为了实现对Woofer-Tweeter双变形镜自适应光学系统的解耦控制, 提出了一种基于拉普拉斯本征函数的解耦控制算法。通过求解不同齐次Neumann边界条件下的拉普拉斯本征方程, 获得不同光瞳区域下自身和一阶偏导数均正交的拉普拉斯本征函数。利用不同光瞳区域下的拉普拉斯本征函数, 实现了对不同光瞳区域下Woofer-Tweeter双变形镜自适应光学系统的解耦控制。此外, 拉普拉斯本征函数的一阶偏导数具备正交性, 这使得在构建Tweeter耦合抑制矩阵时无需对Tweeter驱动器响应函数面形进行逐个测量, 极大简化了Tweeter耦合抑制矩阵的构造过程。采用Woofer-Tweeter双变形镜自适应光学系统对该算法的有效性进行了实验验证, 结果表明：基于拉普拉斯本征函数的解耦控制算法能够实现对Woofer和Tweeter同步控制, 并能有效地抑制Woofer和Tweeter之间的耦合误差。

In order to realize the decoupling control for the Woofer-Tweeter adaptive optics system, we propose a decoupling control algorithm based on Laplacian eigenfunction. By solving Laplacian eigen equations under different homogeneous Neumann boundary conditions, we can obtain Laplacian eigenfunctions which are orthogonal to themselves and whose first-order partial derivatives are orthogonal under different pupil regions. Using the Laplacian eigenfunctions under different pupil regions, we achieve the decoupling control for the Woofer-Tweeter adaptive optics system in different pupil regions. In addition, the first-order partial derivatives of the Laplacian eigenfunction is orthogonality, so that it is not necessary to measure the response function surface shape of Tweeter actuator to construct a constraint matrix for Tweeter. A Woofer-Tweeter adaptive optics system is used to verify the validity of this algorithm. The experimental results show that the decoupling control algorithm based on Laplacian eigenfunctions can synchronously control Woofer and Tweeter, and effectively suppress the coupling error between Woofer and Tweeter.