Static modeling for membrane deformable mirror used in high-power laser

The technology of membrane deformable mirror (DMs) that has the potential to achieve comprehensive wavefront compensation and control in high power laser has been developed rapidly in recent years. Experimental results reveal that strong nonlinearity is induced to the deformation of DMs with respect to the square of input voltage when operating voltage is more than 120V. The nonlinear response and strong coupling effect of control channel in DMs make it difficult to obtain the desired mirror surface shapes. A test bed is built up to measure the deformation of DMs driven by specified voltages. An efficient nonlinear model of deformation with respect to input voltages is presented using a back propagation neural network (BPNN). Deformation due to arbitrary actuator voltages applied to actuators to correct wavefront aberration can be calculated directly with a higher precision using the BPNN model proposed. The residual relative error of the proposed model shows the improvement of accuracy of an order about 5 as compared to that of linear model, and with no significant increase of time consumption. A preliminary open-loop control experiment of laser wavefront compensation is performed to exam the validity of applying the proposed BPNN model in laser wavefront compensation application.