采用直接最小二乘法和自由谐振法对大口径高刚度S iC主镜进行主动校正易引入较多解算误差,故本文提出以主镜的本征模式进行主镜面型校正来优化解算校正力幅值,以改进系统校正效果.该方法首先对主镜的响应矩阵进行一系列数学转换,得到一组相互正交的主镜本征模式,然后以各模式面形拟合校正目标,解算校正力.对1.23 m SiC主镜和主动支撑系统进行了有限元建模,通过仿真验证了提出方法的正确性.在此基础上,在搭建的1.23 m SiC主镜主动光学实验系统上进行了主动光学校正实验,并针对实验系统进一步优化了提出的方法.实验结果显示:利用该方法可将实验系统主镜面形误差由0.23λRM S校正至0.048λRM S,表明以主镜本征模式进行主动校正,可有效抑制解算校正力幅值,提高系统校正能力.该方法适用于大口径、高刚度S iC主镜的主动校正.%As active correction of a large aperture SiC mirror with high stiffness is vulnerable to many calculation errors by direction least square method or free resonance method ,this paper proposes a primary surface correction algorithm using bending mode to calculate and optimize the active force and to improve the correction capability .Firstly ,a series of mathematical transformations were performed on the influence matrix of the primary mirror ,and a set of orthogonal bending modes of primary mir-ror were obtained .Then ,correction targets were fitted in bending modes to calculate the correction force .An 1 .23 m SiC mirror and a support system were modeled by finite element analysis and the al-gorithm was verified by simulation experiments .Moreover ,an active support system for the 1 .23 m SiC mirror was set up to correct primary surface and a further optimization for the algorithm was con-ducted based on this system .The experiments show that the surface error is corrected from 0 .23λRMS to 0 .048λRMS by the proposed bending mode .Results of analysis and experiment demonstrate that the algorithm by bending mode efficiently reduces active force ranges and improves correction ca-pability .It is significant for the active correction of large aperture SiC mirrors with high stiffness .
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