Model Predictive Control of Time-Varying Aberrations for Sensorless Adaptive Optics

We propose a model predictive control (MPC) method to compensate for the time-varying phase aberrations in a sensorless adaptive optics (AO) system. The approximate model for the point spread function (PSF) of the imaging system with phase diversity is mathematically derived, and its validity is verified. The proposed MPC, which considers the operating limits of the deformable mirror (DM), computes the optimal applied voltage of each actuator over a prediction horizon, and the receding horizon scheme is applied as feedback control. Numerical case studies with the time-varying phase aberrations generated by an atmospheric turbulence simulator are presented to demonstrate the correction performance of the MPC strategy. The proposed method caused a 50% improvement in the reduction in residual aberration, making it competitive with a saturation linear quadratic regulator (LQR). The computational feasibility of the proposed method is validated using fast MPC, which approximates the primal barrier method.