外差式光栅三自由度精密测量系统设计

Design of Heterodyne Grating Three-Degree-of-Freedom Precision Measurement System

摘要: 为了实现结构紧凑、测量精度高的三自由度位移测量，提出了一种外差式光栅三自由度精密测量系统的设计。系统采用了Littow入射的光路结构，有效简化了光路结构并降低了能量损耗。系统中引入二维反射式光栅作为核心测量元件，提升了系统的测量能力与结构紧凑性，并且对设计的系统的光学结构、测量原理进行了研究，在二维光栅衍射的特性和外差式结构设计的基础上对系统进行了仿真，该系统设计实现了2倍光学细分。基于ZEMAX软件完成了光学路径建模与光束追迹仿真，获得干涉光的相干性图像；随后利用MATLAB对干涉信号进行处理与对比度分析，结果表明系统干涉条纹对比度达到0.992，验证了所设计系统在理想状态下具备良好的相干干涉性能。此外，系统理论分辨率达到0.10 nm，表明了其在纳米级位移检测中的潜力。该系统具备结构简单、稳定性高、易于集成等优点，适用于高精度多自由度位移测量场景。

Abstract: To achieve a compact structure and high-precision measurement in three degrees of freedom (3-DOF) displacement sensing, a heterodyne grating-based precision measurement system is proposed and designed. The system adopts a Littrow-incident optical configuration, which effectively simplifies the optical path and reduces energy loss. A two-dimensional reflective grating is introduced as the core sensing element to enhance the system’s measurement capability and structural compactness. The optical architecture and measurement principles of the proposed system are systematically investigated. Based on the diffraction characteristics of the two-dimensional grating and the heterodyne optical design, the system is simulated and achieves a two-fold optical subdivision. The optical path modeling and ray-tracing simulation are conducted using ZEMAX, and the coherence of the interference field is obtained. Subsequently, the interference signals are processed and analyzed in MATLAB, yielding a fringe contrast ratio of 0.992, which verifies the excellent coherent performance of the system under ideal conditions. Furthermore, the theoretical resolution of the system reaches 0.10 nm, demonstrating its potential for nanoscale displacement detection. The proposed system offers advantages such as structural simplicity, high stability, and ease of integration, making it suitable for high-precision multi-degree-of-freedom displacement measurement applications.