<title>Optimal phase reconstruction in large field of view: application to multiconjugate adaptive optics systems</title>

Abstract

We propose an optimal approach for the phase reconstruction in a large Field Of View (FOV) for Multiconjugate Adaptive Optics (MCAO). This optimal approach is based on a Minimal Mean Square Error (MMSE) estimator that minimizes the mean residual phase variance in the FOV of interest. It accounts for the C<SUB>n</SUB><SUP>2</SUP> profile in order to optimally estimate the correction wavefront to be applied to each DM. This optimal approach also accounts for the fact that the number of DM will always be smaller than the number of turbulent layers since the C<SUB>n</SUB><SUP>2</SUP> profile is a continuous function of the altitude h. Links between this optimal approach and a tomographic reconstruction of the turbulence volume are established. In particular, it is shown that the optimal approach consist in a full tomographic reconstruction of the turbulence volume followed by a projection on the deformable mirrors accounting for the considered FOV of interest. The case where the turbulent layers are assumed to match the mirror positions (model- approximation approach), which might be a crude approximation, is also considered for comparison. This model-approximation approach will rely on the notion of equivalent turbulent layers. A comparison between the optimal and model-approximation approach is proposed. It is shown that the optimal approach provides very good performance even with small number of DM's (typically one of two). Accurate results are obtained, on simulation for a 4- m telescope on a 150 x 150 arcseconds FOV only using 3 guide stars and 2 DM.