提出采用基于变形镜(DM)本征模式的自适应光学波前误差校正方法校正高分辨率空间光学遥感器的在轨波前误差。该方法利用变形镜各致动器的影响函数得到一组符合导数正交关系的变形镜本征模式，以图像功率谱密度在低频区域的积分和为评价函数，根据本征模式系数与评价函数之间的关系直接求解出各阶模式所需的校正量。利用实测的37单元变形镜的影响函数得到变形镜本征模式，基于该模式对泽尼克像差进行了开环和闭环仿真校正，定量分析了相位偏置和图像频率范围对算法精度的影响。针对遥感器主镜镜面热变形误差给出了仿真校正结果，分析了图像噪声和不同遥感图像对算法校正精度的影响。仿真结果表明基于变形镜本征模式的自适应光学校正方法可以有效校正波前误差，算法收敛速度快，对图像噪声和内容不敏感，适合用于空间光学遥感器的波前误差校正。

An adaptive optics wavefront error correction method based on deformable mirror (DM) eigen modes is proposed for high-resolution space optical remote sensors. The influence functions of DM actuators are used to obtain a set of DM eigen modes whose derivatives are orthogonal with each other. The integration of image power spectrum at low spacial frequence area is used as merit function. The required correction amount of each mode is directly solved from the relationship between eigen-mode coefficients and the merit function. The eigen modes are obtained from the 37-channel DM. The correction accuracy of Zernike aberrations is discussed by simulation in open-loop and closed-loop modes. The effect of phase bias and spatial frequency range of image on correction accuracy is analyzed quantitatively. The simulation result of thermal deformations of the primary mirror of optical remote sensor is provided. The influence of image noise and different remote images on the method is discussed. The simulation results show that the method effectively corrects wavefront errors. With the advantage of fast convergence speed and insensitivity to image noise and image content, the DM eigen modes based wavefront error correction method is appropriate for space optical remote sensors.