Overview: The space gravitational wave detection telescope is one of the core payloads of the gravitational wave detection satellite, simultaneously expanding and contracting the transmitted beam. Optical path stability is one of the core indices for the telescope, closely related to its structural stability. To meet the ultra-high path stability and structural stability requirements posed by the gravitational wave detection mission, it is essential to study the structural deformation measurement of the telescope. Currently, there are still several shortcomings in the research of multi-degree-of-freedom deformation measurement methods for gravitational wave detection telescopes, such as inaccurate selection of measurement points, inability to decouple multi-degree-of-freedom coupling, and unclear identification of error sources in multi-degree-of-freedom measurement. This paper deeply investigates the high-precision measurement of structural deformation of space-borne telescopes designed for space gravitational wave detection. It preliminarily establishes a framework and method system for measuring the structural deformation of space-borne telescopes, theoretically describing the measurement principle of the method. The feasibility of this method applied to space gravitational wave detection is verified through simulation analysis and error decomposition. The paper focuses on resolving the issue of decoupling multiple degrees of freedom, establishing a mathematical model using analytical methods, and conducting preliminary validation using Zemax. Finally, noise analysis of the measurement system is carried out, with experimental testing of the main noise components in the measurement system, validating the correctness of the theoretical noise model proposed in this paper. The experimental results show that near 1 Hz, the displacement noise background of the single-link interferometer is 100 pm/Hz^1/2. At 1 mHz in the low-frequency range, the displacement noise background reaches 10 nm/Hz^1/2. The noise level of the measurement system below 1 mHz is mainly limited by environmental temperature noise, while above 10 mHz, it is primarily constrained by laser frequency noise, phase acquisition background noise, and vibration noise. During the development phase of the space gravitational wave detection telescope, the research on this measurement method is expected to fulfill the telescope's multi-degree-of-freedom deformation measurement needs. It also provides data feedback for telescope design and offers guidance for the study of the telescope's optical path stability.

基于条纹投影的三维形貌测量技术，已经在提升测量精度、提高测量速度、扩大测量景深、增加测量场景适应性等方面被进行了大量研究。但由于条纹投影技术本身的原理限制，仅利用传统条纹投影方法难于实现准确的对应点匹配。而依赖于对应点追踪的形变测量和应变分析可以进一步分析物体的运动状态、材料特性以及结构力学参数，在运动仿生学、材料力学、结构力学等诸多领域中起着不可或缺的作用。本文回顾了近年来新发展出的一系列基于条纹投影的三维形貌与形变测量技术，论述了学者们如何在条纹投影系统上一步步实现从简单刚体位移的测量到复杂、精细结构的形变测量和应变分析。分析了此类技术在测量完整度、分辨率以及计算效率上相比于已有形变测量技术的优势，给出了此技术所面临的挑战和潜在发展动向。

为实现玻璃光纤、石英光纤等光学产品高精度、低成本的三维微纳尺度形变检测，提出了一种单目显微成像系统三维形变测量新方法。根据图像球面化算法建立了面内位移与离面位移的几何关系，在采用数字图像相关算法或光流法测量变形前后图像的面内位移后，根据常规斜面模型从面内位移中提取离面位移，完成三维形变测量。模拟实验与应用实验的结果表明在50倍光学显微镜下测量的绝对误差均小于0.2 μm，证实了方法的有效性。该方法充分利用了面内位移场携带的离面位移信息，只需要一部工业相机拍摄显微镜下两幅图像即可完成测量，提取离面位移时无需转换到频域和相位解包操作，具有检测成本低、光路简单、普适性强等优势。目前该方法已被用于玻璃光纤、石英光纤等光学产品的工业生产检测与监控中，同时为其它固体材料的微纳米尺度形变动态测量提供了新的思路。

在数字散斑干涉测量中，对于给定尺寸的CCD，很难在不影响形变测量横向分辨率的情况下扩大视野。针对该问题，提出了一种在不影响横向分辨率的情况下拼接多个子图像相位以扩大视野的方法。设计并搭建了一套多CCD实验装置来获取多个子图像。利用重叠区域解包裹后的相位图估计相邻子图像之间的相对位置并补偿相位偏差，实现正确的相位拼接。为了使用尽可能少的CCD获得尽可能大的视野，分析了重叠区域大小对拼接效果的影响。权衡视野和精度，重叠区域的最佳尺寸约为10%。所提方法在只使用两个CCD的条件下实现了视野从5.5 cm×4 cm扩大到10 cm×4 cm。拼接前后重叠区域的最大相对误差小于1%，证明了该方法的有效性。此外，还比较了所提方法与单CCD的形变测量均方根误差（RMSE）。结果表明，提出的方法具有与单CCD形变测量接近的测量精度。