基于可变相位延迟的激光干涉式亚纳米级微位移测量系统

激光光源具有单色性好、亮度高、方向性强和相干性强等优势，所以基于干涉原理对激光光谱进行积分可以应用于微位移测量领域。在重力方法探测过程中，因地质结构不同引起万有引力差异而造成的探测质量块位移十分微小，通常为纳米级，所以研制高精度纳米级微位移测量系统尤为重要。然而传统电容位移测量法在防止电磁干扰等方面存在不足。相比较而言，光学干涉法具备抗电磁干扰、环境适应性强等优点，且精度不亚于电容法。传统干涉系统光路复杂、难于集成，对重力仪的小型化与集成化不利。所以研制一种结构紧凑的光学干涉系统用于实现纳米级微位移测量成为亟需。基于可变相位延迟的激光干涉式方法，能够实现亚纳米级微位移测量，较传统干涉系统具备结构紧凑、易于集成的优势。本微位移测量系统由半导体激光器、起偏器、检偏器、楔形双折射晶体组和光谱仪组成。研究从以下方面展开：首先是确定测量系统方案，提出了偏振光干涉双路结构，以楔形双折射晶体组作为核心器件，将晶体间相对位移转化为o光和e光的差别化相位延迟，并对激光光谱进行积分，进而将位移变化转变为合成光强的变化；其次是建立测量位移物理模型，根据设计的双折射晶体组几何结构、位移过程与光路，确定光强变化与待测位移量之间的关系；第三是系统参数优化，为了使系统的测量误差和量程满足实际需求，利用已建立的物理模型，将测量误差和量程分别与晶体切割角度α、激光器激射波长λ建立函数关系。根据应用需求，确定适当的误差和量程取值范围，进而得到角度α和波长λ取值范围；最后加工晶体、搭建系统并进行测试。具体即以α和λ为调控参量，联合考虑“近似线性化”和“激光器光强波动误差”对系统量程进行优化仿真。同样，联合考虑“激光器光强波动误差”和“激光器波长波动误差”，并利用“系统最大位移量”（与量程有关）对系统测量误差进行优化仿真。最终确定钒酸钇晶体切割角度α为20°，激光器激射波长λ为635 nm。实验中，以10 nm为间隔利用压电陶瓷设置位移量进行位移测试，包括：系统的线性标定、系统量程和测量误差测试。另外，在保持待测位置不变的条件下，利用本位移测量系统进行了2 h不间断测量，并通过阿伦方差确定了系统的位移探测下限。实验结果表明，位移量程范围大于150 nm，位移测量误差约0.5 nm，位移探测下限为0.32 nm@23 s，探测线性度判定系数(R2)为0.999 85。综上所述，以自制楔形双折射晶体组作为核心器件的可变相位延迟激光干涉式微位移测量系统，可作为重力探测中的质量块位移测量单元。与电容法相比具有更强的环境适应性；与传统干涉系统相比具有结构简易、光路紧凑等优点，便于重力仪的小型化与集成化。

A Laser Interferometric Subnano-Scale Micro-Displacement Measurement System Based on Variable Phase Retardation

Laser has many advantages in good monochromatic, high brightness, strong directional and good coherence. Therefore, the integral of laser spectrum can be applied to the field of micro displacement measurement, which is based on the interference principle. In the process of gravimetry, gravity differences caused by different geological structures make the micro nano-scale displacements of detection mass. Therefore, development of micro displacement measurement system with nanometer precision is vital. However, traditional capacitance displacement measurement method (CDMM) is not sufficient to prevent electromagnetic interference. In comparison, the optical interference method (OIM) has the advantages of anti-electromagnetic interference, strong environmental adaptability, and higher precision than CDMM. For the traditional OIM system, the optical path is complex and difficult to integrate, which is unfavorable to the miniaturization and integration of the gravimeter. Therefore, developing a compact OIM system to measure the micro displacement with nanometer precision has become an urgent requirement. A laser interferometric method based on variable phase retardation was designed to achieve sub-nanometer resolution displacement measurement, which has the advantage of compact structure and easy integration compared to traditional OIM system. This system was composed with diode laser, polarizer, analyzer, birefringent crystal group and spectrometer. This paper studies the following aspects: firstly, the measurement system scheme is determined. The structure with dual optical path of polarized light interference is introduced, and the wedge birefringent crystal group is used as the core device, which transforms relative displacement among crystals into differential phase delay between ordinary light (o) and extraordinary light (e). Integrate the laser spectrum, and then the displacement change is transformed to the variance of the synthesis light intensity. Secondly, the physical model of displacement measurement is set. According to the design of birefringent crystal group geometry structure, displacement process and optical path, the relationship between light intensity variance and measured displacement is determined. The third is the optimization of system parameters. In order to make the system measurement error (ME) and measurement range (MR) to meet the practical requirements, using the established physical model, the ME and the MR are set up as a function of crystal cutting angle α and laser wavelength λ. According to application requirements, appropriate bounds of ME and MR is determined, and then α and λ is obtained. Finally, crystal process, systems build and the system measurement test were carried out. In detail, α and λ are chosen as control parameters to optimize and simulate the system, jointly considering “approximate linearization” and “laser intensity fluctuation error”. Meanwhile, jointly considering “laser wavelength fluctuation error” and “laser intensity fluctuation error”, and using the maximum displacement related to system MR, to optimize system ME. Eventually, yαis selected as 20 ° and λ is 635 nm. In testing experiments, displacement measurement is carried out by means of piezoelectric ceramic actuator generating micro-displacement with 10 nm intervals, which includes linear calibration, MR and ME of the system. In addition, a two-hour continuous measurement is carried out using this system when measured position is fixed, and the displacement detection limit is determined by Allan variance. Experimental results show that the displacement MR is longer than 150 nm, and displacement ME is around 0.5 nm, and a detection limit is 0.32 nm @ 23 s, and the linearity determination coefficient R2 is 0.999 85. In conclusion, the system using self-made birefringent crystal group as the core device with adjustable phase retardation can be used as the displacement measurement unit of mass in gravity detection. This system has the advantage of strong environmental adaptability compared with CDMM, and laconic structure and compact light path compared with the conventional laser interference system, so as to facilitate the miniaturization and integration of the gravimeter.