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波前重构是主动光学的关键技术之一,分析了薄镜面的自由谐振模态振型的特点,以其为底基函数,拟合了薄镜面主镜的变形。首先,用有限元方法给出了主镜的前10阶模态振型图,把它们的RMS值归一化为1 000 nm,对比分析了主镜模态振型和Zernike多项式在圆域内的径向变特点。利用模态振型在环域内的正交性和完备性,采用最小二乘法拟合主镜变形,并与环域内的Zernike多项式拟合结果做了对比。分析结果表明,自由模式可以拟合波前变形,采用相同项数拟合主镜变形时,模态振型拟合主镜变形可以获得更小的残余误差。
Wavefront reconstruction is one of the key technologies in active optics. The characteristics of the free resonance mode shape of the thin mirror are analyzed. The deformation of the thin mirror primary mirror is fitted by using it as the basis function. First, the first ten modes of the main mirror are given by the finite element method, and their RMS values are normalized to 1 000 nm. The modes of the main mirror and the Zernike polynomials are compared in the circular domain Radial change characteristics. Using the orthogonality and completeness of modal vibration modes in the torus, the least square method was used to fit the deformation of the main mirror, and the results were compared with the Zernike polynomial fitting results in the toroidal region. The analysis results show that the free mode can fit the wave front deformation, and the smaller the residual error can be obtained when the modal of the main mirror is modified by using the same number of items to fit the deformation of the main mirror.