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

Abstract

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.

Filtered Influence Function of Deformable Mirror for Wavefront Correction in Laser Systems

“…With the filtered IF, the control signal of the closed-loop correction could converge to the optimal one, which improves the correction capability of the AO system. Compared with the measurement accuracy improvement methods proposed in [26][27][28], which require multiple IF measurements in the closed-loop correction process, the IFFM requires only a single IF measurement in the precorrection process, making the overall correction process more controllable. Meanwhile, the high precision IF measurement and fitting methods proposed in [29][30][31] could also help improve the closed-loop correction ability, while these methods are implemented with additional high precision surface measuring equipment.…”

“…Some studies have been focused on the improvement of the measurement accuracy of the IF to obtain good wavefront correction capability [26][27][28][29]. An adaptive-influence-matrix (AIM) method was proposed, in which the IF was measured and calibrated multiple times during the closed-loop correction process to improve the measurement accuracy [26].…”

“…This method took the nonlinearity effect of the actuators into consideration while leaving out the random and irregular measurement noise. Then, a two-step high-precision system identification method in wavefront control was proposed [27] with the measurement noise being considered, in which multiple tentative measured wavefronts were used to suppress the measurement noise and obtain optimized influence functions. Besides, a wavefront reconstruction method was proposed [28] to estimate the high-resolution wavefront using multiple wavefront measurements.…”

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

“…Thus, the approach proposed in [31] iteratively calibrates a DM influence function during the correction process. The approach developed in [32] uses a recursive least-squares method to dynamically estimate DM influence function during DM operation. The main limitation of the approaches developed in [31], [32] is that they do not explicitly take into account actuator saturation.…”

“…The approach developed in [32] uses a recursive least-squares method to dynamically estimate DM influence function during DM operation. The main limitation of the approaches developed in [31], [32] is that they do not explicitly take into account actuator saturation. A reliable control method has to take into account actuator physical constraints and has to be able to deal with actuator saturation.…”