大口径长条形反射镜组件自重变形的仿真与试验

Analysis and experiment of gravity deformation for large aperture rectangular mirror set

研究了空间光学遥感器的大口径长条形反射镜组件在自重载荷作用下的面形变化,实验验证和定量分析了Zernike多项式拟合法以及球面方程拟合法得到的仿真分析结果的精度。介绍了Zernike多项式拟合法以及球面方程拟合法的基本原理,分别用这两种算法对大口径长条形反射镜组件在自重载荷作用下的面形变化进行了仿真分析。根据误差合成原理,提出了依据翻转前后两个状态的面形检测结果计算镜面面形变化的方法;针对离轴反射镜在面形检测过程中存在离轴量与镜面像散互相补偿的现象,求解了离轴量变化量与镜面像散的关系。试验结果显示:Zernike多项式拟合法的计算精度为74.2%,而球面方程拟合法的计算精度为12.6%;对仿真分析结果的误差评价表明,采用有限元法得到的仿真分析结果的理论精度值为10%左右,与球面方程拟合方法的计算精度12.6%基本吻合。研究表明,由于Zernike多项式拟合法自身的局限性,不适合对长条形反射镜面形变化进行拟合,而球面方程拟合法的计算精度能够满足工程要求。

The surface figure deformation of a large aperture rectangular mirror set in a space optical remote sensor under the gravity was explored and the accuracy of simulation analysis results by Zernike polynomial fitting and spherical equation fitting methods were verified and analyzed quantitatively.The basic principles of Zernike polynomial fitting and spherical equation fitting were introduced,and the gravity deformation of the large aperture rectangular mirror set under the gravity was simulated and analyzed by the two fitting methods mentioned above.On the basis of error composition principle,a calculation method of the mirror surface figure change was proposed according to the two test results in the grounded turn-over experiment.For the compensation phenomenon between the off-axis magnitude and the surface astigmatism of an off-axis mirror in the process of the mirror surface test,a method was proposed to determine the relationship between the amount of off-axis magnitude and the surface astigmatism.Experimental results show that the fitting accuracy of Zernike polynomial method is 74.2%,and that of spherical equation fitting method is 12.6%,which is in good agreement with the error evaluation of simulation results 10%.It suggests that the polynomial fitting method is not suitable for the rectangle mirror due to its limitation,however the accuracy of the spherical equation fitting method can meet the engineering requirements.