基于刚体运动完备方程的光机热集成分析方法

对于环境载荷恶劣、光学面变形复杂的光机系统，传统光机热集成分析方法的计算误差较大。提出了基于刚体运动完备方程的光机热集成分析方法，利用双立方样条插值法对光学面进行修正，然后建立光学面刚体运动完备方程，采用优化的求解方式分离光学镜面刚体运动，最后采用最小二乘方法求解Zernike多项式系数，实现对光学镜面弹性变形的表征。采用数值案例和工程案例验证了所提方法的有效性和正确性，定量分析了刚体运动方程、镜面修正方法、镜面点阵分布以及面形等关键因素对光机热分析结果的影响，结果表明，所提方法比传统方法更为精确地分离出光学面刚体运动和弹性变形量，且不依赖于光学面的解析方程，镜面变形的复杂程度对分析结果的影响较大。

Thermal-structural-optical integrated analysis method based on the complete equations of rigid body motion

The thermal-structural-optical integrated analysis method has been widely used to evaluate the impact of environmental load on performances of opto-mechanical systems. However, for opto-mechanical systems with complex optical surface deformation mode and large rigid body motion, the results obtained by the traditional thermal-structural-optical integrated analysis method are inaccurate. A modified thermal-structural-optical integrated analysis method based on the complete equations of rigid body motion was proposed. Firstly, the deformed optical mirror was modified by bicubic spline interpolation method, then the complete equations of rigid body motion of the optical surface was established. The rigid body motion of the optical mirror was separated by a common optimization algorithm, and finally Zernike polynomial coefficients were solved by the least square method to characterize the elastic deformation of the optical mirror. Numerical and engineering cases were used to verify the effectiveness and correctness of the proposed method. The effects of key factors such as rigid body motion equation, surface correction method, node distribution and surface shape on the results were also quantitatively analyzed. The results show that the proposed method can identify the rigid body motion and elastic deformation of the optical surface more accurately than the traditional method, and does not depend on the analytical equation of the optical surface, and the shape of the mirror surface has a great influence on the analysis results.