Estimating turbulent phase characteristics in MCAO systems

The presence of atmospheric turbulence heavily affects the resolution of images formed on large ground telescopes. To reduce the atmosphere effect, large telescopes are provided with adaptive optics (AO) systems, which adapt their shape to the current atmospheric turbulence. As shown in recent works the AO systems performance can be significatively improved by taking advantage of the knowledge of the current turbulence characteristics. In this paper we formalize the problem of estimating such turbulence dynamic characteristics by using the measurements provided by a multi-conjugated adaptive optics (MCAO) system. From a temporal dynamics point of view, the turbulence here is represented as the superposition of a finite set of layers, which are characterized by their velocities, energies and altitudes. Taking advantage of a spatial innovation representation of the turbulence, we provide conditions on the identifiability of such parameters and bounds on the estimation errors. Finally, we propose a procedure for the estimation of the turbulence structure (number of layers, their velocities, energies and altitudes) and we test its performances in simulations.