Kalman-filter-based optimal control law for star-oriented and layer-oriented multiconjugate adaptive optics

We first recall in this paper the optimal closed loop control law for multiconjugate adaptive optics [MCAO]. It is based on a Kalman filter and a feedback control. The prior model on which is based the Kalman filter is developped in a state-space representation and the differences in the model between Star Oriented [SO] MCAO and Layer Oriented [LO] MCAO are presented. This approach allows to take into account the wavefront sensing noise, the turbulence profil model, the Kolmogorov statistics and a temporal model of the turbulence. Simulation results are given in SO MCAO and the Kalman based approach is compared to the more standard Optimized Modal Gain Integrator [OMGI].