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Suppression of backscattering-induced noise in a resonator optic gyro by the dual-frequency modulation method
Optics Communications 459 (2020) 124766
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Suppression of backscattering-induced noise in a resonator optic gyro by the dual-frequency modulation method Haoyu Wang, Wenyao Liu ∗, Ziwen Pan, Yu Tao, Jian Niu, Jun Tang, Jun Liu ∗ National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China Key Laboratory of Instrumentation Science and Dynamic Measurement Ministry of Education, North University of China, Taiyuan 030051, China
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Keywords: Backscattering noise Resonant optical gyroscope Dual-frequency modulation High frequency modulation Carrier rejection ratio
ABSTRACT Backscattering noise is one of the main noises affecting the accuracy of resonant optical gyroscope (ROG) systems. A method of suppressing backscattering noise in a ROG is demonstrated using a dual frequency modulation technique. On the premise of obtaining the Sagnac frequency difference, the frequency interval between the forward and backward beams is increased. Among them, high frequency modulation is used in the frequency-locked circuit, low-frequency modulation is used in the output path and the modulated optical components have a certain frequency difference. Firstly, the frequency difference between the clockwise and counterclockwise optical paths is increased by high and low frequency modulation to increase the carrier rejection ratio, and the noise generated by backscattering and signal light is suppressed. Then, bandpass filtering is used to eliminate the noise caused by the backscattering itself. Through theoretical analysis and experiment, the feasibility and effectiveness of the scheme are verified. The method effectively improves the output precision of the gyro, and the final output of the gyroscope reaches 0.0054◦ /s (10 s integration time).
1. Introduction Currently, resonant optical gyro based on the Sagnac effect is the most promising angular velocity sensors in inertial navigation. Due to the characteristics of integration, light weight, vibration resistance, and impact resistance, ROG is expected to become the next generation optical gyro [1–4]. The core sensing element of the resonant microoptical gyroscope is the silicon-based SiO2 optical waveguide resonator, which determines the sensitivity of the gyroscope [5,6]. However, due to the manufacturing problems of the resonator itself, the backscattering noise is difficult to ignore, which is even considered to be the most important problem affecting sensitivity [7,8], and many methods have been proposed for suppressing backscattering noise. In recent years, many methods have been developed to suppress backscattering noise. Binary phase shift keying (B-PSK) is used to reduce the influence of the interference phase between the input light wave signal and the backscattered light wave signal, but the bandwidth of the thermal optical (TO) phase modulation is narrow. In order to effectively utilize the narrow bandwidth of the modulator, an electrical signal processing scheme and a frequency compensated modulation waveform are proposed [9,10]. Sinusoidal phase modulation techniques is widely used in resonant fiber optic gyros to suppress backscattering noise [11,12]. Different frequency modulation of CW and CCW [13–15] is a simple and feasible method and is currently used more, but there is still interference between the backscattered
beam and the main propagating beam. The double phase modulation based on ROG adding an additional phase modulators to the traditional single-phase modulation, which can obviously reduce the effects of backscatter noise by providing additional carrier suppression [16,17]. Later, Feng et al. proposed a sideband locking technique based on PDH technology [18], which improves the carrier rejection ratio by utilizing the filtering characteristics of the resonant cavity [19]. The sideband locking technique utilizes a resonant cavity as a bandpass filter, and the carriers will be filtered by the cavity itself, which is beneficial for suppressing noise caused by backscattering. Although the sideband locking technique has significant advantages in suppressing back-scattering noise when the two signals have a specific phase difference, the linear region of the demodulation curve is deformed [20]. Simultaneously, the three-laser scheme is proposed by Honeywell International to increase the frequency difference between the frequency components, and the error signal generated by the interference is filtered to achieve the purpose of suppressing backscattering noise. But there are three lasers in this structure, which will increase the cost and complexity of the prototype [21,22]. Therefore, a better method needs to be proposed to take advantage of sideband modulation to achieve the best effect of suppressing backscattering noise. In this paper, a new method for suppressing backscattering noise in a ROG using dual-frequency modulation technique is proposed, which distinguishes the traditional dual-channel low-frequency modulation
∗ Corresponding authors. E-mail addresses: [email protected] (W. Liu), [email protected] (J. Liu).
https://doi.org/10.1016/j.optcom.2019.124766 Received 19 July 2019; Received in revised form 24 September 2019; Accepted 14 October 2019 Available online 6 December 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
H. Wang, W. Liu, Z. Pan et al.
Optics Communications 459 (2020) 124766
Fig. 1. (a) Resonant optical gyro based on high and low-frequency modulation to suppress backscattering noise; (b) Illustration of backscattering mechanism in the cavity.
or dual-channel high-frequency modulation method. The frequencylocked channel and output channel light wave is modulated by highfrequency modulation and low-frequency, respectively. Firstly, through spectrum comparison and formula simulation, it is found that the highfrequency carrier suppression ratio is higher. Secondly, the test system was built for carrier suppression ratio experiments and final output testing of the gyro system. Finally, better results are obtained than traditional systems. The scheme not only exerts the advantages of the sideband locking technique but also avoids the influence of phase fluctuation on the output path, and makes the gyro output more stable.
Fig. 2. Relationship between slope of demodulation curve and modulation frequency.
where 𝐸0 is the electric field amplitude, 𝑤 is the angular frequency, 𝑓0 is the center frequency of the laser, 𝜙0 is the initial phase of the light wave, 𝑀 is the modulation depth, 𝛺 is the phase modulation frequency. According to Eq. (1), the single-frequency beam modulated by the phase modulator is divided into a series of equally spaced frequency components, including the carrier with angular frequency 𝑤 and the sidebands with angular frequencies, such as 𝑤 ± 𝛺, 𝑤 ± 2𝛺, 𝑤 ± 3𝛺 …, and 𝛺 = 2𝜋𝑓 [16]. Therefore, we can equivalently treat the beam after phase modulation as a beam of light incident on the WRR at a series of different frequencies. When CW and CCW use low frequency modulation with different frequencies, CW and CCW still have a common spectral component 𝑤0 . There is still interference between the backscattered beam and the main propagating beam. Although this method of modulation and filtering can suppress the influence of the backscattered light itself in the gyro signal, the interference noise generated by the backscattered light and the signal cannot be completely eliminated. The amplitude of the interference noise is related to the product of the Bessel function. The noise could be suppressed by selecting the appropriate modulation coefficient M to make the Bessel function amplitude equal to 0. In fact, there is no way to completely suppress it to zero. Therefore, a new method to improve the carrier suppression ratio needs to be found, and the backscattering noise is better suppressed [21]. In general, the frequencies of CW and CCW under highfrequency modulation are outside the passband range by using the frequency selection characteristics of the resonator. However, due to the small difference of the modulation frequency between the two beams, the interference under some other frequency components cannot be completely suppressed. Therefore, a dual-frequency modulation and demodulation scheme be proposed as shown in Fig. 1. According to the experiment and simulation, as shown in Fig. 2, the demodulation curve of the high-frequency modulation has a high slope, so the optical path under the high-frequency modulation is used as the lock frequency path. The high frequency modulation output circuit is selected as a frequency lock circuit to improve the sensitivity and frequency locking accuracy of the system. Selecting the low-frequency path as the output path can find the optimal shift frequency by adjusting the low-frequency modulation frequency, thereby backscatter noise of the system can be better suppressed and the bias stability of the system can be improved. In this mode of modulation, the frequency difference between the two beams is increased. There are no or less similar spectral components in the optical path and the carrier suppression ratio is further improved. The beam of low frequency modulation
2. Principles and simulation In order to suppress backscattering noise, the phase modulator is typically fused at the input of the clockwise (CW) and counterclockwise (CCW) optical paths, an beam is marked by a modulation of a different frequency applied by the phase modulator. Based on the Pound–Drever–Hall (PDH) technique, this paper proposes a scheme to increase the frequency separation between the CW and CCW beams. In this way, the carrier suppression ratio is further improved and the backscattered noise is reduced. The schematic of dual-frequency modulation ROG structure is shown in Fig. 1(a). The center wavelength of the laser is about 1550 nm and the line width is about 5 kHz. The Y-branch waveguide LiNbO3 phase modulator is used for sinusoidal phase modulation of CW and CCW light waves. SG1 and SG2 are signal generators that generate sine waves. The modulation frequency of CCW and CW is 𝑓𝐶𝐶𝑊 (high frequency) and 𝑓𝐶𝑊 (low frequency) respectively. The frequency of CCW light wave is shifted by an acousto-optic frequency shifter (AOFS) to generate a frequency difference to reduce backscatter noise. The CCW and CW light waves from the waveguide ring resonator (WRR) are detected by the photodetectors PD1 and PD2, respectively. The first-order harmonic demodulation signal of the CCW direction is obtained by the digital lock-in amplifier LIA1, and the center frequency of the laser is locked to the first sideband frequency of the CCW direction through the feedback servo loop. At the same time, the output of LIA2 is used as the gyro output to measure the angular velocity. Generally, scattering is caused by the unevenness of the medium or scatterer in the SiO2 waveguide cavity. It should be noted that the partially scattered light of the forward propagation is reciprocal and does not cause any parasitic effects. However, the backward backscattering is randomly distributed and has a certain negative impact on the gyro output. Taking the CW direction as an example, the backscattered light of CCW direction interferes with the CW signal light in the SiO2 waveguide cavity as shown in Fig. 1(b), thereby the light intensity detected by the detector will be affected. After passing through the phase modulator, the incident beam is modulated by the phase modulator, the electric field 𝐸in (𝑡) can be described as: [ ] 𝐸in (𝑡) = 𝐸0 exp 𝑖(2𝜋𝑓0 𝑡 + 𝜙0 ) +∞ ∑ = 𝐸0 exp[𝑖(𝑤𝑡 + 𝑀 sin 𝛺𝑡)] = 𝐽𝑛 (𝑀) exp[𝑖(𝛺𝑡)] (1) 𝑛=−∞ [ ≈ 𝐸0 𝐽0 (𝑀) exp(𝑖𝑤𝑡) + 𝐽1 (𝑀) exp[𝑖(𝑤 + 𝛺)𝑡] − 𝐽1 (𝑀) ] × exp[𝑖(𝑤 + 𝛺)𝑡] 2
H. Wang, W. Liu, Z. Pan et al.
Optics Communications 459 (2020) 124766
Fig. 3. Spectrum analysis diagram of high and low frequency modulated gyro system . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) +∞ √ ∑ 𝐼𝐵2 = 2 𝑃 𝐸02
is frequency-shifted by AOFS to overlap the linear portions of the demodulation curves of CW and CCW. In this scheme, backscattering noise is suppressed to the greatest extent and the output stability of gyro is greatly improved. The Lorentz curve shown in Fig. 3 is used to represent the mode frequency characteristics of the cavity. The blue and orange solid lines indicate the frequency distribution modulated by high frequency and low frequency, respectively. The solid red line indicates the spectrum distribution of the beam modulated by low frequency after frequency shift of AOFS. The difference value of 𝑤0 ± 𝑘 ∙ 𝑓𝐶𝐶𝑊 and 𝑤0 + 𝑓𝑠ℎ𝑖𝑓 𝑡 ± 𝑛 ∙ 𝑓𝐶𝑊 (𝑘, 𝑛 represents the order of the harmonic components, both integers, respectively) determines whether the two optical paths have overlapping carrier components after the 𝑛th harmonic. For instance, we set k to be 1 because 𝑓𝐶𝐶𝑊 ≫ 𝑓𝑠ℎ𝑖𝑓 𝑡 ± 𝑛 ∙ 𝑓𝐶𝑊 . When 𝑤0 + 𝑓𝐶𝐶𝑊 = 𝑤0 + 𝑓𝑠ℎ𝑖𝑓 𝑡 + 𝑛 ∙ 𝑓𝐶𝑊 , the amplitude of the harmonic component after the 20th order is very small. As shown in Fig. 4, the amplitude of the harmonic component decreases with increasing number of stages. In this work, since 𝑓𝐶𝑊 and 𝑓𝐶𝐶𝑊 are the levels of kHz and MHz, respectively, 𝑛 > 100, the amplitude of the 𝑛th harmonic component is close to zero, and the interference to the high frequency harmonic component can be ignored accordingly. In the experiment, when 𝑤0 + 𝑓𝐶𝐶𝑊 ≠ 𝑤0 +𝑓𝑠ℎ𝑖𝑓 𝑡 +𝑛∙𝑓𝐶𝑊 , the two spectral components are completely staggered. Theoretically, the same spectral components do not exist in the two optical paths, and the backscattering noise is suppressed to the maximum extent. In the resonant cavity, taking the CW direction as an example, the backscattering coefficient is 𝑃 . According to the light field superposition principle, the total light field of CW direction should be the superposition of the main beam and the backscattered beam:
+∞ ∑ +∞ ∑
|𝐽𝑛 |2 + 2𝐸 2 |𝐽𝑛−𝑘 𝐽𝑛 |2 ∙ cos(𝑘 × 2𝜋𝑓𝐶𝑊 𝑡) | | | | 0 n=−∞ 𝑘=1 n=−∞ +∞ +∞ ∑ +∞ ∑ ∑ |𝐽𝑛 |2 + 2𝑃 𝐸 2 |𝐽𝑛−𝑘 𝐽𝑛 |2 ∙ cos(𝑘 × 2𝜋 𝑓𝐶𝐶𝑊 𝑃 𝐸02 | | | | 0 n=−∞ 𝑘=1 n=−∞
𝐼𝐶𝑊 = 𝐸02 𝐼𝐵1 =
+∞ ∑
𝐽𝑛 (𝑀)𝐽𝑛′ (𝑀 ′ ) ∙ cos[2𝜋(𝑛𝑓𝑐 − 𝑛′ 𝑓𝑐 )𝑡
n=−∞ n′ =−∞
+ 2𝜋 (𝑓𝐶𝑊 − 𝑓𝐶𝐶𝑊 )𝑡]
(5)
The modulated CW optical signal 𝐼𝐶𝑊 ′ is filtered by a band-pass filter whose center frequency is the modulation frequency 𝑓𝐶𝑊 , then only the cos(2𝜋𝑓𝐶𝑊 𝑡) term is left in 𝐼𝐵1 , and the total optical field becomes: 𝐼𝐶𝑊 ′ = 2𝐸02
+∞ ∑ n=−∞
|𝐽𝑛−𝑘 𝐽𝑛 |2 cos(2𝜋𝑓𝐶𝑊 𝑡) + 0 | |
√ + 2 𝑃 𝐸02 ||𝐽𝑛 (𝑀)|| ||𝐽𝑛′ (𝑀 ′ )|| ∙ cos[2𝜋(𝑓𝐶𝑊 − 𝑓𝐶𝐶𝑊 )𝑡]
(6)
The CW and CCW modulation frequency difference is 𝛥f = |𝑓𝐶𝐶𝑊 − (𝑓𝐶𝑊 + 𝑓𝑠ℎ𝑖𝑓 𝑡 )|. It can be observed that the mixed beat frequency can be filtered out by a low-pass filter when 𝛥𝑓 is large enough. Through this method, the interference between the backscattering of the carrier and the relative carrier can be greatly reduced, and the backscattering noise in the optical path can be suppressed greatly. The simulation results of n-order Bessel function are shown in Fig. 4. According to the principle of phase modulator electro-optic modulation, the phase modulation coefficient M is determined by the combination of half-wave voltage and modulation voltage: 𝑀=
𝜋𝑉 𝑉𝜋
(7)
where 𝑉𝜋 is the half-wave voltage of PM, 𝑉 is the amplitude of the sine wave, and phase modulation coefficient 𝑀 is generally set to 2.405 to suppress the backscattering noise in ROG [23]. Considering the phase modulator output power, the carrier suppression method changes the voltage of the phase modulator, 𝐽0 (𝑀) is set at the first zero points 𝑀 = 2.405. The primary frequency signal interference with the backscattered signal when the carrier component is not zero. At this point, certain error which is the source of backscatter noise is generated in the demodulated output. So, changing the voltage of the phase modulator to make 𝐽0 (𝑀) = 0 when the system parameters are determined in experimentation.
(2)
𝐼𝐶𝑊 ′ = 𝐼𝐶𝑊 + 𝐼𝐵1 + 𝐼𝐵2
+∞ ∑
(3)
𝑡) (4) 3
H. Wang, W. Liu, Z. Pan et al.
Optics Communications 459 (2020) 124766
Fig. 6. Transmission spectrum and demodulation curve.
𝑓𝐶𝐶𝑊 ≠ 𝑓𝑠ℎ𝑖𝑓 𝑡 +𝑛∙𝑓𝐶𝑊 as much as possible, that is to say, 𝑓𝐶𝐶𝑊 −𝑓𝑠ℎ𝑖𝑓 𝑡 and 𝑓𝐶𝑊 do not have a common divisor. According to the above reasons, the low-frequency modulation frequency of 700 kHz is selected, and then the frequency shift of 40 MHz is performed. Different from the traditional scheme that the resonant frequency of the cavity is tracked by the laser frequency, the sideband is locked by laser. Therefore, the experiment requires an independent and distinct sideband of the transmission spectrum. The silicon-based SiO2 resonator has a diameter D of 0.06 m, the incident light wavelength 𝜆 is 1550 nm, and the full-width at half maximum (FWHM) is 27.5 MHz. Considering the resonance amplification, the macroscopic dispersion coefficient 𝜎𝑅 is 1.33%, 𝑀 = 2.405. The CW modulation frequency 𝑓𝐶𝑊 is 700 kHz, the AOFS frequency shift 𝑓𝑠ℎ𝑖𝑓 𝑡 is 40 MHz, the CCW frequency 𝑓𝐶𝐶𝑊 is 43 MHz, and the modulation voltage is 2.02 V. As shown in Fig. 6, the curve (1) is the laser scanning voltage; the curve (2) is the transmission spectrum curve of the high-frequency modulation path. Due to the RIO laser intensity varies with the feedback voltage, the transmission spectrum is synchronized with the laser scanning voltage. Curve (3) is a demodulation curve of high-frequency modulation; curve (4) is a demodulation curve of low-frequency modulation. As can be seen from the test results, the difference of modulation frequency is 2.3 MHz. Even if the temperature or control voltage fluctuation, the backscattering noise can be suppressed by bandpass filtering. Fig. 7 shows the gyro output Allan variance for two hours of normal low-frequency modulation and dual-frequency modulation, respectively. The results show that the Allan variance of the dual-frequency modulation gyro system is 0.0054 ◦ /s, and the low-frequency system is 0.0188 ◦ /s, system stability is 2.8 times than traditional systems. Thus, the use of dual-frequency modulation have a certain inhibitory effect on backscattering noise, and the gyro output bias stability improved greatly (see Fig. 7).
Fig. 4. n-order Bessel function and the value of each order Bessel function under 𝑀 = 2.405.
3. Experimental setup The carrier suppression ratio test system is built, and the experimental results at different modulation frequencies are obtained through the spectrum analyzer. As shown in Fig. 5, with the modulation frequency increasing at a modulation voltage of 𝑉 = 2.65 V, 𝑉 = 6.31 V, and 𝑉 = 9.97 V, the carrier suppression ratio is also increased, correspondingly. When the modulation voltage 𝑉 = 2.65 V, the carrier suppression ratio difference under the modulation frequency in 40 MHz and 80 MHz is only 4.3 dB. And the carrier suppression tends to flat while the modulation frequency larger than 40 MHz. At the same time, the lowfrequency modulated beam is shifted by the acousto-optic frequency shifter. The frequency shifter can only perform frequency shifting at a fixed frequency of 40 MHz, so we choose to generate a sideband with a best frequency 𝑓𝑚 of 43 MHz. In fact, compared with 80 MHz, the carrier suppression ratio is no much difference. In order to make 𝐽0 (𝑀) → 0, in the range of ±10 V accepted by the actual circuit, 𝑀 can choose 2.405 or 5.516. In the experiment, the Y-branch waveguide phase modulator with a half-wave voltage 𝑉𝜋 = 3.59 V is selected. The theoretical modulation voltage is 2.75 V or 6.31 V. As shown in Fig. 5, the best carrier suppression effect can be achieved when 𝑓𝑚 = 43 MHz, 𝑉 = 2.64 V in experimentation. At the same time, in order to suppress the first type of backscattering noise (noise caused by the backscattered light itself), it is necessary to ensure that 𝛥f = |𝑓𝐶𝐶𝑊 − (𝑓𝐶𝑊 + 𝑓𝑠ℎ𝑖𝑓 𝑡 )| is large enough, so 43 MHz is selected as the modulation frequency. The selection of the low-frequency modulation frequency should satisfy
Fig. 5. Selection of modulation frequency and modulation voltage.
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Optics Communications 459 (2020) 124766
Fig. 7. High and low modulation gyro system output.
4. Conclusion
[2] D.M. Shupe, Fiber resonator gyroscope: sensitivity and thermal nonreciprocity, Appl. Opt. 20 (2) (1981) 286–289. [3] W.W. Chow, J. Gea-Banacloche, L.M. Pedrotti, V.E. Sanders, W. Schleich, M.O. Scully, The ring laser gyro, Rev. Modern Phys. 57 (1) (1985) 61–104. [4] R.E. Meyer, S. Ezekiel, D.W. Stowe, V.J. Tekippe, Passive fiber-optic ring resonator for rotation sensing, Opt. Lett. 8 (12) (1983) 644. [5] Hsiao Hsien-kai, K.A. Winick, Planar glass waveguide ring resonators with gain, Opt. Express 15 (26) (2007) 17783–17797. [6] M.C. Tien, J.F. Bauters, M.J. Heck, D.T. Spencer, D.J. Blumenthal, J.E. Bowers, Ultra-high quality factor planar Si3N4 ring resonators on Si substrates, Opt. Express 19 (14) (2011) 13551–13556. [7] X.S. Yao, L. Maleki, J. Yu, G. Lutes, M. Tu, Dual-loop optoelectronic oscillator, in: IEEE International Frequency Control Symposium, 1998. [8] Kazumasa Takada, Calculation of Rayleigh backscattering noise in fiber-optic gyroscopes, J. Opt. Soc. Amer. A 2 (6) (1985) 872–877. [9] D. Yelin, D. Oron, S. Thiberge, E. Moses, Y. Silberberg, Multiphoton plasmon-resonance microscopy, Opt. Express 11 (12) (2003) 1385–1391. [10] Mao Hui, H. Ma, Z. Jin, Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique, Opt. Express 19 (5) (2011) 4632–4643. [11] Todd J. Kaiser, Experimental developments in the RFOG, Proc. SPIE - Int. Soc. Opt. Eng. 21 (1) (1991) 1–4. [12] Glen A. Sanders, Strandjord Lee, Wu Jianfeng, Williams Wes, Smiciklas Marc, Salt Mary, Narayanan Chellappan, Qiu Tiequn, Development of compact resonator fiber optic gyroscopes, in: IEEE International Symposium on Inertial Sensors & Systems, 2017. [13] G. Liang, M. Wang, X. Chen, J. Yao, Frequency- and phase-tunable optoelectronic oscillator, IEEE Photonics Technol. Lett. 25 (11) (2013) 1011–1013. [14] Ma Huilian, Z. He, K. Hotate, Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro, J. Lightwave Technol. 29 (1) (2011) 85–90. [15] Cao Huiliang, Yingjie Zhang, Yu Liu, Xinwang Wang, Temperature energy influence compensation for MEMS vibration gyroscope based on RBF NN-GA-KF method, Shock Vib. 2018 (2018) 1–10. [16] J.M. Mackintosh, J.L. Mcmillan, B. Culshaw, Coherent backscatter in the phasemodulated fibre optic gyroscope, Proc. SPIE - Int. Soc. Opt. Eng. 630 (630) (1985) 196–204. [17] H. Ma, J. Zhang, L. Wang, Z. Jin, Double closed-loop resonant micro-optic gyro using hybrid digital phase modulation, Opt. Express 23 (12) (2015) 15088–15097. [18] Chong Shen, Rui Song, Jie Li, Xiaoming Zhang, Jun Tang, Yunbo Shi, Jun, Liu Huiliang Cao, Temperature drift modeling of MEMS gyroscope based on genetic-Elman neural network, Mech. Syst. Signal Process. 72–73 (2016) 897–905. [19] Nin Liu, Yanxiong Niu, Lishuang Feng, Hongchen Jiao, Xiao Wang, Suppression of backscattering induced noise by the sideband locking technique in a resonant fiber optic gyroscope, Chin. Opt. Lett. 16 (1) (2018) 010608. [20] Nin Liu, Yanxiong Niu, Lishuang Feng, Hongchen Jiao, Xiao Wang, Suppression of backscattering-induced noise by sideband locking based on high and low modulation frequencies in ROG, Appl. Opt. 57 (2018) 7455–7461. [21] K. Suzuki, K. Takiguchi, K. Hotate, Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit, J. Lightwave Technol. 18 (1) (2000) 66–72. [22] Suzuki Kenya, K. Takiguchi, Integrated optical ring-resonator gyro using a silica planar lightwave circuit, 1999. [23] Eric D. Black, An introduction to Pound–Drever–Hall laser frequency stabilization, Amer. J. Phys. 69 (1) (2000) 79–87.
The interference between the backscattered beam and the main propagating beam in the cavity of the ROG is the main reason of backscattering noise, which is an important factor limiting the accuracy of the gyro. Different from the traditional method of suppressing backscattering noise, this paper adopts the method of dual-frequency modulation to increase the frequency interval between CW and CCW beams before the Sagnac frequency difference is obtained. The error caused by backscattering noise is eliminated by bandpass filter. At the same time, both the modulated CW and CCW optical wave components have a certain frequency difference, which can suppress the backscattering noise to a large extent. The phase modulator that mainly is used to modulate the beam cooperates with the AOFS that has a sufficient overlap range for the linear portion of the CW and CCW demodulation curves. The final output of the gyro is 0.0054 ◦ /s, which is greatly improved compared with the low-frequency modulation. The carrier suppression ratio of the modulation frequency at 42 MHz can reach 24.4 dB, which is about 6 times that of the low-frequency modulation. This scheme provides a new scheme for suppressing backscattered noise. Due to some problems such as the low-frequency accuracy of the system, the overall index improvement is not obvious, but the carrier suppression ratio is significantly improved. In this paper, the feasibility and effectiveness of the scheme are verified by theoretical analysis, simulation, and experiments. The optical frequency components of the two optical paths are staggered from each other, which not only suppresses the influence of the backscattered light itself but also suppresses the interference between the backscattered light and the signal light. This method can radiate to other systems with backscattering noise and has great potential for backscattering noise suppression. Acknowledgments Natural National Science Foundation of China (NSFC) (No. 61803350, 51635011 and 61571406); Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi; Science and Technology on Underwater Information and Control Laboratory: 6142218051810; the Shanxi ‘‘1331 KSC’’; Applied Basic Research Programs of Science and Technology Commission Foundation of Shanxi Province (No. 201801D121149). References [1] H.J. Arditty, H.C. Leèfovre, Sagnac effect in fiber gyroscopes, Opt. Lett. 6 (8) (1981) 401–403; K. Gallo, G. Assanto, All-optical diode based on second-harmonic generation in an asymmetric waveguide, J. Opt. Soc. Am. B 16 (2) (1999) 267–269.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Suppression of backscattering-induced noise in a resonator optic gyro by the dual-frequency modulation method Haoyu Wang, Wenyao Liu ∗, Ziwen Pan, Yu Tao, Jian Niu, Jun Tang, Jun Liu ∗ National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan 030051, China Key Laboratory of Instrumentation Science and Dynamic Measurement Ministry of Education, North University of China, Taiyuan 030051, China
ARTICLE
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Keywords: Backscattering noise Resonant optical gyroscope Dual-frequency modulation High frequency modulation Carrier rejection ratio
ABSTRACT Backscattering noise is one of the main noises affecting the accuracy of resonant optical gyroscope (ROG) systems. A method of suppressing backscattering noise in a ROG is demonstrated using a dual frequency modulation technique. On the premise of obtaining the Sagnac frequency difference, the frequency interval between the forward and backward beams is increased. Among them, high frequency modulation is used in the frequency-locked circuit, low-frequency modulation is used in the output path and the modulated optical components have a certain frequency difference. Firstly, the frequency difference between the clockwise and counterclockwise optical paths is increased by high and low frequency modulation to increase the carrier rejection ratio, and the noise generated by backscattering and signal light is suppressed. Then, bandpass filtering is used to eliminate the noise caused by the backscattering itself. Through theoretical analysis and experiment, the feasibility and effectiveness of the scheme are verified. The method effectively improves the output precision of the gyro, and the final output of the gyroscope reaches 0.0054◦ /s (10 s integration time).
1. Introduction Currently, resonant optical gyro based on the Sagnac effect is the most promising angular velocity sensors in inertial navigation. Due to the characteristics of integration, light weight, vibration resistance, and impact resistance, ROG is expected to become the next generation optical gyro [1–4]. The core sensing element of the resonant microoptical gyroscope is the silicon-based SiO2 optical waveguide resonator, which determines the sensitivity of the gyroscope [5,6]. However, due to the manufacturing problems of the resonator itself, the backscattering noise is difficult to ignore, which is even considered to be the most important problem affecting sensitivity [7,8], and many methods have been proposed for suppressing backscattering noise. In recent years, many methods have been developed to suppress backscattering noise. Binary phase shift keying (B-PSK) is used to reduce the influence of the interference phase between the input light wave signal and the backscattered light wave signal, but the bandwidth of the thermal optical (TO) phase modulation is narrow. In order to effectively utilize the narrow bandwidth of the modulator, an electrical signal processing scheme and a frequency compensated modulation waveform are proposed [9,10]. Sinusoidal phase modulation techniques is widely used in resonant fiber optic gyros to suppress backscattering noise [11,12]. Different frequency modulation of CW and CCW [13–15] is a simple and feasible method and is currently used more, but there is still interference between the backscattered
beam and the main propagating beam. The double phase modulation based on ROG adding an additional phase modulators to the traditional single-phase modulation, which can obviously reduce the effects of backscatter noise by providing additional carrier suppression [16,17]. Later, Feng et al. proposed a sideband locking technique based on PDH technology [18], which improves the carrier rejection ratio by utilizing the filtering characteristics of the resonant cavity [19]. The sideband locking technique utilizes a resonant cavity as a bandpass filter, and the carriers will be filtered by the cavity itself, which is beneficial for suppressing noise caused by backscattering. Although the sideband locking technique has significant advantages in suppressing back-scattering noise when the two signals have a specific phase difference, the linear region of the demodulation curve is deformed [20]. Simultaneously, the three-laser scheme is proposed by Honeywell International to increase the frequency difference between the frequency components, and the error signal generated by the interference is filtered to achieve the purpose of suppressing backscattering noise. But there are three lasers in this structure, which will increase the cost and complexity of the prototype [21,22]. Therefore, a better method needs to be proposed to take advantage of sideband modulation to achieve the best effect of suppressing backscattering noise. In this paper, a new method for suppressing backscattering noise in a ROG using dual-frequency modulation technique is proposed, which distinguishes the traditional dual-channel low-frequency modulation
∗ Corresponding authors. E-mail addresses: [email protected] (W. Liu), [email protected] (J. Liu).
https://doi.org/10.1016/j.optcom.2019.124766 Received 19 July 2019; Received in revised form 24 September 2019; Accepted 14 October 2019 Available online 6 December 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
H. Wang, W. Liu, Z. Pan et al.
Optics Communications 459 (2020) 124766
Fig. 1. (a) Resonant optical gyro based on high and low-frequency modulation to suppress backscattering noise; (b) Illustration of backscattering mechanism in the cavity.
or dual-channel high-frequency modulation method. The frequencylocked channel and output channel light wave is modulated by highfrequency modulation and low-frequency, respectively. Firstly, through spectrum comparison and formula simulation, it is found that the highfrequency carrier suppression ratio is higher. Secondly, the test system was built for carrier suppression ratio experiments and final output testing of the gyro system. Finally, better results are obtained than traditional systems. The scheme not only exerts the advantages of the sideband locking technique but also avoids the influence of phase fluctuation on the output path, and makes the gyro output more stable.
Fig. 2. Relationship between slope of demodulation curve and modulation frequency.
where 𝐸0 is the electric field amplitude, 𝑤 is the angular frequency, 𝑓0 is the center frequency of the laser, 𝜙0 is the initial phase of the light wave, 𝑀 is the modulation depth, 𝛺 is the phase modulation frequency. According to Eq. (1), the single-frequency beam modulated by the phase modulator is divided into a series of equally spaced frequency components, including the carrier with angular frequency 𝑤 and the sidebands with angular frequencies, such as 𝑤 ± 𝛺, 𝑤 ± 2𝛺, 𝑤 ± 3𝛺 …, and 𝛺 = 2𝜋𝑓 [16]. Therefore, we can equivalently treat the beam after phase modulation as a beam of light incident on the WRR at a series of different frequencies. When CW and CCW use low frequency modulation with different frequencies, CW and CCW still have a common spectral component 𝑤0 . There is still interference between the backscattered beam and the main propagating beam. Although this method of modulation and filtering can suppress the influence of the backscattered light itself in the gyro signal, the interference noise generated by the backscattered light and the signal cannot be completely eliminated. The amplitude of the interference noise is related to the product of the Bessel function. The noise could be suppressed by selecting the appropriate modulation coefficient M to make the Bessel function amplitude equal to 0. In fact, there is no way to completely suppress it to zero. Therefore, a new method to improve the carrier suppression ratio needs to be found, and the backscattering noise is better suppressed [21]. In general, the frequencies of CW and CCW under highfrequency modulation are outside the passband range by using the frequency selection characteristics of the resonator. However, due to the small difference of the modulation frequency between the two beams, the interference under some other frequency components cannot be completely suppressed. Therefore, a dual-frequency modulation and demodulation scheme be proposed as shown in Fig. 1. According to the experiment and simulation, as shown in Fig. 2, the demodulation curve of the high-frequency modulation has a high slope, so the optical path under the high-frequency modulation is used as the lock frequency path. The high frequency modulation output circuit is selected as a frequency lock circuit to improve the sensitivity and frequency locking accuracy of the system. Selecting the low-frequency path as the output path can find the optimal shift frequency by adjusting the low-frequency modulation frequency, thereby backscatter noise of the system can be better suppressed and the bias stability of the system can be improved. In this mode of modulation, the frequency difference between the two beams is increased. There are no or less similar spectral components in the optical path and the carrier suppression ratio is further improved. The beam of low frequency modulation
2. Principles and simulation In order to suppress backscattering noise, the phase modulator is typically fused at the input of the clockwise (CW) and counterclockwise (CCW) optical paths, an beam is marked by a modulation of a different frequency applied by the phase modulator. Based on the Pound–Drever–Hall (PDH) technique, this paper proposes a scheme to increase the frequency separation between the CW and CCW beams. In this way, the carrier suppression ratio is further improved and the backscattered noise is reduced. The schematic of dual-frequency modulation ROG structure is shown in Fig. 1(a). The center wavelength of the laser is about 1550 nm and the line width is about 5 kHz. The Y-branch waveguide LiNbO3 phase modulator is used for sinusoidal phase modulation of CW and CCW light waves. SG1 and SG2 are signal generators that generate sine waves. The modulation frequency of CCW and CW is 𝑓𝐶𝐶𝑊 (high frequency) and 𝑓𝐶𝑊 (low frequency) respectively. The frequency of CCW light wave is shifted by an acousto-optic frequency shifter (AOFS) to generate a frequency difference to reduce backscatter noise. The CCW and CW light waves from the waveguide ring resonator (WRR) are detected by the photodetectors PD1 and PD2, respectively. The first-order harmonic demodulation signal of the CCW direction is obtained by the digital lock-in amplifier LIA1, and the center frequency of the laser is locked to the first sideband frequency of the CCW direction through the feedback servo loop. At the same time, the output of LIA2 is used as the gyro output to measure the angular velocity. Generally, scattering is caused by the unevenness of the medium or scatterer in the SiO2 waveguide cavity. It should be noted that the partially scattered light of the forward propagation is reciprocal and does not cause any parasitic effects. However, the backward backscattering is randomly distributed and has a certain negative impact on the gyro output. Taking the CW direction as an example, the backscattered light of CCW direction interferes with the CW signal light in the SiO2 waveguide cavity as shown in Fig. 1(b), thereby the light intensity detected by the detector will be affected. After passing through the phase modulator, the incident beam is modulated by the phase modulator, the electric field 𝐸in (𝑡) can be described as: [ ] 𝐸in (𝑡) = 𝐸0 exp 𝑖(2𝜋𝑓0 𝑡 + 𝜙0 ) +∞ ∑ = 𝐸0 exp[𝑖(𝑤𝑡 + 𝑀 sin 𝛺𝑡)] = 𝐽𝑛 (𝑀) exp[𝑖(𝛺𝑡)] (1) 𝑛=−∞ [ ≈ 𝐸0 𝐽0 (𝑀) exp(𝑖𝑤𝑡) + 𝐽1 (𝑀) exp[𝑖(𝑤 + 𝛺)𝑡] − 𝐽1 (𝑀) ] × exp[𝑖(𝑤 + 𝛺)𝑡] 2
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Optics Communications 459 (2020) 124766
Fig. 3. Spectrum analysis diagram of high and low frequency modulated gyro system . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) +∞ √ ∑ 𝐼𝐵2 = 2 𝑃 𝐸02
is frequency-shifted by AOFS to overlap the linear portions of the demodulation curves of CW and CCW. In this scheme, backscattering noise is suppressed to the greatest extent and the output stability of gyro is greatly improved. The Lorentz curve shown in Fig. 3 is used to represent the mode frequency characteristics of the cavity. The blue and orange solid lines indicate the frequency distribution modulated by high frequency and low frequency, respectively. The solid red line indicates the spectrum distribution of the beam modulated by low frequency after frequency shift of AOFS. The difference value of 𝑤0 ± 𝑘 ∙ 𝑓𝐶𝐶𝑊 and 𝑤0 + 𝑓𝑠ℎ𝑖𝑓 𝑡 ± 𝑛 ∙ 𝑓𝐶𝑊 (𝑘, 𝑛 represents the order of the harmonic components, both integers, respectively) determines whether the two optical paths have overlapping carrier components after the 𝑛th harmonic. For instance, we set k to be 1 because 𝑓𝐶𝐶𝑊 ≫ 𝑓𝑠ℎ𝑖𝑓 𝑡 ± 𝑛 ∙ 𝑓𝐶𝑊 . When 𝑤0 + 𝑓𝐶𝐶𝑊 = 𝑤0 + 𝑓𝑠ℎ𝑖𝑓 𝑡 + 𝑛 ∙ 𝑓𝐶𝑊 , the amplitude of the harmonic component after the 20th order is very small. As shown in Fig. 4, the amplitude of the harmonic component decreases with increasing number of stages. In this work, since 𝑓𝐶𝑊 and 𝑓𝐶𝐶𝑊 are the levels of kHz and MHz, respectively, 𝑛 > 100, the amplitude of the 𝑛th harmonic component is close to zero, and the interference to the high frequency harmonic component can be ignored accordingly. In the experiment, when 𝑤0 + 𝑓𝐶𝐶𝑊 ≠ 𝑤0 +𝑓𝑠ℎ𝑖𝑓 𝑡 +𝑛∙𝑓𝐶𝑊 , the two spectral components are completely staggered. Theoretically, the same spectral components do not exist in the two optical paths, and the backscattering noise is suppressed to the maximum extent. In the resonant cavity, taking the CW direction as an example, the backscattering coefficient is 𝑃 . According to the light field superposition principle, the total light field of CW direction should be the superposition of the main beam and the backscattered beam:
+∞ ∑ +∞ ∑
|𝐽𝑛 |2 + 2𝐸 2 |𝐽𝑛−𝑘 𝐽𝑛 |2 ∙ cos(𝑘 × 2𝜋𝑓𝐶𝑊 𝑡) | | | | 0 n=−∞ 𝑘=1 n=−∞ +∞ +∞ ∑ +∞ ∑ ∑ |𝐽𝑛 |2 + 2𝑃 𝐸 2 |𝐽𝑛−𝑘 𝐽𝑛 |2 ∙ cos(𝑘 × 2𝜋 𝑓𝐶𝐶𝑊 𝑃 𝐸02 | | | | 0 n=−∞ 𝑘=1 n=−∞
𝐼𝐶𝑊 = 𝐸02 𝐼𝐵1 =
+∞ ∑
𝐽𝑛 (𝑀)𝐽𝑛′ (𝑀 ′ ) ∙ cos[2𝜋(𝑛𝑓𝑐 − 𝑛′ 𝑓𝑐 )𝑡
n=−∞ n′ =−∞
+ 2𝜋 (𝑓𝐶𝑊 − 𝑓𝐶𝐶𝑊 )𝑡]
(5)
The modulated CW optical signal 𝐼𝐶𝑊 ′ is filtered by a band-pass filter whose center frequency is the modulation frequency 𝑓𝐶𝑊 , then only the cos(2𝜋𝑓𝐶𝑊 𝑡) term is left in 𝐼𝐵1 , and the total optical field becomes: 𝐼𝐶𝑊 ′ = 2𝐸02
+∞ ∑ n=−∞
|𝐽𝑛−𝑘 𝐽𝑛 |2 cos(2𝜋𝑓𝐶𝑊 𝑡) + 0 | |
√ + 2 𝑃 𝐸02 ||𝐽𝑛 (𝑀)|| ||𝐽𝑛′ (𝑀 ′ )|| ∙ cos[2𝜋(𝑓𝐶𝑊 − 𝑓𝐶𝐶𝑊 )𝑡]
(6)
The CW and CCW modulation frequency difference is 𝛥f = |𝑓𝐶𝐶𝑊 − (𝑓𝐶𝑊 + 𝑓𝑠ℎ𝑖𝑓 𝑡 )|. It can be observed that the mixed beat frequency can be filtered out by a low-pass filter when 𝛥𝑓 is large enough. Through this method, the interference between the backscattering of the carrier and the relative carrier can be greatly reduced, and the backscattering noise in the optical path can be suppressed greatly. The simulation results of n-order Bessel function are shown in Fig. 4. According to the principle of phase modulator electro-optic modulation, the phase modulation coefficient M is determined by the combination of half-wave voltage and modulation voltage: 𝑀=
𝜋𝑉 𝑉𝜋
(7)
where 𝑉𝜋 is the half-wave voltage of PM, 𝑉 is the amplitude of the sine wave, and phase modulation coefficient 𝑀 is generally set to 2.405 to suppress the backscattering noise in ROG [23]. Considering the phase modulator output power, the carrier suppression method changes the voltage of the phase modulator, 𝐽0 (𝑀) is set at the first zero points 𝑀 = 2.405. The primary frequency signal interference with the backscattered signal when the carrier component is not zero. At this point, certain error which is the source of backscatter noise is generated in the demodulated output. So, changing the voltage of the phase modulator to make 𝐽0 (𝑀) = 0 when the system parameters are determined in experimentation.
(2)
𝐼𝐶𝑊 ′ = 𝐼𝐶𝑊 + 𝐼𝐵1 + 𝐼𝐵2
+∞ ∑
(3)
𝑡) (4) 3
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Optics Communications 459 (2020) 124766
Fig. 6. Transmission spectrum and demodulation curve.
𝑓𝐶𝐶𝑊 ≠ 𝑓𝑠ℎ𝑖𝑓 𝑡 +𝑛∙𝑓𝐶𝑊 as much as possible, that is to say, 𝑓𝐶𝐶𝑊 −𝑓𝑠ℎ𝑖𝑓 𝑡 and 𝑓𝐶𝑊 do not have a common divisor. According to the above reasons, the low-frequency modulation frequency of 700 kHz is selected, and then the frequency shift of 40 MHz is performed. Different from the traditional scheme that the resonant frequency of the cavity is tracked by the laser frequency, the sideband is locked by laser. Therefore, the experiment requires an independent and distinct sideband of the transmission spectrum. The silicon-based SiO2 resonator has a diameter D of 0.06 m, the incident light wavelength 𝜆 is 1550 nm, and the full-width at half maximum (FWHM) is 27.5 MHz. Considering the resonance amplification, the macroscopic dispersion coefficient 𝜎𝑅 is 1.33%, 𝑀 = 2.405. The CW modulation frequency 𝑓𝐶𝑊 is 700 kHz, the AOFS frequency shift 𝑓𝑠ℎ𝑖𝑓 𝑡 is 40 MHz, the CCW frequency 𝑓𝐶𝐶𝑊 is 43 MHz, and the modulation voltage is 2.02 V. As shown in Fig. 6, the curve (1) is the laser scanning voltage; the curve (2) is the transmission spectrum curve of the high-frequency modulation path. Due to the RIO laser intensity varies with the feedback voltage, the transmission spectrum is synchronized with the laser scanning voltage. Curve (3) is a demodulation curve of high-frequency modulation; curve (4) is a demodulation curve of low-frequency modulation. As can be seen from the test results, the difference of modulation frequency is 2.3 MHz. Even if the temperature or control voltage fluctuation, the backscattering noise can be suppressed by bandpass filtering. Fig. 7 shows the gyro output Allan variance for two hours of normal low-frequency modulation and dual-frequency modulation, respectively. The results show that the Allan variance of the dual-frequency modulation gyro system is 0.0054 ◦ /s, and the low-frequency system is 0.0188 ◦ /s, system stability is 2.8 times than traditional systems. Thus, the use of dual-frequency modulation have a certain inhibitory effect on backscattering noise, and the gyro output bias stability improved greatly (see Fig. 7).
Fig. 4. n-order Bessel function and the value of each order Bessel function under 𝑀 = 2.405.
3. Experimental setup The carrier suppression ratio test system is built, and the experimental results at different modulation frequencies are obtained through the spectrum analyzer. As shown in Fig. 5, with the modulation frequency increasing at a modulation voltage of 𝑉 = 2.65 V, 𝑉 = 6.31 V, and 𝑉 = 9.97 V, the carrier suppression ratio is also increased, correspondingly. When the modulation voltage 𝑉 = 2.65 V, the carrier suppression ratio difference under the modulation frequency in 40 MHz and 80 MHz is only 4.3 dB. And the carrier suppression tends to flat while the modulation frequency larger than 40 MHz. At the same time, the lowfrequency modulated beam is shifted by the acousto-optic frequency shifter. The frequency shifter can only perform frequency shifting at a fixed frequency of 40 MHz, so we choose to generate a sideband with a best frequency 𝑓𝑚 of 43 MHz. In fact, compared with 80 MHz, the carrier suppression ratio is no much difference. In order to make 𝐽0 (𝑀) → 0, in the range of ±10 V accepted by the actual circuit, 𝑀 can choose 2.405 or 5.516. In the experiment, the Y-branch waveguide phase modulator with a half-wave voltage 𝑉𝜋 = 3.59 V is selected. The theoretical modulation voltage is 2.75 V or 6.31 V. As shown in Fig. 5, the best carrier suppression effect can be achieved when 𝑓𝑚 = 43 MHz, 𝑉 = 2.64 V in experimentation. At the same time, in order to suppress the first type of backscattering noise (noise caused by the backscattered light itself), it is necessary to ensure that 𝛥f = |𝑓𝐶𝐶𝑊 − (𝑓𝐶𝑊 + 𝑓𝑠ℎ𝑖𝑓 𝑡 )| is large enough, so 43 MHz is selected as the modulation frequency. The selection of the low-frequency modulation frequency should satisfy
Fig. 5. Selection of modulation frequency and modulation voltage.
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Fig. 7. High and low modulation gyro system output.
4. Conclusion
[2] D.M. Shupe, Fiber resonator gyroscope: sensitivity and thermal nonreciprocity, Appl. Opt. 20 (2) (1981) 286–289. [3] W.W. Chow, J. Gea-Banacloche, L.M. Pedrotti, V.E. Sanders, W. Schleich, M.O. Scully, The ring laser gyro, Rev. Modern Phys. 57 (1) (1985) 61–104. [4] R.E. Meyer, S. Ezekiel, D.W. Stowe, V.J. Tekippe, Passive fiber-optic ring resonator for rotation sensing, Opt. Lett. 8 (12) (1983) 644. [5] Hsiao Hsien-kai, K.A. Winick, Planar glass waveguide ring resonators with gain, Opt. Express 15 (26) (2007) 17783–17797. [6] M.C. Tien, J.F. Bauters, M.J. Heck, D.T. Spencer, D.J. Blumenthal, J.E. Bowers, Ultra-high quality factor planar Si3N4 ring resonators on Si substrates, Opt. Express 19 (14) (2011) 13551–13556. [7] X.S. Yao, L. Maleki, J. Yu, G. Lutes, M. Tu, Dual-loop optoelectronic oscillator, in: IEEE International Frequency Control Symposium, 1998. [8] Kazumasa Takada, Calculation of Rayleigh backscattering noise in fiber-optic gyroscopes, J. Opt. Soc. Amer. A 2 (6) (1985) 872–877. [9] D. Yelin, D. Oron, S. Thiberge, E. Moses, Y. Silberberg, Multiphoton plasmon-resonance microscopy, Opt. Express 11 (12) (2003) 1385–1391. [10] Mao Hui, H. Ma, Z. Jin, Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique, Opt. Express 19 (5) (2011) 4632–4643. [11] Todd J. Kaiser, Experimental developments in the RFOG, Proc. SPIE - Int. Soc. Opt. Eng. 21 (1) (1991) 1–4. [12] Glen A. Sanders, Strandjord Lee, Wu Jianfeng, Williams Wes, Smiciklas Marc, Salt Mary, Narayanan Chellappan, Qiu Tiequn, Development of compact resonator fiber optic gyroscopes, in: IEEE International Symposium on Inertial Sensors & Systems, 2017. [13] G. Liang, M. Wang, X. Chen, J. Yao, Frequency- and phase-tunable optoelectronic oscillator, IEEE Photonics Technol. Lett. 25 (11) (2013) 1011–1013. [14] Ma Huilian, Z. He, K. Hotate, Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro, J. Lightwave Technol. 29 (1) (2011) 85–90. [15] Cao Huiliang, Yingjie Zhang, Yu Liu, Xinwang Wang, Temperature energy influence compensation for MEMS vibration gyroscope based on RBF NN-GA-KF method, Shock Vib. 2018 (2018) 1–10. [16] J.M. Mackintosh, J.L. Mcmillan, B. Culshaw, Coherent backscatter in the phasemodulated fibre optic gyroscope, Proc. SPIE - Int. Soc. Opt. Eng. 630 (630) (1985) 196–204. [17] H. Ma, J. Zhang, L. Wang, Z. Jin, Double closed-loop resonant micro-optic gyro using hybrid digital phase modulation, Opt. Express 23 (12) (2015) 15088–15097. [18] Chong Shen, Rui Song, Jie Li, Xiaoming Zhang, Jun Tang, Yunbo Shi, Jun, Liu Huiliang Cao, Temperature drift modeling of MEMS gyroscope based on genetic-Elman neural network, Mech. Syst. Signal Process. 72–73 (2016) 897–905. [19] Nin Liu, Yanxiong Niu, Lishuang Feng, Hongchen Jiao, Xiao Wang, Suppression of backscattering induced noise by the sideband locking technique in a resonant fiber optic gyroscope, Chin. Opt. Lett. 16 (1) (2018) 010608. [20] Nin Liu, Yanxiong Niu, Lishuang Feng, Hongchen Jiao, Xiao Wang, Suppression of backscattering-induced noise by sideband locking based on high and low modulation frequencies in ROG, Appl. Opt. 57 (2018) 7455–7461. [21] K. Suzuki, K. Takiguchi, K. Hotate, Monolithically integrated resonator microoptic gyro on silica planar lightwave circuit, J. Lightwave Technol. 18 (1) (2000) 66–72. [22] Suzuki Kenya, K. Takiguchi, Integrated optical ring-resonator gyro using a silica planar lightwave circuit, 1999. [23] Eric D. Black, An introduction to Pound–Drever–Hall laser frequency stabilization, Amer. J. Phys. 69 (1) (2000) 79–87.
The interference between the backscattered beam and the main propagating beam in the cavity of the ROG is the main reason of backscattering noise, which is an important factor limiting the accuracy of the gyro. Different from the traditional method of suppressing backscattering noise, this paper adopts the method of dual-frequency modulation to increase the frequency interval between CW and CCW beams before the Sagnac frequency difference is obtained. The error caused by backscattering noise is eliminated by bandpass filter. At the same time, both the modulated CW and CCW optical wave components have a certain frequency difference, which can suppress the backscattering noise to a large extent. The phase modulator that mainly is used to modulate the beam cooperates with the AOFS that has a sufficient overlap range for the linear portion of the CW and CCW demodulation curves. The final output of the gyro is 0.0054 ◦ /s, which is greatly improved compared with the low-frequency modulation. The carrier suppression ratio of the modulation frequency at 42 MHz can reach 24.4 dB, which is about 6 times that of the low-frequency modulation. This scheme provides a new scheme for suppressing backscattered noise. Due to some problems such as the low-frequency accuracy of the system, the overall index improvement is not obvious, but the carrier suppression ratio is significantly improved. In this paper, the feasibility and effectiveness of the scheme are verified by theoretical analysis, simulation, and experiments. The optical frequency components of the two optical paths are staggered from each other, which not only suppresses the influence of the backscattered light itself but also suppresses the interference between the backscattered light and the signal light. This method can radiate to other systems with backscattering noise and has great potential for backscattering noise suppression. Acknowledgments Natural National Science Foundation of China (NSFC) (No. 61803350, 51635011 and 61571406); Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi; Science and Technology on Underwater Information and Control Laboratory: 6142218051810; the Shanxi ‘‘1331 KSC’’; Applied Basic Research Programs of Science and Technology Commission Foundation of Shanxi Province (No. 201801D121149). References [1] H.J. Arditty, H.C. Leèfovre, Sagnac effect in fiber gyroscopes, Opt. Lett. 6 (8) (1981) 401–403; K. Gallo, G. Assanto, All-optical diode based on second-harmonic generation in an asymmetric waveguide, J. Opt. Soc. Am. B 16 (2) (1999) 267–269.
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