Fractal iterative method for fast atmospheric tomography on extremely large telescopes

Abstract

A challenge of adaptive optics (AO) on Extremely Large Telescopes (ELTs) is to overcome the difficulty of solving a huge number of equations in real time, especially when atmospheric tomography is involved. This is particularly the case for multi-conjugate or multi-objects AO systems. In addition, the quality of the wavefront estimation is crucial to optimize the performances of the future systems in a situation where measurements are missing and noises are correlated. The Fractal Iterative Method has been introduced as a fast iterative algorithm for minimum variance wavefront reconstruction and control on ELTs. This method has been successfully tested on Classical Single Conjugate AO systems on Octopus numerical simulator at ESO. But the minimum variance approach is expected to be mostly useful with atmospheric tomography. We present the first results obtained with FrIM in the context of atmospheric tomography. We recall the principle of the algorithm and we summarize the formalism used for modeling the measurements obtained from laser guide stars that entail spot elongation and tip/tilt indetermination, mixed with low order measurements from natural guide stars. We show the respective effects of tip/tilt indetermination, spot elongation, unseen modes on various configurations, as well as the usefulness of priors and correct noise models in the reconstruction. This analysis is essential for balancing the various errors that combine in a quite complex way and to optimize the configuration of the future AO systems for specific science cases and instrument requirements.