theory of gravitation,” Phys. Rev. D 2(8), 1428–1435 (1970).
[Crossref]

Ben, F.

F. Chen, Y. Li, R. Luo, F. Ben, D. He, C. Peng, and Z. Li, “Cost effective dual-polarization interferometric fiber optic gyroscope with ultra-simple configuration,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), p. JW2A.172.

Bergh, R. A.

Bernauer, F.

F. Bernauer, J. Wassermann, and H. Igel, “Rotational sensors—a comparison of different sensor types,” J. Seism. 16(4), 595–602 (2012).
[Crossref]

Bigueur, A.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Bobra, P.

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Bogue, R.

R. Bogue, “Recent developments in MEMS sensors: A review of applications, markets and technologies,” Sens. Rev. 33(4), 300–304 (2013).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
[Crossref]

Burns, W. K.

Campanella, C. E.

V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
[Crossref]

Carrara, S. L. A.

Chamoun, J. N.

J. N. Chamoun and M. J. F. Digonnet, “Noise and bias error due to polarization coupling in a fiber optic gyroscope,” J. Lightw. Technol. 33(13), 2839–2847 (2015).
[Crossref]

Chen, F.

F. Chen, Y. Li, R. Luo, F. Ben, D. He, C. Peng, and Z. Li, “Cost effective dual-polarization interferometric fiber optic gyroscope with ultra-simple configuration,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), p. JW2A.172.

Chow, W. W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Cuccovillo, A.

V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
[Crossref]

Cutler, C. C.

De Carlo, M.

V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
[Crossref]

de Toldi, E.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Deng, S.

Digonnet, M. J. F.

J. N. Chamoun and M. J. F. Digonnet, “Noise and bias error due to polarization coupling in a fiber optic gyroscope,” J. Lightw. Technol. 33(13), 2839–2847 (2015).
[Crossref]

Ducloux, E.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Gea-Banacloche, J.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Gronau, Y.

Guattari, F.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

He, D.

R. Luo, Y. Li, S. Deng, D. He, C. Peng, and Z. Li, “Compensation of thermal strain induced polarization nonreciprocity in dual-polarization fiber optic gyroscope,” Opt. Express 25(22), 26747–26759 (2017).
[Crossref] [PubMed]

F. Chen, Y. Li, R. Luo, F. Ben, D. He, C. Peng, and Z. Li, “Cost effective dual-polarization interferometric fiber optic gyroscope with ultra-simple configuration,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), p. JW2A.172.

Herdman, C.

R. A. Bergh, L. Arnesen, and C. Herdman, “Fiber optic gyro development at Fibernetics,” Proc. SPIE 9852, 98520E (2016).

Ho, W.

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

Igel, H.

F. Bernauer, J. Wassermann, and H. Igel, “Rotational sensors—a comparison of different sensor types,” J. Seism. 16(4), 595–602 (2012).
[Crossref]

Jankowski, R.

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Jaroszewicz, L. R.

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Kaminow, I.

I. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. 17(1), 15–22 (1981).
[Crossref]

Kim, B. Y.

Kowalski, J. K.

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Krajewski, Z.

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Kurzych, A.

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Lefevre, H. C.

Lefèvre, H.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Lefèvre, H. C.

H. C. Lefèvre, The Fiber-Optic Gyroscope, 2nd ed. (Artech house, 2014).

Li, Y.

R. Luo, Y. Li, S. Deng, C. Peng, and Z. Li, “Effective suppression of residual coherent phase error in a dual-polarization fiber optic gyroscope,” Opt. Lett. 43(4), 815–818 (2018).
[Crossref] [PubMed]

R. Luo, Y. Li, S. Deng, D. He, C. Peng, and Z. Li, “Compensation of thermal strain induced polarization nonreciprocity in dual-polarization fiber optic gyroscope,” Opt. Express 25(22), 26747–26759 (2017).
[Crossref] [PubMed]

P. Lu, Z. Wang, Y. Yang, D. Zhao, S. Xiong, Y. Li, C. Peng, and Z. Li, “Multiple optical compensation in interferometric fiber-optic gyroscope for polarization nonreciprocal error suppression,” IEEE Photon. J. 6(5), 7200608 (2014).

Z. Wang, Y. Yang, P. Lu, R. Luo, Y. Li, D. Zhao, C. Peng, and Z. Li, “Dual-polarization interferometric fiber-optic gyroscope with an ultra-simple configuration,” Opt. Lett. 39(8), 2463–2466 (2014).
[Crossref] [PubMed]

F. Chen, Y. Li, R. Luo, F. Ben, D. He, C. Peng, and Z. Li, “Cost effective dual-polarization interferometric fiber optic gyroscope with ultra-simple configuration,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), p. JW2A.172.

Li, Z.

R. Luo, Y. Li, S. Deng, C. Peng, and Z. Li, “Effective suppression of residual coherent phase error in a dual-polarization fiber optic gyroscope,” Opt. Lett. 43(4), 815–818 (2018).
[Crossref] [PubMed]

R. Luo, Y. Li, S. Deng, D. He, C. Peng, and Z. Li, “Compensation of thermal strain induced polarization nonreciprocity in dual-polarization fiber optic gyroscope,” Opt. Express 25(22), 26747–26759 (2017).
[Crossref] [PubMed]

Z. Li and M. van der Baan, “Tutorial on rotational seismology and its applications in exploration geophysics seismology for exploration,” Geophysics 82(5), W17–W30 (2017).
[Crossref]

P. Lu, Z. Wang, Y. Yang, D. Zhao, S. Xiong, Y. Li, C. Peng, and Z. Li, “Multiple optical compensation in interferometric fiber-optic gyroscope for polarization nonreciprocal error suppression,” IEEE Photon. J. 6(5), 7200608 (2014).

Z. Wang, Y. Yang, P. Lu, R. Luo, Y. Li, D. Zhao, C. Peng, and Z. Li, “Dual-polarization interferometric fiber-optic gyroscope with an ultra-simple configuration,” Opt. Lett. 39(8), 2463–2466 (2014).
[Crossref] [PubMed]

Z. Wang, Y. Yang, P. Lu, C. Liu, D. Zhao, C. Peng, Z. Zhang, and Z. Li, “Optically compensated polarization reciprocity in interferometric fiber-optic gyroscopes,” Opt. Express 22(5), 4908–4919 (2014).
[Crossref] [PubMed]

Y. Yang, Z. Wang, and Z. Li, “Optically compensated dual-polarization interferometric fiber-optic gyroscope,” Opt. Lett. 37(14), 2841–2843 (2012).
[Crossref] [PubMed]

F. Chen, Y. Li, R. Luo, F. Ben, D. He, C. Peng, and Z. Li, “Cost effective dual-polarization interferometric fiber optic gyroscope with ultra-simple configuration,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), p. JW2A.172.

Liu, C.

Lu, P.

Luo, R.

Marc, P.

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Mead, D.

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

Mitani, S.

S. Mitani, T. Mizutani, and S. Sakai, “Current status of fiber optic gyro efforts for space applications in Japan,” Proc. SPIE 9852, 985208 (2016).
[Crossref]

Mizutani, T.

S. Mitani, T. Mizutani, and S. Sakai, “Current status of fiber optic gyro efforts for space applications in Japan,” Proc. SPIE 9852, 985208 (2016).
[Crossref]

Moeller, R. P.

Moluçon, C.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Moslehi, B.

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightw. Technol. 4(9), 1334–1351 (1986).
[Crossref]

Napoli, J.

J. Napoli and R. Ward, “Two decades of KVH fiber optic gyro technology: From large, low performance FOGs to compact, precise FOGs and FOG-based inertial systems,” in DGON Intertial Sensors and Systems (ISS), (IEEE, 2016), pp. 1–19.

Newton, S. A.

O’Connell, R. F.

B. M. Barker and R. F. O’Connell, “Derivation of the equations of motion of a gyroscope from the quantum theory of gravitation,” Phys. Rev. D 2(8), 1428–1435 (1970).
[Crossref]

Passaro, V. M. N.

V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
[Crossref]

Pedrotti, L. M.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Peng, C.

Ponceau, D.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Qiu, T.

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

Rashleigh, S. C.

Sakai, S.

S. Mitani, T. Mizutani, and S. Sakai, “Current status of fiber optic gyro efforts for space applications in Japan,” Proc. SPIE 9852, 985208 (2016).
[Crossref]

Sakowicz, B.

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Salit, M.

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

Sanders, G. A.

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

Sanders, V. E.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Schleich, W.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Schreiber, K. U.

K. U. Schreiber and J.-P. R. Wells, “Invited review article: Large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84(4), 041101 (2013).
[Crossref] [PubMed]

Schreiber, U.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Scully, M. O.

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Shaw, H. J.

Shorthill, R. W.

Smiciklas, M.

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

Steib, A.

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Strandjord, L. K.

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

Tur, M.

Ulrich, R.

Vaiani, L.

V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
[Crossref]

Vali, V.

van der Baan, M.

Z. Li and M. van der Baan, “Tutorial on rotational seismology and its applications in exploration geophysics seismology for exploration,” Geophysics 82(5), W17–W30 (2017).
[Crossref]

Wang, Z.

Ward, R.

J. Napoli and R. Ward, “Two decades of KVH fiber optic gyro technology: From large, low performance FOGs to compact, precise FOGs and FOG-based inertial systems,” in DGON Intertial Sensors and Systems (ISS), (IEEE, 2016), pp. 1–19.

Wassermann, J.

F. Bernauer, J. Wassermann, and H. Igel, “Rotational sensors—a comparison of different sensor types,” J. Seism. 16(4), 595–602 (2012).
[Crossref]

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

Wells, J.-P. R.

K. U. Schreiber and J.-P. R. Wells, “Invited review article: Large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84(4), 041101 (2013).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
[Crossref]

Wu, J.

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

Xiong, S.

P. Lu, Z. Wang, Y. Yang, D. Zhao, S. Xiong, Y. Li, C. Peng, and Z. Li, “Multiple optical compensation in interferometric fiber-optic gyroscope for polarization nonreciprocal error suppression,” IEEE Photon. J. 6(5), 7200608 (2014).

Yang, Y.

Zembaty, Z.

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Zhang, Z.

Zhao, D.

Appl. Opt. (2)

Geophysics (1)

Z. Li and M. van der Baan, “Tutorial on rotational seismology and its applications in exploration geophysics seismology for exploration,” Geophysics 82(5), W17–W30 (2017).
[Crossref]

IEEE J. Quantum Electron. (1)

I. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. 17(1), 15–22 (1981).
[Crossref]

IEEE Photon. J. (1)

P. Lu, Z. Wang, Y. Yang, D. Zhao, S. Xiong, Y. Li, C. Peng, and Z. Li, “Multiple optical compensation in interferometric fiber-optic gyroscope for polarization nonreciprocal error suppression,” IEEE Photon. J. 6(5), 7200608 (2014).

J. Lightw. Technol. (3)

A. Kurzych, L. R. Jaroszewicz, Z. Krajewski, B. Sakowicz, J. K. Kowalski, and P. Marć, “Fibre-optic Sagnac interferometer in a FOG minimum configuration as instrumental challenge for rotational seismology,” J. Lightw. Technol. 36(4), 879–884 (2018).
[Crossref]

B. Moslehi, “Analysis of optical phase noise in fiber-optic systems employing a laser source with arbitrary coherence time,” J. Lightw. Technol. 4(9), 1334–1351 (1986).
[Crossref]

J. N. Chamoun and M. J. F. Digonnet, “Noise and bias error due to polarization coupling in a fiber optic gyroscope,” J. Lightw. Technol. 33(13), 2839–2847 (2015).
[Crossref]

J. Seism. (1)

F. Bernauer, J. Wassermann, and H. Igel, “Rotational sensors—a comparison of different sensor types,” J. Seism. 16(4), 595–602 (2012).
[Crossref]

Opt. Express (2)

Opt. Lett. (8)

Phys. Rev. D (1)

B. M. Barker and R. F. O’Connell, “Derivation of the equations of motion of a gyroscope from the quantum theory of gravitation,” Phys. Rev. D 2(8), 1428–1435 (1970).
[Crossref]

Proc. SPIE (3)

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

R. A. Bergh, L. Arnesen, and C. Herdman, “Fiber optic gyro development at Fibernetics,” Proc. SPIE 9852, 98520E (2016).

S. Mitani, T. Mizutani, and S. Sakai, “Current status of fiber optic gyro efforts for space applications in Japan,” Proc. SPIE 9852, 985208 (2016).
[Crossref]

Rev. Mod. Phys. (1)

W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E. Sanders, W. Schleich, and M. O. Scully, “The ring laser gyro,” Rev. Mod. Phys. 57(1), 61–104 (1985).
[Crossref]

Rev. Sci. Instrum. (1)

K. U. Schreiber and J.-P. R. Wells, “Invited review article: Large ring lasers for rotation sensing,” Rev. Sci. Instrum. 84(4), 041101 (2013).
[Crossref] [PubMed]

Sens. Rev. (1)

R. Bogue, “Recent developments in MEMS sensors: A review of applications, markets and technologies,” Sens. Rev. 33(4), 300–304 (2013).
[Crossref]

Sensors (2)

V. M. N. Passaro, A. Cuccovillo, L. Vaiani, M. De Carlo, and C. E. Campanella, “Gyroscope technology and applications: A review in the industrial perspective,” Sensors 17(10), 2284 (2017).
[Crossref]

L. R. Jaroszewicz, A. Kurzych, Z. Krajewski, P. Marć, J. K. Kowalski, P. Bobra, Z. Zembaty, B. Sakowicz, and R. Jankowski, “Review of the usefulness of various rotational seismometers with laboratory results of fibre-optic ones tested for engineering applications,” Sensors 16(12), 2161 (2016).
[Crossref]

Other (6)

E. de Toldi, H. Lefèvre, F. Guattari, A. Bigueur, A. Steib, D. Ponceau, C. Moluçon, E. Ducloux, J. Wassermann, and U. Schreiber, “First steps for a Giant FOG: Searching for the limits,” in DGON Inertial Sensors and Systems (ISS), (IEEE, 2017), pp. 1–14.

F. Chen, Y. Li, R. Luo, F. Ben, D. He, C. Peng, and Z. Li, “Cost effective dual-polarization interferometric fiber optic gyroscope with ultra-simple configuration,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2018), p. JW2A.172.

H. C. Lefèvre, The Fiber-Optic Gyroscope, 2nd ed. (Artech house, 2014).

J. Napoli and R. Ward, “Two decades of KVH fiber optic gyro technology: From large, low performance FOGs to compact, precise FOGs and FOG-based inertial systems,” in DGON Intertial Sensors and Systems (ISS), (IEEE, 2016), pp. 1–19.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
[Crossref]

Z. Wang, Dual-Polarization Two-Port Fiber-Optic Gyroscope (Springer, 2017).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 (a) Structure of dual-polarization IFOG. (b) An equivalent model of a MIOC.
Fig. 2
Fig. 2 The dual-polarization-intensity-type error for different Δθm, this error with/without compensation and the amplitude-type error are illustrated.
Fig. 3
Fig. 3 Experimental results of dual-polarization IFOG in reverse phase modulation. (a) 12-hour and (b) half-hour test data of each channel and summed-up output.
Fig. 4
Fig. 4 ADEV curves for comparison of results of single polarization scheme, PD 1 and the sum outputs using in-phase and reverse modulation of dual-polarization scheme.

Tables (1)

Tables Icon

Table 1 Comparison of angle random walk (ARW) and bias instability (BI).

Equations (23)

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E 1 in = [ E 1 x E 1 y ] exp { j [ ω t + θ 1 ( t ) + θ 10 ] }
E 2 in = [ E 2 x E 2 y ] exp { j [ ω t + θ 2 ( t ) + θ 20 ] }
P i = 2 2 [ η i 0 0 ε i ] , ( i = 1 , 2 )
ϕ mi ± = ± 1 2 ϕ 0 sin ( 2 π f m t + θ mi ) , ( i = 1 , 2 )
M m = [ cos ( θ m ) sin ( θ m ) sin ( θ m ) cos ( θ m ) ] [ exp ( j β x L m ) 0 0 exp ( j β y L m ) ] , ( m = A , B , C , D )
C cw = n = 1 M K ( κ n ) exp ( j ϕ s / 2 ) = [ C 1 cw C 2 cw C 3 cw C 4 cw ] exp ( j ϕ s / 2 )
C ccw = n = M 1 K ( κ n * ) exp ( j ϕ s / 2 ) = [ C 1 ccw C 2 ccw C 3 ccw C 4 ccw ] exp ( j ϕ s / 2 )
K ( κ n ) = 1 4 B [ ( B + Δ β ) exp ( j β 1 z ) + ( B Δ β ) exp ( j β 2 z ) j κ 12 [ exp ( j β 1 z ) exp ( j β 2 z ) ] j κ 21 [ exp ( j β 1 z ) exp ( j β 2 z ) ] ( B Δ β ) exp ( j β 1 z ) + ( B + Δ β ) exp ( j β 2 z ) ]
E PD 1 = P 1 { M b T C cw M a P 1 exp [ ϕ m 1 + ( t ) + ϕ m 1 ( t τ g ) ] + M a T C ccw M b P 1 exp [ ϕ m 1 ( t ) + ϕ m 1 + ( t τ g ) ] } E 1 + P 1 { M b T C cw M c P 2 exp [ ϕ m 2 + ( t ) + ϕ m 1 ( t τ g ) ] + M a T C ccw M d P 2 exp [ ϕ m 2 ( t ) + ϕ m 1 + ( t τ g ) ] } E 2
E PD 2 = P 2 { M d T C cw M a P 1 exp [ ϕ m 1 + ( t ) + ϕ m 2 ( t τ g ) ] + M c T C ccw M b P 1 exp [ ϕ m 1 ( t ) + ϕ m 2 + ( t τ g ) ] } E 1 + P 2 { M d T C cw M c P 2 exp [ ϕ m 2 + ( t ) + ϕ m 2 ( t τ g ) ] + M c T C ccw M d P 2 exp [ ϕ m 2 ( t ) + ϕ m 2 + ( t τ g ) ] } E 2
E PD 1 ( t ) = E 1 x 1 x cw ( t ) + E 1 x 1 x ccw ( t ) + E 1 y 1 x cw ( t ) + E 1 y 1 x ccw ( t ) + E 2 y 1 x cw ( t ) + E 2 y 1 x ccw ( t )
E PD 2 ( t ) = E 2 y 2 y cw ( t ) + E 2 y 2 y cw ( t ) + E 2 x 2 y ccw ( t ) + E 2 x 2 y cw ( t ) + E 1 x 2 y cw ( t ) + E 1 x 2 y ccw ( t )
I PD 1 = D . C . + I p 1 + I a 1 + I c 1 + I di 1 + I h 1
I PD 2 = D . C . + I p 2 + I a 2 + I c 2 + I di 2 + I h 2
I di 1 ( t ) = E 2 y 1 x cw ( t ) E 2 y 1 x ccw * ( t ) + E 2 y 1 x cw * ( t ) E 2 y 1 x ccw ( t ) = K 1 cos [ ϕ s + ϕ err 1 + ϕ mod 1 ( t ) ]
I di 2 ( t ) = E 1 x 2 y cw ( t ) E 1 x 2 y ccw * ( t ) + E 1 x 2 y cw * ( t ) + E 1 x 2 y ccw ( t ) = K 2 cos [ ϕ s + ϕ err 2 + ϕ mod 2 ( t ) ]
K 1 E 1 x 2 | C 2 cw C 3 ccw | γ d ( r ) , K 2 E 2 y 2 | C 2 cw C 3 ccw | γ d ( r ) , γ d ( r ) = L pc / L
ϕ mod 1 ( t ) = ϕ m 2 + ( t ) + ϕ m 1 ( t τ ) ϕ m 2 ( t ) ϕ m 1 + ( t τ )
ϕ mod 2 ( t ) = ϕ m 1 + ( t ) + ϕ m 2 ( t τ ) ϕ m 1 ( t ) ϕ m 2 + ( t τ )
ϕ mod ϕ mod 1 ( t ) = ϕ mod 2 ( t ) = 2 ϕ 0 cos Δ θ m 2 sin ( 2 π f m t + θ m 1 + θ m 2 2 )
ϕ di 1 , 2 ; dem = arcsin [ J 1 ( 2 ϕ 0 cos Δ θ m 2 ) sin ( ϕ s + ϕ err 1 , 2 ) / J 1 ( 2 ϕ 0 ) ]
I PD 1 = D . C . + I 1 cos [ ϕ s + ϕ r e 1 + ϕ m ( t ) ]
I PD 2 = D . C . + I 2 cos [ ϕ s + ϕ r e 2 ϕ m ( t ) ]

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