gyroscopyГироскопия и навигацияGiroskopiya i Navigatsiya / Gyroscopy and Navigation0869-70352075-0927AO «Концерн «ЦНИИ «Электроприбор»ERALEWgyroscopy-72Research ArticleСтатьиСовременное состояние оптических резонаторных гироскоповState-of-the-Art Optical Resonator GyroscopesВенедиктовВ. Ю.VenediktovV. Yu.

Венедиктов Владимир Юрьевич. Доктор физико-математических наук, профессор кафедры ЛИНС 

С.-Петербург 

St. Petersburg 

ФилатовЮ. В.FilatovYu. V.

Филатов Юрий Владимирович. Доктор технических наук, профессор, заведующий кафедрой ЛИНС. Действительный член международной общественной организации «Академия навигации и управления движением»

С.-Петербург 

St. Petersburg 

ШалымовЕ. В.ShalymovE. V.

Шалымов Егор Вадимович. Кандидат технических наук, доцент кафедры ЛИНС 

С.-Петербург 

St. Petersburg 

СПбГЭТУ «ЛЭТИ»РоссияSt. Petersburg State Electrotechnical University LETIRussian Federation2023200520253114557Copyright © Венедиктов В.Ю., Филатов Ю.В., Шалымов Е.В., 20252025Венедиктов В.Ю., Филатов Ю.В., Шалымов Е.В.Venediktov V.Y., Filatov Y.V., Shalymov E.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.gyroscopy.ru/jour/article/view/72

В статье рассматривается современное состояние оптических резонаторных гироскопов. Излагается идея, положенная в основу этого типа гироскопов. Описываются подходы к их конструкции и способу определения угловой скорости. При этом главное внимание уделено исторически первому и наиболее популярному на сегодняшний день подходу, который базируется на применении фазово-модуляционной спектроскопии и перестраиваемого лазера. Анализируется также альтернативный подход, основанный на использовании низкокогерентных источников излучения. Представлен обзор наиболее распространенных источников погрешности измерений и методов борьбы с ними. Минимальный случайный дрейф пока был достигнут за счет применения волоконных кольцевых резонаторов: 2,0 °/ч при диаметре кольца 60 мм при времени интегрирования 1 с и 1,23 °/ч при 5 с; при диаметре 120 мм достигнуто 0,37 °/ч при времени интегрирования 1 с и 0,06 °/ч при 370 с. Рассмотрены причины, в силу которых на сегодняшний день затруднено коммерческое освоение оптических резонаторных гироскопов.

The paper discusses the modern state of optical resonator gyroscopes. The basic concept of this type of gyros is described. The main approaches to their design and the method for angular rate measurement are considered, with the main focus made on the pioneer and most popular approach based on the use of phase modulation spectroscopy and a tuned laser. An alternative approach based on low-coherent sources of light is also analyzed. The main sources of measurement errors and the methods to overcome them are considered. The best value of random drift has been so far achieved using fiber ring resonators: 2.0 deg/h with the ring diameter 60 mm and the integration time 1 s, and 1.23 deg/h in 5 s; with the diameter 120 mm, 0.37 deg/h has been achieved with the integration time 1 s and 0.06 deg/h with 370 s. The reasons that currently hinder the commercial development of optical resonator gyros are studied.

эффект Саньякаоптический резонаторный гироскопрезонаторный волоконно-оптический гироскопинтегрально-оптический гироскопмикрооптический гироскоппассивный кольцевой резонаторSagnac effectoptical resonator gyroresonant fiber-optic gyrointegrated optical gyromicro-optic gyropassive ring resonatorРабота выполнена при поддержке Министерства науки и высшего образования Российской Федерации (грант № FSEE-2020-0005).ReferencesMalykin, G.B., The Sagnac effect: correct and incorrect explanations, Phys. Usp.,2000, vol. 43, no.12, p. 1229.Malykin, G.B., The Sagnac effect: correct and incorrect explanations, Phys. Usp.,2000, vol. 43, no.12, p. 1229.Sagnac, G., L’ether lumineux demontre par l’effet du vent relatif d’ether dans un interferometre en rotation uniforme, Comptes Rendus, 1913, vol. 157, pp. 708–710.Sagnac, G., L’ether lumineux demontre par l’effet du vent relatif d’ether dans un interferometre en rotation uniforme, Comptes Rendus, 1913, vol. 157, pp. 708–710.Ezekiel, S., Balsamo, S.R., Passive ring resonator laser gyroscope, Appl. Phys. Lett., 1977, vol. 30, no. 9, p. 478.Ezekiel, S., Balsamo, S.R., Passive ring resonator laser gyroscope, Appl. Phys. Lett., 1977, vol. 30, no. 9, p. 478.Sanders, G.A., Prentiss, M.G., Ezekiel, S., Passive ring resonator method for sensitive inertial rotation measurements in geophysics and relativity, Opt. Lett., 1981, vol. 6, no. 11, pp. 569–571.Sanders, G.A., Prentiss, M.G., Ezekiel, S., Passive ring resonator method for sensitive inertial rotation measurements in geophysics and relativity, Opt. Lett., 1981, vol. 6, no. 11, pp. 569–571.Meyer, R.E., Ezekiel, S., Stowe, D.W., Tekippe, V.J., Passive fiber-optic ring resonator for rotation sensing, Opt. Lett., 1983, vol. 8, no. 12, pp. 644–646.Meyer, R.E., Ezekiel, S., Stowe, D.W., Tekippe, V.J., Passive fiber-optic ring resonator for rotation sensing, Opt. Lett., 1983, vol. 8, no. 12, pp. 644–646.Ohtsu, M., Araki, S., Using a 1.5-μm DFB InGaAsP laser in a passive ring cavity-type fiber gyroscope, Appl. Opt., 1987, vol. 26, no. 3, pp. 464–470.Ohtsu, M., Araki, S., Using a 1.5-μm DFB InGaAsP laser in a passive ring cavity-type fiber gyroscope, Appl. Opt., 1987, vol. 26, no. 3, pp. 464–470.Ezekiel, S., Cole, J.A., Harrison, J., Sanders, G., Passive cavity optical rotation sensor, Proc. Soc. Photo-Opt. Instrum. Eng., 1978, vol. 157, p. 68.Ezekiel, S., Cole, J.A., Harrison, J., Sanders, G., Passive cavity optical rotation sensor, Proc. Soc. Photo-Opt. Instrum. Eng., 1978, vol. 157, p. 68.Lefevre, H.C., The Fiber Optic Gyroscope, Boston, MA, USA, Artech House, 2014, pp. 15–18.Lefevre, H.C., The Fiber Optic Gyroscope, Boston, MA, USA, Artech House, 2014, pp. 15–18.Armenise, M.N., Ciminelli, C., Dell’olio, F., Advances In Gyroscope Technologies, Springer Heidelberg Dordrecht London New York, Springer, 2010, pp. 29–49.Armenise, M.N., Ciminelli, C., Dell’olio, F., Advances In Gyroscope Technologies, Springer Heidelberg Dordrecht London New York, Springer, 2010, pp. 29–49.Shupe, D.M., Fiber resonator gyroscope: sensitivity and thermal nonreciprocity, Appl. Opt., 1981, vol. 20, pp. 286–289.Shupe, D.M., Fiber resonator gyroscope: sensitivity and thermal nonreciprocity, Appl. Opt., 1981, vol. 20, pp. 286–289.Carroll, R., Coccoli, C.D., Cardarelli, D., Coate, G.T., The Passive Resonator Fiber Optic Gyro and Comparison to the Interferometer Fiber Gyro, Proc. SPIE, 1987, vol. 0719, pp. 169–177.Carroll, R., Coccoli, C.D., Cardarelli, D., Coate, G.T., The Passive Resonator Fiber Optic Gyro and Comparison to the Interferometer Fiber Gyro, Proc. SPIE, 1987, vol. 0719, pp. 169–177.Hotate, K., Kikuchi, Y., Analysis of the thermo-optically induced bias drift in resonator fiber optic gyro, Proc. SPIE, 2001, vol. 4204, pp. 81–88.Hotate, K., Kikuchi, Y., Analysis of the thermo-optically induced bias drift in resonator fiber optic gyro, Proc. SPIE, 2001, vol. 4204, pp. 81–88.Haavisto, J.R., Thin-Film Waveguides For Inertial Sensors, Proc. SPIE, 1983, vol. 0412, pp. 221–228.Haavisto, J.R., Thin-Film Waveguides For Inertial Sensors, Proc. SPIE, 1983, vol. 0412, pp. 221–228.Rosenthal, A.H., Regenerative Circulatory Multiple-Beam Interferometry for the Study of Light-Propagation Effects, J. Opt. Soc. Am., 1962, vol. 52, no. 10, pp. 1143–1148.Rosenthal, A.H., Regenerative Circulatory Multiple-Beam Interferometry for the Study of Light-Propagation Effects, J. Opt. Soc. Am., 1962, vol. 52, no. 10, pp. 1143–1148.Iwatsuki, K., Hotate, K., Higashiguchi, M., Effect of Rayleigh backscattering in an optical passive ring-resonator gyro, Appl Opt., 1984, vol. 23, no. 21, pp. 3916–3924.Iwatsuki, K., Hotate, K., Higashiguchi, M., Effect of Rayleigh backscattering in an optical passive ring-resonator gyro, Appl Opt., 1984, vol. 23, no. 21, pp. 3916–3924.Ma, H., He, Z., Hotate, K., Reduction of Backscattering Induced Noise by Carrier Suppression in Waveguide-Type Optical Ring Resonator Gyro, J. Lightwave Technol.,2011, vol. 29, no. 1, pp. 85–90.Ma, H., He, Z., Hotate, K., Reduction of Backscattering Induced Noise by Carrier Suppression in Waveguide-Type Optical Ring Resonator Gyro, J. Lightwave Technol.,2011, vol. 29, no. 1, pp. 85–90.Wang, J., Feng, L., Wang, Q., Wang, X., Jiao, H., Reduction of Angle Random Walk by In-Phase Triangular Phase Modulation Technique for Resonator Integrated Optic Gyro, Opt. Express, 2016, vol. 24, no. 5, pp. 5463–5468.Wang, J., Feng, L., Wang, Q., Wang, X., Jiao, H., Reduction of Angle Random Walk by In-Phase Triangular Phase Modulation Technique for Resonator Integrated Optic Gyro, Opt. Express, 2016, vol. 24, no. 5, pp. 5463–5468.Zhu, J., Liu, W., Pan, Z., Tao, Y., Yin, S., Tang, J., Liu, J., Combined Frequency-Locking Technology of a Digital Integrated Resonator Optic Gyroscope with a Phase-Modulated Feedback Loop, Appl. Opt., 2019, vol. 58, no. 36, pp. 9914–9920.Zhu, J., Liu, W., Pan, Z., Tao, Y., Yin, S., Tang, J., Liu, J., Combined Frequency-Locking Technology of a Digital Integrated Resonator Optic Gyroscope with a Phase-Modulated Feedback Loop, Appl. Opt., 2019, vol. 58, no. 36, pp. 9914–9920.Mao, H., Ma H., Jin, Z., Resonator micro-optic gyroscope based on the double phase modulation technique, CLEO/QELS: 2010 Laser Science to Photonic Applications, San Jose, CA, USA, 2010, pp. JWA52.Mao, H., Ma H., Jin, Z., Resonator micro-optic gyroscope based on the double phase modulation technique, CLEO/QELS: 2010 Laser Science to Photonic Applications, San Jose, CA, USA, 2010, pp. JWA52.Wang, Q., Feng, L., Li, H., Wang, X., Jia, Y., Liu, D., Enhanced differential detection technique for the resonator integrated optic gyro, Opt Lett., 2018, vol. 43, no. 12, pp. 2941–2944.Wang, Q., Feng, L., Li, H., Wang, X., Jia, Y., Liu, D., Enhanced differential detection technique for the resonator integrated optic gyro, Opt Lett., 2018, vol. 43, no. 12, pp. 2941–2944.Liu, L., Liu, S., Hu, J., Ma, H., Jin, Z., Resonant fiber optic gyroscope using a reciprocal modulation and double demodulation technique,Opt Express., 2022, vol. 30, no. 7, pp. 12192–12203.Liu, L., Liu, S., Hu, J., Ma, H., Jin, Z., Resonant fiber optic gyroscope using a reciprocal modulation and double demodulation technique,Opt Express., 2022, vol. 30, no. 7, pp. 12192–12203.Zhang, Y., Feng, L., Li, H., Jiao, H., Liu, N., Zhang, C., Resonant fiber optic gyroscope with three-frequency differential detection by sideband locking, Opt. Express, 2020, vol. 28, no. 6, pp. 8423–8435.Zhang, Y., Feng, L., Li, H., Jiao, H., Liu, N., Zhang, C., Resonant fiber optic gyroscope with three-frequency differential detection by sideband locking, Opt. Express, 2020, vol. 28, no. 6, pp. 8423–8435.Liu, L., Li, H., Liu, S., Jin, Z., Ma, H., Suppressing backscattering noise of a resonant fiber optic gyroscope using coherent detection, Appl. Opt., 2022, vol. 61, no. 15, pp. 4421–4428.Liu, L., Li, H., Liu, S., Jin, Z., Ma, H., Suppressing backscattering noise of a resonant fiber optic gyroscope using coherent detection, Appl. Opt., 2022, vol. 61, no. 15, pp. 4421–4428.Benser, E., Sanders, G., Smickilas, M., Wu, J., Strandjord, L., Development and evaluation of a navigation grade resonator fiber optic gyroscope, 2015 DGON Inertial Sensors and Systems Symposium (ISS), Karlsruhe, Germany, 2015, pp. 1–11.Benser, E., Sanders, G., Smickilas, M., Wu, J., Strandjord, L., Development and evaluation of a navigation grade resonator fiber optic gyroscope, 2015 DGON Inertial Sensors and Systems Symposium (ISS), Karlsruhe, Germany, 2015, pp. 1–11.Strandjord, L.K., Qiu, T., Salit, M., Narayanan, C., Smiciklas, M., Wu, J., Sanders, G.A., Improved Bias Performance in Resonator Fiber Optic Gyros using a Novel Modulation Method for Error Suppression, in 26th International Conference on Optical Fiber Sensors, OSA Technical Digest (Optica Publishing Group, 2018), 2018, p. ThD3.Strandjord, L.K., Qiu, T., Salit, M., Narayanan, C., Smiciklas, M., Wu, J., Sanders, G.A., Improved Bias Performance in Resonator Fiber Optic Gyros using a Novel Modulation Method for Error Suppression, in 26th International Conference on Optical Fiber Sensors, OSA Technical Digest (Optica Publishing Group, 2018), 2018, p. ThD3.Niu, J., Liu, W., Pan, Z., Tao, Y., Zhou, Y., Xing, E., Tang, J., Liu, J., The Noise Suppression in Resonant Micro Optic Gyroscopes Based on Dual Light Sources Method, Optics Communications, 2021, vol. 488, p. 126839.Niu, J., Liu, W., Pan, Z., Tao, Y., Zhou, Y., Xing, E., Tang, J., Liu, J., The Noise Suppression in Resonant Micro Optic Gyroscopes Based on Dual Light Sources Method, Optics Communications, 2021, vol. 488, p. 126839.Shen, H., Chen, K., Zou, K., Gong, Y., Bi, R., Shu, X., A Hollow-Core Photonic-Crystal Fiber-Optic Gyroscope Based on a Parallel Double-Ring Resonator, Sensors (Basel), 2021, vol. 21, no. 24, p. 8317.Shen, H., Chen, K., Zou, K., Gong, Y., Bi, R., Shu, X., A Hollow-Core Photonic-Crystal Fiber-Optic Gyroscope Based on a Parallel Double-Ring Resonator, Sensors (Basel), 2021, vol. 21, no. 24, p. 8317.Iwatsuki, K., Hotate, K., Higashiguchi, M., Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring-resonator gyro. Appl Opt. 1986, vol. 25, no. 15, pp. 2606–2612.Iwatsuki, K., Hotate, K., Higashiguchi, M., Eigenstate of polarization in a fiber ring resonator and its effect in an optical passive ring-resonator gyro. Appl Opt. 1986, vol. 25, no. 15, pp. 2606–2612.Strandjord, L.K., Sanders, G.A., Resonator fiber optic gyro employing a polarization-rotating resonator, Proc. SPIE, 1992, vol. 1585, pp. 163–172.Strandjord, L.K., Sanders, G.A., Resonator fiber optic gyro employing a polarization-rotating resonator, Proc. SPIE, 1992, vol. 1585, pp. 163–172.Ma, H., Yan, Y., Chen, Y., Jin, Z., Improving Long-Term Stability of a Resonant Micro-Optic Gyro by Reducing Polarization Fluctuation, IEEE Photonics Journal, 2012, vol. 4, no. 6, pp. 2372–2381.Ma, H., Yan, Y., Chen, Y., Jin, Z., Improving Long-Term Stability of a Resonant Micro-Optic Gyro by Reducing Polarization Fluctuation, IEEE Photonics Journal, 2012, vol. 4, no. 6, pp. 2372–2381.Ma, H., Chen, Z., Yang, Z., Yu, X., Jin, Z., Polarization-induced noise in resonator fiber optic gyro, Appl. Opt., 2012, vol. 51, no. 28, pp. 6708–6717.Ma, H., Chen, Z., Yang, Z., Yu, X., Jin, Z., Polarization-induced noise in resonator fiber optic gyro, Appl. Opt., 2012, vol. 51, no. 28, pp. 6708–6717.Bobbili, P.R., Nayak, J., Pinnoji, P.D., Reddy, D.V.R.K., Parameter optimization analysis to minimize the polarization error in a localized thermal tunable fiber ring resonator gyro, Appl. Opt., 2016, vol. 55, no. 8, pp. 1996–2001.Bobbili, P.R., Nayak, J., Pinnoji, P.D., Reddy, D.V.R.K., Parameter optimization analysis to minimize the polarization error in a localized thermal tunable fiber ring resonator gyro, Appl. Opt., 2016, vol. 55, no. 8, pp. 1996–2001.Ma, H., Zhang, J., Chen, Z., Jin, Z., Tilted Waveguide Gratings and Implications for Optical Waveguide-Ring Resonator, J. Lightwave Technol., 2015, vol. 33, no. 19, pp. 4176–4183.Ma, H., Zhang, J., Chen, Z., Jin, Z., Tilted Waveguide Gratings and Implications for Optical Waveguide-Ring Resonator, J. Lightwave Technol., 2015, vol. 33, no. 19, pp. 4176–4183.Yan, Y., Ma, H., Jin, Z., Reducing polarization-fluctuation induced drift in resonant fiber optic gyro by using single-polarization fiber, Opt. Express, 2015, vol. 23, no. 3, pp. 2002–2009.Yan, Y., Ma, H., Jin, Z., Reducing polarization-fluctuation induced drift in resonant fiber optic gyro by using single-polarization fiber, Opt. Express, 2015, vol. 23, no. 3, pp. 2002–2009.Feng, C., Zhang, D., Zhang, Y., Qing, C., Ma, H., Li, H., Feng, L., Resonant integrated optical gyroscope based on Si3N4 waveguide ring resonator, Opt. Express, 2021, vol. 29, no. 26, pp. 43875–43884.Feng, C., Zhang, D., Zhang, Y., Qing, C., Ma, H., Li, H., Feng, L., Resonant integrated optical gyroscope based on Si3N4 waveguide ring resonator, Opt. Express, 2021, vol. 29, no. 26, pp. 43875–43884.Feng, C., Zhang, Y., Ma, H., Li, H., Feng, L., Improving long-term temperature bias stability of an integrated optical gyroscope employing a Si3N4 resonator, Photon. Res., 2022, vol. 10, no. 7, pp. 1661–1668.Feng, C., Zhang, Y., Ma, H., Li, H., Feng, L., Improving long-term temperature bias stability of an integrated optical gyroscope employing a Si3N4 resonator, Photon. Res., 2022, vol. 10, no. 7, pp. 1661–1668.Liu, S., Lin, Y., Jin, X., Ma, H., Jin, Z., Polarization error in resonant micro-optic gyroscope with different waveguide-type ring resonator structures, Appl. Opt., 2022, vol. 61, no. 15, pp. 4287–4295.Liu, S., Lin, Y., Jin, X., Ma, H., Jin, Z., Polarization error in resonant micro-optic gyroscope with different waveguide-type ring resonator structures, Appl. Opt., 2022, vol. 61, no. 15, pp. 4287–4295.Iwatsuki, X., Hotate, K., Higashiguchi, M., Kerr Effect in Optical Passive Ring-Resonator Gyros, Optical Fiber Sensors (Optica Publishing Group, 1985), 1985, p. ThGG13.Iwatsuki, X., Hotate, K., Higashiguchi, M., Kerr Effect in Optical Passive Ring-Resonator Gyros, Optical Fiber Sensors (Optica Publishing Group, 1985), 1985, p. ThGG13.Takiguchi, K., Hotate, K., Method to reduce the optical kerr-effect-induced bias in an optical passive ring-resonator gyro, IEEE Photonics Technol. Lett., 1992, vol. 4, no. 2, pp. 203–206.Takiguchi, K., Hotate, K., Method to reduce the optical kerr-effect-induced bias in an optical passive ring-resonator gyro, IEEE Photonics Technol. Lett., 1992, vol. 4, no. 2, pp. 203–206.Li, X., Zhang, J., Ma, H., Jin, Z., Test and Analysis of the Optical Kerr-Effect in Resonant Micro-Optic Gyros, IEEE Photonics Journal, 2014, vol. 6, no. 5, pp. 1–7.Li, X., Zhang, J., Ma, H., Jin, Z., Test and Analysis of the Optical Kerr-Effect in Resonant Micro-Optic Gyros, IEEE Photonics Journal, 2014, vol. 6, no. 5, pp. 1–7.Ma, H., Li, X., Zhang, G., Jin, Z., Reduction of optical Kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique, Appl Opt., 2014, vol. 53, no. 16, pp. 3465–3472.Ma, H., Li, X., Zhang, G., Jin, Z., Reduction of optical Kerr-effect induced error in a resonant micro-optic gyro by light-intensity feedback technique, Appl Opt., 2014, vol. 53, no. 16, pp. 3465–3472.Yin, S., Liu, W., Xing, E., Pan, Z., Tao, Y., Zhu, J., Tang, J., Tang, J., Suppression of laser intensity fluctuation in resonator optical gyro by a simple light intensity feedback technique, Optical Engineering, 2020, vol. 59, no. 3, p. 036112.Yin, S., Liu, W., Xing, E., Pan, Z., Tao, Y., Zhu, J., Tang, J., Tang, J., Suppression of laser intensity fluctuation in resonator optical gyro by a simple light intensity feedback technique, Optical Engineering, 2020, vol. 59, no. 3, p. 036112.Niu, J., Liu, W., Pan, Z., Tao, Y., Zhou, Y., Xing, E., Liu, J., Tang, J., Reducing backscattering and the Kerr noise in a resonant micro-optic gyro using two independent lasers, Appl. Opt., 2021, vol. 60, no. 10, pp. 2761–2766.Niu, J., Liu, W., Pan, Z., Tao, Y., Zhou, Y., Xing, E., Liu, J., Tang, J., Reducing backscattering and the Kerr noise in a resonant micro-optic gyro using two independent lasers, Appl. Opt., 2021, vol. 60, no. 10, pp. 2761–2766.Iwatsuki, K., Hotate, K., Higashiguchi, M., Kerr effect in an optical passive ring-resonator gyro, Journal of Lightwave Technology, 1986, vol. 4, no. 6, pp. 645–651.Iwatsuki, K., Hotate, K., Higashiguchi, M., Kerr effect in an optical passive ring-resonator gyro, Journal of Lightwave Technology, 1986, vol. 4, no. 6, pp. 645–651.Ying, D., Ye, K., Wang, Z., Xie, T., Jin, Z., A harmonic subtraction technique to suppress intensity modulation induced Kerr effect drift in a closed-loop RFOG, Optics Communications, 2018, vol. 426, pp. 562–569.Ying, D., Ye, K., Wang, Z., Xie, T., Jin, Z., A harmonic subtraction technique to suppress intensity modulation induced Kerr effect drift in a closed-loop RFOG, Optics Communications, 2018, vol. 426, pp. 562–569.Yu, X., Liao, Y., Zhang, M., Shi, Q., Yu, Y., Li, D., Kerr effect in a passive optical ring-resonator gyroscope using a hollow-core photonic-band fiber, Proc. SPIE, 2008, vol. 6830, p. 683024.Yu, X., Liao, Y., Zhang, M., Shi, Q., Yu, Y., Li, D., Kerr effect in a passive optical ring-resonator gyroscope using a hollow-core photonic-band fiber, Proc. SPIE, 2008, vol. 6830, p. 683024.Ying, D., Demokan, M.S., Zhang, X., Jin, W., Analysis of Kerr effect in resonator fiber optic gyros with triangular wave phase modulation, Appl. Opt., 2010, vol. 49, no. 3, pp. 529–535.Ying, D., Demokan, M.S., Zhang, X., Jin, W., Analysis of Kerr effect in resonator fiber optic gyros with triangular wave phase modulation, Appl. Opt., 2010, vol. 49, no. 3, pp. 529–535.Filatov, Y.V., Kukaev, A.S., Shalymov, E.V., Venediktov, V.Yu., Investigation of a ring confocal resonator sample designed to work as an optical resonator gyroscope sensitive element, Proc. SPIE, 2022, vol. 12274, pp. 1227417.Filatov, Y.V., Kukaev, A.S., Shalymov, E.V., Venediktov, V.Yu., Investigation of a ring confocal resonator sample designed to work as an optical resonator gyroscope sensitive element, Proc. SPIE, 2022, vol. 12274, pp. 1227417.Ito, T., Hotate, K., Closed-loop operation in the resonator fiber optic gyro using faraday effect with a twisted single-mode-fiber resonator, in Fiber Optic Gyros: 20th Anniversary Conference, 1996, vol. 2837, pp. 260–271.Ito, T., Hotate, K., Closed-loop operation in the resonator fiber optic gyro using faraday effect with a twisted single-mode-fiber resonator, in Fiber Optic Gyros: 20th Anniversary Conference, 1996, vol. 2837, pp. 260–271.Wang, Z., Wang, G., Gao, W., Cheng, Y., Suppression of Kerr-effect induced error in resonant fiber optic gyro by a resonator with spun fiber, Opt. Express, 2021, vol. 29, no. 13, pp. 19631–19642.Wang, Z., Wang, G., Gao, W., Cheng, Y., Suppression of Kerr-effect induced error in resonant fiber optic gyro by a resonator with spun fiber, Opt. Express, 2021, vol. 29, no. 13, pp. 19631–19642.Li, H., Lin, Y., Liu, L., Ma, H., Jin, Z., Signal processing improvement of passive resonant fiber optic gyroscope using a reciprocal modulation-demodulation technique, Opt. Express, 2020, vol. 28, no. 12, pp. 18103–18111.Li, H., Lin, Y., Liu, L., Ma, H., Jin, Z., Signal processing improvement of passive resonant fiber optic gyroscope using a reciprocal modulation-demodulation technique, Opt. Express, 2020, vol. 28, no. 12, pp. 18103–18111.Zhang, X., Ma, H., Jin, Z., Ding, C., Open-loop operation experiments in a resonator fiber-optic gyro using the phase modulation spectroscopy technique, Appl. Opt. 2006, vol. 45, no. 31, pp. 7961–7965.Zhang, X., Ma, H., Jin, Z., Ding, C., Open-loop operation experiments in a resonator fiber-optic gyro using the phase modulation spectroscopy technique, Appl. Opt. 2006, vol. 45, no. 31, pp. 7961–7965.Jin, Z., Yu, X., Ma, H., Closed-loop resonant fiber optic gyro with an improved digital serrodyne modulation, Optics express, 2013, vol. 21, no. 22, pp. 26578–26588.Jin, Z., Yu, X., Ma, H., Closed-loop resonant fiber optic gyro with an improved digital serrodyne modulation, Optics express, 2013, vol. 21, no. 22, pp. 26578–26588.Ma, H., Zhang, J., Wang, L., Jin, Z., Double closed-loop resonant micro optic gyro using hybrid digital phase modulation, Opt. Express, 2015, vol. 23, no. 12, pp. 15088–15097.Ma, H., Zhang, J., Wang, L., Jin, Z., Double closed-loop resonant micro optic gyro using hybrid digital phase modulation, Opt. Express, 2015, vol. 23, no. 12, pp. 15088–15097.Ying, D., Ma, H., Jin, Z., Resonator fiber optic gyro using the triangle wave phase modulation technique, Optics Communications, 2008, vol. 281, no. 4, pp. 580–586.Ying, D., Ma, H., Jin, Z., Resonator fiber optic gyro using the triangle wave phase modulation technique, Optics Communications, 2008, vol. 281, no. 4, pp. 580–586.Ma, H., Chen, Y., Li, M., Jin, Z., Transient response of a resonator fiber optic gyro with triangular wave phase modulation, Appl. Opt., 2010, vol. 49, no. 32, pp. 6253–6263.Ma, H., Chen, Y., Li, M., Jin, Z., Transient response of a resonator fiber optic gyro with triangular wave phase modulation, Appl. Opt., 2010, vol. 49, no. 32, pp. 6253–6263.Jiang, Z., Hu, Z., Kang, W., Wang, J., Fu, C., Residual intensity modulation-induced error in resonator fiber optic gyroscopes with triangular phase modulation, Appl. Opt., 2019, vol. 58, no. 27, pp. 7597–7602.Jiang, Z., Hu, Z., Kang, W., Wang, J., Fu, C., Residual intensity modulation-induced error in resonator fiber optic gyroscopes with triangular phase modulation, Appl. Opt., 2019, vol. 58, no. 27, pp. 7597–7602.Ma, H., Yu, X., Jin, Z., Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers, Opt. Lett., 2012, vol. 37, no. 16, pp. 3342–3344.Ma, H., Yu, X., Jin, Z., Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator integrating in-line polarizers, Opt. Lett., 2012, vol. 37, no. 16, pp. 3342–3344.Wang, J., Feng, L., Tang, Y., Zhi, Y., Resonator integrated optic gyro employing trapezoidal phase modulation technique, Opt. Lett., vol. 40, no. 2, pp. 155–158.Wang, J., Feng, L., Tang, Y., Zhi, Y., Resonator integrated optic gyro employing trapezoidal phase modulation technique, Opt. Lett., vol. 40, no. 2, pp. 155–158.Hotate, K., Harumoto, M., Resonator Fiber Optic Gyro using Digital Serrodyne Modulation, in Optical Fiber Sensors (Optica Publishing Group, 1996), pp. Tu35.Hotate, K., Harumoto, M., Resonator Fiber Optic Gyro using Digital Serrodyne Modulation, in Optical Fiber Sensors (Optica Publishing Group, 1996), pp. Tu35.Mao, H., Ma, H., Jin, Z., Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique, Opt. Express, 2011, vol. 19, no. 5, pp. 4632–4643.Mao, H., Ma, H., Jin, Z., Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique, Opt. Express, 2011, vol. 19, no. 5, pp. 4632–4643.Feng, L., Lei, M., Liu, H., Zhi, Y., Wang, J., Suppression of backreflection noise in a resonator integrated optic gyro by hybrid phase-modulation technology, Appl. Opt., 2013, vol. 52, no. 8, pp. 1668–1675.Feng, L., Lei, M., Liu, H., Zhi, Y., Wang, J., Suppression of backreflection noise in a resonator integrated optic gyro by hybrid phase-modulation technology, Appl. Opt., 2013, vol. 52, no. 8, pp. 1668–1675.Hotate, K., Takiguchi, K., Hirose, A. Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro, IEEE Photonics Technology Letters, 1990, vol. 2, no. 1, pp. 75–77.Hotate, K., Takiguchi, K., Hirose, A. Adjustment-free method to eliminate the noise induced by the backscattering in an optical passive ring-resonator gyro, IEEE Photonics Technology Letters, 1990, vol. 2, no. 1, pp. 75–77.Jiao, H., Feng, L., Zhang, C., Liu, N., Zhang, Y., Ma, H., Design of low-crosstalk polarizing resonator and homologous multi-frequency differential detection for hollow-core photonic-crystal fiber optic gyro, Opt. Express, 2019, vol. 27, no. 14, pp. 19536–19547.Jiao, H., Feng, L., Zhang, C., Liu, N., Zhang, Y., Ma, H., Design of low-crosstalk polarizing resonator and homologous multi-frequency differential detection for hollow-core photonic-crystal fiber optic gyro, Opt. Express, 2019, vol. 27, no. 14, pp. 19536–19547.Jiao, H., Wang, T., Gao, H., Feng, L., Ma, H., Dynamic Free-Spectral-Range Measurement for Fiber Resonator Based on Digital-Heterodyne Optical Phase-Locked Loop, Optics and Photonics J., 2021, vol. 11, pp. 332–340.Jiao, H., Wang, T., Gao, H., Feng, L., Ma, H., Dynamic Free-Spectral-Range Measurement for Fiber Resonator Based on Digital-Heterodyne Optical Phase-Locked Loop, Optics and Photonics J., 2021, vol. 11, pp. 332–340.Ma, H., Zhang, X., Jin, Z., Ding,C., Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique, Optical Engineering, 2006, vol. 45, no. 8, p. 080506.Ma, H., Zhang, X., Jin, Z., Ding,C., Waveguide-type optical passive ring resonator gyro using phase modulation spectroscopy technique, Optical Engineering, 2006, vol. 45, no. 8, p. 080506.Duan, R., Feng, L., Jiao,H., Wang, X., Research on Reducing the Influence of Laser Frequency Noise on Resonator Optical Gyro, IEEE Sensors Journal, 2017, vol. 17, no. 8, pp. 2422–2427.Duan, R., Feng, L., Jiao,H., Wang, X., Research on Reducing the Influence of Laser Frequency Noise on Resonator Optical Gyro, IEEE Sensors Journal, 2017, vol. 17, no. 8, pp. 2422–2427.Filatov, Y.V., Kukaev, A.S., Nikolaeva, N.A., Shalymov, E.V., Venediktov, V.Y., Method for measuring angular velocity using a passive ring resonator and a Mach-Zehnder modulator, Optical Engineering, 2020, vol. 59, no. 7, p. 074106.Filatov, Y.V., Kukaev, A.S., Nikolaeva, N.A., Shalymov, E.V., Venediktov, V.Y., Method for measuring angular velocity using a passive ring resonator and a Mach-Zehnder modulator, Optical Engineering, 2020, vol. 59, no. 7, p. 074106.Filatov, Y.V., Gilev, D.G., Goncharova, P.S., Krishtop, V.V., Kukaev, A.S., Ovchinnikov, K.A., Sevryugin, A.A., Shalymov, E.V., Venediktov, V.Y., Experimental Investigation of an Optical Resonator Gyroscope with a Mach–Zehnder Modulator and Its Sensitive Elements, Photonics, 2023, vol. 10, no. 1, p. 4.Filatov, Y.V., Gilev, D.G., Goncharova, P.S., Krishtop, V.V., Kukaev, A.S., Ovchinnikov, K.A., Sevryugin, A.A., Shalymov, E.V., Venediktov, V.Y., Experimental Investigation of an Optical Resonator Gyroscope with a Mach–Zehnder Modulator and Its Sensitive Elements, Photonics, 2023, vol. 10, no. 1, p. 4.Geng, J., Yang, L., Zhao, S., Zhang, Y., Resonant micro-optical gyro based on self-injection locking, Opt. Express, 2020, vol. 28, no. 22, pp. 32907–32915.Geng, J., Yang, L., Zhao, S., Zhang, Y., Resonant micro-optical gyro based on self-injection locking, Opt. Express, 2020, vol. 28, no. 22, pp. 32907–32915.Li, Y., Liu, W., Pan, Z., Tao, Y., Zhang, W., Xing, T., Xing, E., Zhou, Y., Tang, J., Liu, J., Self-injection locking technique for resonant micro-optical gyroscope, Optical Engineering, 2022, vol. 60, no. 1, p. 014103.Li, Y., Liu, W., Pan, Z., Tao, Y., Zhang, W., Xing, T., Xing, E., Zhou, Y., Tang, J., Liu, J., Self-injection locking technique for resonant micro-optical gyroscope, Optical Engineering, 2022, vol. 60, no. 1, p. 014103.Новиков М.А., Иванов В.В. Оптический гироскоп с пассивным кольцевым резонатором. Российское агентство по патентам и товарным знакам. Патент на изобретение № 2124185. Приоритет от 13.05.97.Новиков М.А., Иванов В.В. Оптический гироскоп с пассивным кольцевым резонатором. Российское агентство по патентам и товарным знакам. Патент на изобретение № 2124185. Приоритет от 13.05.97.Новиков М.А., Иванов В.В. Резонансная кольцевая интерферометрия на некогерентном свете // Письма в ЖТФ. 1998.Т. 24, № 17. С. 24–29.Новиков М.А., Иванов В.В. Резонансная кольцевая интерферометрия на некогерентном свете // Письма в ЖТФ. 1998.Т. 24, № 17. С. 24–29.Иванов В.В., Новиков М.А., Геликонов В.М. Наблюдение эффекта Саньяка в кольцевом резонансном интерферометре с низкокогерентным источником света // Квантовая электроника. 2000. Т. 30. № 2. С.119–124.Иванов В.В., Новиков М.А., Геликонов В.М. Наблюдение эффекта Саньяка в кольцевом резонансном интерферометре с низкокогерентным источником света // Квантовая электроника. 2000. Т. 30. № 2. С.119–124.Zhao, S., Liu, Q., Liu, Y., Ma, H., He, Z., Navigation-grade resonant fiber-optic gyroscope using ultra-simple white-light multibeam interferometry, Photon. Res., 2022, vol. 10, no. 2, pp. 542–549.Zhao, S., Liu, Q., Liu, Y., Ma, H., He, Z., Navigation-grade resonant fiber-optic gyroscope using ultra-simple white-light multibeam interferometry, Photon. Res., 2022, vol. 10, no. 2, pp. 542–549.Zhao, S., Liu, Q., Ma, H., He, Z., White-light-driven resonant fiber-optic gyro based on round trip filtering scheme, Opt. Lett., 2022, vol. 47, no. 5, pp. 1137–1140.Zhao, S., Liu, Q., Ma, H., He, Z., White-light-driven resonant fiber-optic gyro based on round trip filtering scheme, Opt. Lett., 2022, vol. 47, no. 5, pp. 1137–1140.Liu, S., Liu, L., Hu, J., Liu, Q., Ma, H., He, Z., Reduction of relative intensity noise in a broadband source-driven RFOG using a high-frequency modulation technique, Opt. Lett., 2022, vol. 47, no. 19, pp. 5100–5103.Liu, S., Liu, L., Hu, J., Liu, Q., Ma, H., He, Z., Reduction of relative intensity noise in a broadband source-driven RFOG using a high-frequency modulation technique, Opt. Lett., 2022, vol. 47, no. 19, pp. 5100–5103.Ovchinnikov, K.A., Gilev, D.G., Krishtop, V.V., Volyntsev, A.B., Maximenko, V.A., Garkushin, A.A., Filatov, Y.V., Kukaev, A.S., Sevryugin, A.A., Shalymov, E.V., Venediktova, A.V., Venediktov, V.Y., A Prototype for a Passive Resonant Interferometric Fiber Optic Gyroscope with a 3 × 3 Directional Coupler, Sensors, 2023, vol. 23, no. 3, p. 1319.Ovchinnikov, K.A., Gilev, D.G., Krishtop, V.V., Volyntsev, A.B., Maximenko, V.A., Garkushin, A.A., Filatov, Y.V., Kukaev, A.S., Sevryugin, A.A., Shalymov, E.V., Venediktova, A.V., Venediktov, V.Y., A Prototype for a Passive Resonant Interferometric Fiber Optic Gyroscope with a 3 × 3 Directional Coupler, Sensors, 2023, vol. 23, no. 3, p. 1319.

The authors declare that there are no conflicts of interest present.