13单元双压电晶片变形反射镜控制电极的优化设计

双压电晶片变形反射镜具有动态范围大、工作电压低、结构简单、造价低廉等优点，是自适应光学系统中用作波前校正器的新型器件。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，分别运用Ｇａｕｓｓ迭代法和Ｍｏｎｔｅ－Ｃａｒｌｏ法求解该方程的第一边界条件，得出变形镜的静态影响函数矩阵Ｚ（ｘ，ｙ）；按不同电极设计情况划分，以１３组Ｚ（ｘ，ｙ）为基，对Ｚｅｒｎｉｋｅ多项式低阶模进行逐项拟合，得出变形镜控制电极的大小、形状等优化参数，从而得到最佳静态影响函数矩阵以及反演电压矩阵。

The optimization design of control electrode patten for the 13 segment bimorph mirror

The bimorph deformable mirror has its advantages of large strokes, low operating voltage, simple structure and low cost etc.. Using the differential equation describing performances of bimorph mirror deduced by Kokorowski, which satisfies free boundary condition, the static influence function matrix Z(x,y) of bimorph mirror has been calculated with algorithms of Gaussian and Monte Carlo. The low orders of Zernike polynomials are fitted separately with the base of 13 Z(x,y) , and the optimized control electrode patten are presented. The best static influence function matrix and its reverse voltage matrix are derived thereafter.