主动光学技术在薄镜面中的应用及算法研究

Application and Algorithm Research of Active Optics in Thin Mirrors

针对采用准zernike多项式拟和法求主动光学校正力的过程中,因为准zernike多项式的不正交性造成求解误差大、求解不稳定的问题,提出了对准zernike多项式进行householder变换的方法。该方法不同于传统的最小二乘法和Gram-Schmidt正交化方法,它避免了因构造法方程组出现严重病态而引入的计算误差。根据该方法求出主镜的刚度矩阵,然后采用阻尼最小二乘法求校正力。基于此方法对直径为400 mm的实验镜进行了多次仿真计算,计算结果表明,采用householder变换后波面拟和精确,求解稳定,校正效果较好。

In the process of adopting quasi-zernike polynomial wavefront fitting method to solution the correction force of the active optics, the result error is big and instability because the quasi-zernike polynomial is not orthogonal. A method that householder transform of quasi-zernike polynomial was introduced, which avoids calculation error due to bring ill-conditioned polynomial without constructing normal equation in the traditional least square method and Gram-Schmid orthogonal method. This method resolves the stiffness matrix of the primary mirror, and gets correction force using the damping least square method. For tp 400 m test mirror, the simulation was carded out many times, the result indicats： the householder transform is adopted, and wavefront fitting is precision; and is stability; correction effectiveness is better.