Shape control of piezoelectric deformable mirror by deep neural network-based differential evolution algorithm

Abstract Shape control of multi-channel piezoelectric deformable mirrors presents significant challenges due to nonlinear effects and voltage constraints. This study proposes a deep neural network-based differential evolution (DNN-DE) algorithm to solve the inverse problem of shape control. A DNN is trained on 1000 finite element simulations with randomly generated voltages accurately predicts mirror surface deformations that account for all fine local details. A global optimization DE algorithm interacts with the trained DNN to minimize the root-mean-square (RMS) error function and determine the optimal control voltages for a given target shape. Three representative target surface shapes, Gaussian, elliptical, and arbitrary, are investigated. The corrected surfaces with sub-nanometer RMS errors satisfy diffraction-limited requirements with high adaptability and reproducibility. A comparison with the classical singular value decomposition method based on response functions further validates the robustness of the proposed algorithm. This approach is applicable to various active and adaptive optics without accurate analytical models. Its architecture and training strategy are designed to support generalization implementations in free-electron laser and synchrotron radiation beamlines.