谐振式微光学陀螺研究
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摘要
基于Sagnac效应的光学陀螺是一类非常重要的惯性角速度传感器,在导航和制导领域占有非常重要的地位。谐振式光学陀螺的核心敏感元件是一个无源的光学谐振腔,其突出特点是可以采用很短的光纤环或集成光波导环获得比较高的精度。利用成熟的半导体工艺与光电子集成技术将核心敏感元件和其它关键元器件集成,集成化的谐振式微光学陀螺(Resonator Micro Optic Gyro, R-MOG)具有体积小、重量轻、抗振动和耐冲击等特性。R-MOG是光学陀螺微型化的重要技术途径,研究R-MOG并储备基础关键技术,具有重要意义。
光学Sagnac效应是一种极其微弱的效应,除选择合适的调制／解调方式,克服光学噪声、提高陀螺输出信号信噪比将直接影响着R-MOG的性能。本论文围绕信号检测和光学噪声抑制技术对R-MOG进行了细致深入的研究,通过对严重影响R-MOG性能的瑞利背向散射噪声及闭环回路锁定技术等的理论和实验的研究,全面提高了R-MOG的实际性能。本论文的主要创新点包括：
(1)建立基于双相位调制技术(Double Phase Modulation Technique, DPMT)的信号检测及瑞利背散射噪声抑制相关理论,并在实际R-MOG系统中得到实验验证。瑞利背散射噪声是目前影响R-MOG精度提高的最主要噪声源之一,利用实际测试得到的硅基二氧化硅光波导谐振腔的背散射系数大小,对背散射噪声的影响进行了理论计算和评估。在没有考虑载波抑制时,该背散射噪声影响高达～79rad/s,完全抑制该背散射噪声(低于R-MOG理论极限灵敏度)至少需要120dB的载波抑制比,这对利用传统单相位调制技术(Single Phase Modulation Technique, SPMT)的R-MOG系统,对相位调制器的调制电压、使用环境温度稳定性等都提出了极高的要求。利用DMPT技术,通过调制参数的优化,在不影响陀螺输出信号信噪比的前提下,一方面可以获得更大的载波抑制比,同时大大降低了相位调制器控制电压及使用环境温度稳定性的要求。研究表明,在LiNbO3相位调制器的半波电压为3.0V、半波电压温度系数为500ppm/℃的条件下,若利用SPMT,要将瑞利背散射噪声控制在极限灵敏度之下,对应电压的控制精度是±1.8mV,对应温度的波动范围要求是±1.6℃；利用DPMT,可以将电压控制精度的要求放宽到±60mV,对应的温度的波动范围要求可以放宽到±51℃。上述研究可为R-MOG后续的工程化和实用化提供技术保障。
(2)采用数字比例积分(Proportional Integration, PI)光频率锁定技术,结合实际R-MOG系统,对闭环回路的临界振荡特性进行了实际测试,得到了回路临界增益和临界周期的实际数值；进一步地,利用Z-N整定法则和闭合回路仿真模型,结合实际硅基二氧化硅光波导谐振腔芯片的温度特性,优化了PI参数。其中最佳比例增益为2667,积分增益的3dB截止频率为70Hz。将上述参数应用于实际R-MOG系统,实现了激光频率的长期锁定,频率误差噪声密度为～5.9Hz/√Hz,接近由单个光电探测器引入的极限噪声密度(-4Hz/√Hz)。利用Allan方差对噪声误差进行了进一步的分析,PI锁定误差的Allan方差相对于积分时间τ的双对数坐标的斜率约为-1/2,表明闭合回路中剩余噪声主要是随机噪声。上述结果进一步表明在目前的谐振腔芯片温度特性下,研制的数字PI锁定技术可以使得由温度导致的谐振频率漂移降低到极限噪声量级之下,从而使得锁定输出误差主要由随机噪声占主导。另外,通过分析表明该闭环方案可以满足角加速度1000°/s2范围内的R-MOG实际应用需求。
(3)基于DPMT调制和数字PI光频率锁定技术,建立了R-MOG实验系统,对R-MOG的零偏稳定性、摆动响应、连续转动信号等进行了实际测试。实验系统以可小型化窄线宽光纤激光器(线宽～50KHz)为光源,腔长为7.9cm、直径为2.5cm的保偏硅基二氧化硅光波导谐振腔为核心敏感元件,在锁相放大器等仪器作为陀螺信号处理电路时,R-MOG的短期零偏稳定性达到了38°/h(积分时间为10s)。将该陀螺安装在高精度转台上进行正弦摆动测试,得到了0.10°/s-5°/s的正弦摆动输出信号。进一步地,将处理电路中的信号发生器,数字锁相放大器,数字PI锁定模块等利用现场可编程逻辑器件(Field Programmable Gate Array, FPGA)实现,代替全仪器信号处理电路,得到了从-550°/s-550°/s的连续转动信号,该数字R-MOG的非线性度R2-nonlinearity约0.0169%。
总之,本论文实现的R-MOG系统,短期零偏稳定性38°/h(积分时间10s),0.1°/s的摆动信号测试结果,以及-550°/s-550°/s的连续转动输出结果的测试结果(非线性度0.0169%)都是公开报道的R-MOG中最好实测结果。
Optic gyros with no moving parts based on the Sagnac effect are the perfect candidate for the inertial navigation system. There are two very successful types of optic gyros:He-Ne ring laser gyro (RLG) and interferometric fiber optic gyro (IFOG). With the development over past several decades, these two types of optical gyros show a good measurement performance, although there are some other potential alternatives. However, the conventional RLG and IFOG are not easy to be applied in the areas required for cheap and micro gyros, for the reason that they are complicated in fabrication process with a lot of individual components. With the development of the monolithically integrated optical components on waveguide circuits and batch micro fabrication techniques, R-MOG (Resonator Micro Optic Gyroscope, R-MOG) can solve the difficulty in gyro technology, such as the requirement of light weight and small size, low cost, low power consumption and so on. So, it is meaningful to do research on the key technologies of R-MOG.
Sagnac effect of R-MOG is a very weak effect. It is an important research of optical noise suppression and the signal noise ratio (SNR) improvement. This dissertation will do the research on the gyro signal detection and optical noise suppression, and then propose the suitable countermeasures. Finally, the R-MOG system is constructed with these countermeasures. The experimental results are obtained and the countermeasures are verified very usefully. The main innovational work and achievements can be concluded as follows:
(1) Based on phase modulation spectroscopy, the DPMT (Double phase modulation technique, DPMT) is proposed. The theory and experimental results indicates that the DPMT can be used to detect the gyro signal. Backscattering error is about～79rad/s in R-MOG if there is no countermeasure. A total carrier suppression of 120 dB is required to reduce this backscattering error to the shot noise limited sensitivity of the R-MOG. For the reason that the carrier suppression of DPMT can easily reach 160 dB, the DPMT can easily reduce the backscatter error to the shot noise limited level. With the same experimental condition, the comparison of backscatter noise suppression in the R-MOG has been done with the DPMT and SPMT respectively. The bias stability of the R-MOG has been improved about two orders of magnitude after using the DPMT. And the experimental results indicate that the backscatter noise is not dominant in the output of the R-MOG with DPMT. The accuracy of the modulation amplitude is relaxed from±1.8 mV to±60 mV with a half-wave voltage of 3 V. When the modulation amplitude is stable, the temperature stability requirement relaxes from±1.6℃to±51℃after applying the DPMT, when the temperature coefficient of the half-wave voltage of the LiNbO3 phase modulator is about 500 ppm/℃. That is to say, more than 30 times relaxation is achieved compared with the SPMT for the backscattering error suppression.
(2) The digital PI (Proportional Integration, PI) is adopted in the feedback loop of R-MOG. With the experimental results, Z-N parameter adjusting method and the temperature of the waveguide ring resonator, the optimal parameters of PI are obtained. There are 3-dB break frequency 70Hz and proportional coefficient 2667 respectively. The noise spectral density～5.9Hz/VHz is obtained with the optimal digital PI scheme, which is close to the shot noise limited spectral density 4.OHz/√Hz. The Allan deviationσ(τ) for optimal PI lock is roughly proportional toτ-1/2 up to integration times of 1200s. It indicates that the equivalent output of error Signal is limited by random noise rather than by drifts, when the optimal digital PI lock is implemented. The error signal induced by the optimal PI lock can be negeleted when the R-MOG is with the angular acceleration of less than 1000°/s2。
(3) The R-MOG system is constructed with the optimal DPMT optical modulation and optimal digital PI technology. The backscatter error is verified to be reduced to the level less than the shot noise limited of R-MOG with the DPMT. And based on the digital PI feedback scheme, the reciprocal noise is reduced to the level of minimum sensitivity in R-MOG. Finally, the R-MOG output is obtained when the system is at rest. The noise level of 1.85×10-4 rad/s (～38°/h) for 60 seconds duration is obtained. The rotation tests on R-MOG from 0.1。/s to 5。/s are tested, where the processing circuit of R-MOG is implemented by the instruments. The larger rotation test over a range of±550°/s has been successfully obtained with all the processing circuit implemented in FPGA. R2-nonlinearity of this digitalized R-MOG is 0.0169%. To our knowledge, these results are the best results ever demonstrated in silica WRR and the ring length is as short as 7.9 cm.
In a word, the R-MOG system is constructed and the experiments are obtained. To our knowledge, the short term stability～38°/h, the rotation of 0.1°/s and the continous rotation test results from -550°/s to +550°/s (R2-nonlinearity 0.0169%) of R-MOG are the best results ever demonstrated in the silica waveguide ring resonator with the ring length as short as 7.9 cm.
光学Sagnac效应是一种极其微弱的效应,除选择合适的调制／解调方式,克服光学噪声、提高陀螺输出信号信噪比将直接影响着R-MOG的性能。本论文围绕信号检测和光学噪声抑制技术对R-MOG进行了细致深入的研究,通过对严重影响R-MOG性能的瑞利背向散射噪声及闭环回路锁定技术等的理论和实验的研究,全面提高了R-MOG的实际性能。本论文的主要创新点包括：
(1)建立基于双相位调制技术(Double Phase Modulation Technique, DPMT)的信号检测及瑞利背散射噪声抑制相关理论,并在实际R-MOG系统中得到实验验证。瑞利背散射噪声是目前影响R-MOG精度提高的最主要噪声源之一,利用实际测试得到的硅基二氧化硅光波导谐振腔的背散射系数大小,对背散射噪声的影响进行了理论计算和评估。在没有考虑载波抑制时,该背散射噪声影响高达～79rad/s,完全抑制该背散射噪声(低于R-MOG理论极限灵敏度)至少需要120dB的载波抑制比,这对利用传统单相位调制技术(Single Phase Modulation Technique, SPMT)的R-MOG系统,对相位调制器的调制电压、使用环境温度稳定性等都提出了极高的要求。利用DMPT技术,通过调制参数的优化,在不影响陀螺输出信号信噪比的前提下,一方面可以获得更大的载波抑制比,同时大大降低了相位调制器控制电压及使用环境温度稳定性的要求。研究表明,在LiNbO3相位调制器的半波电压为3.0V、半波电压温度系数为500ppm/℃的条件下,若利用SPMT,要将瑞利背散射噪声控制在极限灵敏度之下,对应电压的控制精度是±1.8mV,对应温度的波动范围要求是±1.6℃；利用DPMT,可以将电压控制精度的要求放宽到±60mV,对应的温度的波动范围要求可以放宽到±51℃。上述研究可为R-MOG后续的工程化和实用化提供技术保障。
(2)采用数字比例积分(Proportional Integration, PI)光频率锁定技术,结合实际R-MOG系统,对闭环回路的临界振荡特性进行了实际测试,得到了回路临界增益和临界周期的实际数值；进一步地,利用Z-N整定法则和闭合回路仿真模型,结合实际硅基二氧化硅光波导谐振腔芯片的温度特性,优化了PI参数。其中最佳比例增益为2667,积分增益的3dB截止频率为70Hz。将上述参数应用于实际R-MOG系统,实现了激光频率的长期锁定,频率误差噪声密度为～5.9Hz/√Hz,接近由单个光电探测器引入的极限噪声密度(-4Hz/√Hz)。利用Allan方差对噪声误差进行了进一步的分析,PI锁定误差的Allan方差相对于积分时间τ的双对数坐标的斜率约为-1/2,表明闭合回路中剩余噪声主要是随机噪声。上述结果进一步表明在目前的谐振腔芯片温度特性下,研制的数字PI锁定技术可以使得由温度导致的谐振频率漂移降低到极限噪声量级之下,从而使得锁定输出误差主要由随机噪声占主导。另外,通过分析表明该闭环方案可以满足角加速度1000°/s2范围内的R-MOG实际应用需求。
(3)基于DPMT调制和数字PI光频率锁定技术,建立了R-MOG实验系统,对R-MOG的零偏稳定性、摆动响应、连续转动信号等进行了实际测试。实验系统以可小型化窄线宽光纤激光器(线宽～50KHz)为光源,腔长为7.9cm、直径为2.5cm的保偏硅基二氧化硅光波导谐振腔为核心敏感元件,在锁相放大器等仪器作为陀螺信号处理电路时,R-MOG的短期零偏稳定性达到了38°/h(积分时间为10s)。将该陀螺安装在高精度转台上进行正弦摆动测试,得到了0.10°/s-5°/s的正弦摆动输出信号。进一步地,将处理电路中的信号发生器,数字锁相放大器,数字PI锁定模块等利用现场可编程逻辑器件(Field Programmable Gate Array, FPGA)实现,代替全仪器信号处理电路,得到了从-550°/s-550°/s的连续转动信号,该数字R-MOG的非线性度R2-nonlinearity约0.0169%。
总之,本论文实现的R-MOG系统,短期零偏稳定性38°/h(积分时间10s),0.1°/s的摆动信号测试结果,以及-550°/s-550°/s的连续转动输出结果的测试结果(非线性度0.0169%)都是公开报道的R-MOG中最好实测结果。
Optic gyros with no moving parts based on the Sagnac effect are the perfect candidate for the inertial navigation system. There are two very successful types of optic gyros:He-Ne ring laser gyro (RLG) and interferometric fiber optic gyro (IFOG). With the development over past several decades, these two types of optical gyros show a good measurement performance, although there are some other potential alternatives. However, the conventional RLG and IFOG are not easy to be applied in the areas required for cheap and micro gyros, for the reason that they are complicated in fabrication process with a lot of individual components. With the development of the monolithically integrated optical components on waveguide circuits and batch micro fabrication techniques, R-MOG (Resonator Micro Optic Gyroscope, R-MOG) can solve the difficulty in gyro technology, such as the requirement of light weight and small size, low cost, low power consumption and so on. So, it is meaningful to do research on the key technologies of R-MOG.
Sagnac effect of R-MOG is a very weak effect. It is an important research of optical noise suppression and the signal noise ratio (SNR) improvement. This dissertation will do the research on the gyro signal detection and optical noise suppression, and then propose the suitable countermeasures. Finally, the R-MOG system is constructed with these countermeasures. The experimental results are obtained and the countermeasures are verified very usefully. The main innovational work and achievements can be concluded as follows:
(1) Based on phase modulation spectroscopy, the DPMT (Double phase modulation technique, DPMT) is proposed. The theory and experimental results indicates that the DPMT can be used to detect the gyro signal. Backscattering error is about～79rad/s in R-MOG if there is no countermeasure. A total carrier suppression of 120 dB is required to reduce this backscattering error to the shot noise limited sensitivity of the R-MOG. For the reason that the carrier suppression of DPMT can easily reach 160 dB, the DPMT can easily reduce the backscatter error to the shot noise limited level. With the same experimental condition, the comparison of backscatter noise suppression in the R-MOG has been done with the DPMT and SPMT respectively. The bias stability of the R-MOG has been improved about two orders of magnitude after using the DPMT. And the experimental results indicate that the backscatter noise is not dominant in the output of the R-MOG with DPMT. The accuracy of the modulation amplitude is relaxed from±1.8 mV to±60 mV with a half-wave voltage of 3 V. When the modulation amplitude is stable, the temperature stability requirement relaxes from±1.6℃to±51℃after applying the DPMT, when the temperature coefficient of the half-wave voltage of the LiNbO3 phase modulator is about 500 ppm/℃. That is to say, more than 30 times relaxation is achieved compared with the SPMT for the backscattering error suppression.
(2) The digital PI (Proportional Integration, PI) is adopted in the feedback loop of R-MOG. With the experimental results, Z-N parameter adjusting method and the temperature of the waveguide ring resonator, the optimal parameters of PI are obtained. There are 3-dB break frequency 70Hz and proportional coefficient 2667 respectively. The noise spectral density～5.9Hz/VHz is obtained with the optimal digital PI scheme, which is close to the shot noise limited spectral density 4.OHz/√Hz. The Allan deviationσ(τ) for optimal PI lock is roughly proportional toτ-1/2 up to integration times of 1200s. It indicates that the equivalent output of error Signal is limited by random noise rather than by drifts, when the optimal digital PI lock is implemented. The error signal induced by the optimal PI lock can be negeleted when the R-MOG is with the angular acceleration of less than 1000°/s2。
(3) The R-MOG system is constructed with the optimal DPMT optical modulation and optimal digital PI technology. The backscatter error is verified to be reduced to the level less than the shot noise limited of R-MOG with the DPMT. And based on the digital PI feedback scheme, the reciprocal noise is reduced to the level of minimum sensitivity in R-MOG. Finally, the R-MOG output is obtained when the system is at rest. The noise level of 1.85×10-4 rad/s (～38°/h) for 60 seconds duration is obtained. The rotation tests on R-MOG from 0.1。/s to 5。/s are tested, where the processing circuit of R-MOG is implemented by the instruments. The larger rotation test over a range of±550°/s has been successfully obtained with all the processing circuit implemented in FPGA. R2-nonlinearity of this digitalized R-MOG is 0.0169%. To our knowledge, these results are the best results ever demonstrated in silica WRR and the ring length is as short as 7.9 cm.
In a word, the R-MOG system is constructed and the experiments are obtained. To our knowledge, the short term stability～38°/h, the rotation of 0.1°/s and the continous rotation test results from -550°/s to +550°/s (R2-nonlinearity 0.0169%) of R-MOG are the best results ever demonstrated in the silica waveguide ring resonator with the ring length as short as 7.9 cm.
引文
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