利用Kokorowski导出的自由边界条件下双压电变形镜表面位移-电压所满足的偏微分方程, 运用高斯迭代法求解该方程, 得出变形镜的静态响应函数矩阵f(r, θ)。 考虑到由大气湍流造成的光学波前畸变中各泽尼克(Zernike)基元模式的统计权重分布, 以及变形镜的实际装夹定位方式, 对双压电变形反射镜的优化设计进行了分析。 结果表明: 变形镜的校正能力随被校正的各项泽尼克模式像差在大气湍流造成的波前畸变中所占统计权重的不同而有很大的差别, 其优化设计结果也随之而变; 变形镜的定位方式对其校正能力有一定的影响, 但影响不大。

Based on the partial differential equation related to the displacement of bimorph deformable mirror with free boundary condition and its applied voltage deduced by S. A. Kokorowski, a matrix of static response functions f(r, θ) of mirror is derived with Gaussian iteration. Considering the statistical weight factors of different Zernike model aberrations caused by atmospheric turbulence, and the different arrangements of mirror positioning, the optimization of the bimorph deformable mirror is analyzed. The results indicate that, the correction capability of bimorph deformable mirror is greatly dependent on the statistic weight function of the corrected Zernike model wave aberrations induced by atmospheric air turbulence, so far as to the optimization design of mirror. And the different ways of mirror positioning will slightly affect its correction capability.