为消除变形镜的建模误差, 提出了基于在线最小二乘支持向量机的变形镜建模方法。首先, 分析了温度和驱动器非线性等因素对变形镜响应矩阵的影响; 然后, 介绍了最小二乘支持向量机及在线更新的原理, 并将其引入97单元变形镜的集成仿真模型。根据变形镜不断更新的运行数据, 最小二乘支持向量机进行在线训练和模型更新, 构建当前状态变形镜的等效模型, 并输出下一时刻的电压预报值。仿真结果表明: 基于在线最小二乘支持向量机的变形镜建模方法摆脱了固定模型的约束, 具有自适应更新的特点, 稳健性好, 控制电压预测精度高, 有利于提高自适应光学系统的控制精度。

The least square support vector machine (LSSVM) was applied for the online modeling of the deformable mirror, and it could be used to forecast the wavefront control voltage at the same time. The drift characteristic of the response matrix was analyzed in the beginning, which attribute mainly to the temperature varying and nonlinearity of the actuator, and the principle of the LSSVM and its updating mechanism were introduced in the following. The optical and electro-mechanical integrated model was built in the early stage for the study of the deformable mirror, and the LSSVM model was combined into the simulation model. When the deformable mirror run in the integrated model, the control voltages and the surface profile data were collected. The data were send to the LSSVM model for the online training and updating, and the control voltages for the following step were predicted by the LSSVM model at the same time. The deformable mirror which employing 97 actuators was taken as an example to illustrate the above processes, and the simulation results were presented in details. It could conclude that the LSSVM use for the online modeling of the control voltage of the deformable mirror is adaptive and self-refreshing, so it could improve the control precision of the adaptive optical system.上海技术物理研究所创新基金(2014-CX25)