光纤陀螺中的相位差与谐振频率差的推导及理论分析  

The derivation and theoretical analysis of the phase difference and the resonant frequency difference of the FOG

作　　者：何聂 李卓燕 刘承香 吴旭 张功申 杨志伟 HE Nie;LI Zhuoyan;LIU Chengxiang;WU Xu;ZHANG Gongshen;YANG Zhiwei(College of Mechatronics and Control Engineering,Shenzhen University,Shenzhen 518060,China;College of Optoelectronic Engineering,Shenzhen University,Shenzhen 518060,China;Sino-German College for Intelligent Manufacturing,Shenzhen Technology University,Shenzhen 518060,China)

机构地区：[1]深圳大学机电与控制工程学院,广东深圳518054 [2]深圳大学光电工程学院,广东深圳518054 [3]深圳技术大学中德智能制造学院,广东深圳518054

出　　处：《应用科技》2018年第4期19-27,共9页Applied Science and Technology

基　　金：深圳市技术攻关项目(JSGG20150512162504354);广东省自然科学基金项目(2015A030310464)

摘　　要：光纤陀螺是一种基于Sagnac效应的环形干涉仪,常见的光纤陀螺包括干涉型和谐振型。首先,对于这2种光纤陀螺,本文采用了以惯性空间为参考系的路程叠加法证明了Sagnac效应是一种与介质无关的纯空间延迟,有效折射率n对Sagnac时间差Δt和光程差Δδ均没有影响;其次,对于干涉型光纤陀螺,有效折射率n对Sagnac相移差Δφ也没有影响;再次,对于谐振型光纤陀螺,文中提出了2种方法,即基于激光物理学中的行波谐振腔理论和基于多光束干涉机理,求出谐振环形腔的谐振频率差Δνq的表达式,其与光纤环匝数N无关。最后,得出光纤陀螺中的相位差Δφ和谐振频率差Δνq之间所满足的关系,并分别从数学形式和物理意义上对这一关系作出分析。2种陀螺的光路结构虽不同,但可使用统一的模型表达及分析光学物理量之间的关系。Fiber optic gyro （FOG） is a kind of annular interferometer based on Sagnac effect. Common FOGs include interferometric FOG （I-FOG） and resonant FOG （R-FOG）. Firstly, for the two types of FOG, the distance superposition method is used, which takes the inertial space as the reference system to prove that Sagnac effect is a media-independent pure space delay, and the effective refractive index n has no effect on the Sagnac time difference △t and the optical path difference △δ; Secondly, the effective refractive index n has no effect on the Sagnac phase shift difference △φ; Thirdly, for the R-FOG, two methods are proposed, which are based on the theory of traveling wave resonator in laser physics and the multi-beam interference mechanism, to obtain the expression of the resonant frequency difference △νq in the fiber ring resonator. Finally, the mathematical relation between the phase difference △φ and resonant frequency difference △νq in the FOG is obtained and analyzed from mathematical expressions and physical significances. Although the optical paths of the two gyros are different, a unified model can be used to express and analyze the relation among the optical physical quantities.

关 键 词：Sagnac效应 惯性空间 转动角速度 干涉型光纤陀螺 相位差 谐振型光纤陀螺 谐振频率差 多光束干涉 

分 类 号：V24[航空宇航科学与技术—飞行器设计]