High-precision system identification method for a deformable mirror in wavefront control

Based on a mathematic model, the relation between the accuracy of the influence matrix and the performance of the wavefront correction is established. Based on the least squares method, a two-step system identification is proposed to improve the accuracy of the influence matrix, where the measurement noise can be suppressed and the nonlinearity of the deformable mirror can be compensated. The validity of the two-step system identification method is tested in the experiment, where improvements in wavefront correction precision as well as closed-loop control efficiency were observed.