中文摘要：

提出了一种基于3×3耦合器的小型化单光栅纳米位移测量方法。基于激光多普勒效应与光纤耦合器散射矩阵理论，首次将3×3耦合器与计量光栅相结合，设计了一种对称式光路结构，利用所提出的新型相位解调算法实现纳米级精度的位移测量。方法具有结构简单、调节方便、对波长变化不敏感和能有效抑制空气扰动等特点，从而使得系统具有良好的稳定性。实验结果显示，3×3耦合器三路输出信号两一两产生的李萨育图形平滑清晰，相位差保持在120。左右，说明本方法具有较好的测量稳定性。数值仿真与理论分析具有较好的一致性，在同时存在相位和幅值误差的情况下可以实现8nm的测量精度。

英文摘要：

A miniature single-grating nano-scale displacement measuring system based on a 3 × 3 coupler is developed. Based on the laser Doppler effect and the scattering matrix theory of fiber couplers, a new symmetrical optical configuration is designed,and the nano-scale measurement precision is achieved with the proposed phase demodulation algorithm. This method has the advantages of simple structure, conven lent adjustment,inhibition of air turbulence and insensitive to the wavelength change, thus making the system have the merit of good robustness. Experiment results show that the Lissajou figures formed by either two of the outputs of the 3 × 3 coupler are smooth and clear,and their phase differences are retaining around 120°, which illustrates that this method has excellent measurement stability. Numerical simulation is well consistent with the theoretical analysis,and achieves a measurement precision of 8 nm in the presence of both phase and amplitude errors,which proves the effectiveness of this method.