Overview: Space gravitational wave detection missions typically consist of three identical satellites, with two laser links between the satellites at an angle of sixty degrees forming a Michelson interferometer. The arm length changes are measured using high-precision inter-satellite laser interferometry. As a key component of the inter-satellite laser interferometry system, the telescope system needs to have picometer-level optical path stability, a wavefront error of λ/30, and stray light less than 10^?10 of the transmitted power. To meet the requirements of space gravitational wave detection for the telescope system, an optical and mechanical integrated analysis and optimization method is proposed to design and optimize the primary mirror and its supporting structure. The off-axis parabolic primary mirror adopts the side three-point support method, and the influence of the support point position on the mirror surface shape and the rigid body displacement under gravity conditions has been studied. Optimization of the size of the triangular lightweighting holes on the primary mirror has been performed, and density-based topology optimization has been used to optimize the support backplate while ensuring that the first-order mode of the primary mirror component remains essentially unchanged. The flexural matrix of the primary mirror component supported by a parallel bipod linkage structure was derived based on spinor theory, and an evaluation function for the support structure was established. The size parameter range of flexible support was preliminarily determined by Matlab analysis. A optical-mechanical integrated simulation platform is set up to optimize the parameters of the support structure using a weighted sum method to convert the multi-objective optimization problem into a single-objective optimization problem. The results showed that the first-order frequency of the primary mirror component system was 392.43 Hz. Under gravity and temperature loads, the deformation of the primary mirror surface was better than λ/60, the translational rigid body displacement was better than 2.5 μm, and the rotational rigid body displacement was better than 0.5 μrad, all of which met the design specifications. Under space thermal disturbance of 10 μK/Hz^1/2, the size stability of the primary mirror component, represented by the displacement of the central point of the mirror, was at a level of 10 pm/Hz^1/2.

随着星间通信系统的迅速发展，数据传输的精度要求不断提高。分光镜作为系统的核心元件，其光谱特性和面形精度直接影响整个系统的传输精度。本文基于薄膜干涉理论，选取Ta₂O₅与SiO₂作为高低折射率膜层材料进行膜系设计，采用电子束蒸发的方式在石英基板上制备高精度分光镜。同时根据膜层应力补偿原理建立面形修正模型，修正分光镜面形。光谱分析仪检测结果显示，分光镜在入射角度为21.5°～23.5°内，1563 nm透过率大于98%，1540 nm反射率大于99%。激光干涉仪检测结果显示，分光镜反射面形精度RMS由λ/10修正至λ/90（λ=632.8 nm），透过面形精度RMS为λ/90。

全口径环形抛光是加工大口径平面光学元件的关键技术之一，其瓶颈问题是元件面形的高效高精度控制。通过研究元件面形的影响因素及其控制方法从而提升其确定性控制水平。围绕影响面形误差的运动速度、抛光盘表面形状误差和钝化状态等关键工艺因素，建立基于运动轨迹有效弧长的环形抛光运动学模型，揭示了抛光盘表面开槽槽型对面形误差的影响规律；提出了采用位移传感器以螺旋路径扫描抛光盘表面并通过插值算法生成其形状误差的方法，建立基于小工具的子口径修正方法，实现了抛光盘形状误差的在位定量修正；提出抛光盘表面钝化状态的监测方法，研究了抛光盘表面钝化状态对面形误差的影响规律。结果表明：抛光盘表面开槽采用环形槽时元件表面容易产生环带特征，采用径向槽、方形槽和螺旋槽时元件表面较为匀滑；通过在位定量检测和修正抛光盘形状误差，可显著提升元件的面形精度；随着抛光盘表面的逐渐钝化，元件面形逐渐恶化。在研制的5 m直径大口径环形抛光机床上加工800 mm×400 mm×100 mm平面元件的面形PV值优于λ/6（λ=632.8 nm），提升了元件的面形控制效率和精度。

为满足点衍射干涉测量对解包算法高精度、高效以及抗干扰的检测需求。提出一种基于空洞空间卷积的相移点衍射干涉图像的相位解包方法，通过将自编码器结构和空洞空间卷积结合获得更高的相位解包精度，实现对包裹相位图像可控的多尺度特征提取。根据点衍射图像特点制作的大量多样化数据集对其进行训练和优化，从而实现准确识别包裹相位所在阶次，最终可以快速处理包裹图像得到高精度的解包结果。利用所提方法对实际点衍射干涉图像进行处理，并与ESDI专业干涉图像处理软件以及其他解包算法处理结果进行比对，结果表明：本文解包结果与软件枝切法解包处理结果均方根误差值为0.022 2 rad，面形拟合结果与软件面形拟合结果峰谷差值仅为0.012 1λ、均方根差值仅为0.004 2λ；时间效率上，完成一幅图像的处理平均仅需0.035 s，而传统方法均大于1 s。与其他方法相比，所提方法在处理包裹相位方面具有快速、高精度的特性，为点衍射干涉图像处理的高精度相位解包提供了新的可行方案。

长波红外差分干涉仪在低温工况下会因光学元件受到非均匀应力作用产生干涉条纹的畸变，从而降低干涉仪系统性能。本文为解决低温工况干涉条纹弯曲畸变问题，基于长波红外差分干涉仪光机系统进行了干涉条纹畸变影响因素分析，结合光-机-热耦合分析方法，对干涉仪系统低温工作状态进行仿真。随后设计了针对影响条纹畸变的关键元件——光栅元件的低温微应力动态稳定支撑安装结构，结构优化后的光栅表面面形均方根（Root Mean Square， RMS）值为3.89×10^-2 nm，面形峰谷值（Peak to Valley， PV）值为2.21×10^-1 nm，分别较优化前初始系统的分析结果减小了5个数量级，系统仿真干涉条纹畸变小于1个探测器像元。全系统低温验证试验表明，优化结构可有效抑制干涉条纹畸变，畸变量小于2个探测器像元，试验与仿真计算结果一致性较好，验证了优化分析方法的有效性。该优化方案对提升反射式光学系统结构低温稳定性，提高系统工作能力有较大意义和价值。

为了实现凹非球面的快速、高精度与通用化检测，文中提出了一种将非球面当做球面，直接采用干涉仪检测的非零位干涉检测方法，并结合相应的数据处理方法，获得非球面的面形误差检测结果。首先，介绍了该方法的检测原理，建立了回程误差、调整误差的计算与去除模型，研究了面形误差的数据处理方法。然后，以两个不同非球面度的凹非球面为例，对其回程误差和调整误差进行了仿真计算，验证了该方法的有效性。最后，搭建了凹非球面的非零位检测实验装置，成功测量得到其面形误差。通过与自准直零位检测法或LUPHOScan轮廓测量法检测结果对比发现，两种方法测量得到的面形分布和评价指标具有高度一致性，验证了该检测方法的正确性。该检测方法在保证高精度测量的同时兼备一定的通用性与便捷性，为凹非球面的通用化检测提供了一种有效手段。