Closing the loop as an inverse problem: the real-time control of THEMIS adaptive optics

Adaptive Optics Systems VIII, Jul 2022, Montr{\'e}al, Canada. pp.1218507 We have taken advantage of the implementation of an adaptive optics system on the Themis solar telescope to implement innovative strategies based on an inverse problem formulation for the control loop. Such an approach encompassing the whole system implies the estimation of the pixel variances of the Shack-Hartmann wavefront sensor, a novel real-time method to extract the wavefront slopes as well as their associated noise covariance, and the computation of pseudo-open loop data. The optimal commands are computed by iteratively solving a regularized inverse problem with spatio-temporal constraints including Kolmogorov statistics. The latency of the dedicated real-time control software with conventional CPU is shorter than 300 $\mu$s from the acquisition of the raw 400 x 400 pixel wavefront sensor image to the sending of the commands.