在单位圆的同心孔径圆域内，某些特定Zernike模式具有相关关系，其中具有较强负相关关系的模式组合在一定系数条件下叠加后，一定的同心孔径内的像差会相互抵消，波面变得更加平坦，这称为模式间的共轭性。文中设置了一组畸变波前，用自适应光学系统进行校正得到残差，然后用Zernike多项式对变形镜的校正残差进行了分解，通过分析首次发现在均方误差值较大的残差波前中，低阶、高阶两部分像差间存在着明显的负相关关系，两部分像差的系数会随着变形镜控制信号的调整体现出有规律的变化，并且在一定的系数组合方式下，这两部分像差呈现出共轭性。基于以上研究结果，提出一种控制方法，该方法通过优化变形镜控制电压来调整镜面面型，使得残差中的低阶、高阶两部分像差系数实现最佳匹配，从而降低光瞳同心孔径圆域内的像差均方根值 (RMS)，最终实现该孔径范围内系统成像质量的提升。分别针对点目标成像和扩展目标成像进行了仿真，结果表明：该方法相比于传统闭环共轭式校正方法，在面对复杂像差时能够得到质量更好的光学成像，有效扩展传统自适应光学系统的适用范围。这种控制方法在变形镜有较大拟合残差的场合具有很好的应用前景。

In the concentric aperture circle of the unit circle, some special Zernike modes have interrelated relationship. When the modes with strong negative correlation is superposed with a certain coefficient, the aberrations in a certain concentric aperture will cancel each other and the wave surface will become smoother. This phenomenon is called the conjugate property between modes. In this paper, a set of distorted wavefront was set up, and the residual error was corrected by adaptive optical system. Then Zernike polynomials were used to decompose the corrected residual of deformable mirror. Through analysis, it was found for the first time that there was an obvious negative correlation between the lower and higher order aberrations in the residual wavefront with large mean square error. The aberration coefficients of the two parts will change regularly with the adjustment of the control signal of the deformable mirror, and in a certain combination of the coefficients, the two parts of aberrations will show conjugation. Based on the above research results, a control method was proposed. By optimizing the control voltage of the deformable mirror, the shape of the mirror surface can be adjusted so that the low-order and high-order aberration coefficients in the residual error can achieve the best matching. In this way, the root mean square (RMS) of the aberration in the concentric aperture circle of the pupil can be reduced, and the imaging quality of the system within this aperture range can be improved. The point target imaging and extended target imaging were simulated respectively. The results show that compared with the traditional closed-loop conjugate correction method, this method can obtain better optical imaging quality in the face of complex aberrations, and can effectively expand the application range of traditional adaptive optical system. This control method has a good application prospect when the deformable mirror has large fitting residual.