Decoupling Control Algorithm Based on Laplacian Eigenfunction for Woofer-Tweeter Adaptive Optics System

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 arc orthogonal to themselves and whose first-order partial derivatives arc 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.