Authors

C. Béchet, É. Thiébaut, M. Tallon, J. Kolb, P-Y. Madec

Affiliations

1,4,5: European Southern Observatory, Germany 2,3: Centre de Recherche astrophysique de Lyon, France

Abstract

The E-ELT will be equipped with a deformable mirror inside the telescope. The performance of reconstruction and control depends on the calibration of the interaction matrix- or a model of the interaction matrix- , which characterizes the system and the relationship between the commands sent to the deformable mirrors (DM) and the wavefront sensors (WFS) slopes. Such a calibration will be more complex than for the current systems at the VLT since it will have to be at least partly measured on sky and for a much larger number of degrees of freedom (more than 5000). In addition, gravity or temperature variations for instance are likely to introduce slow evolution of the matching between the M4 Deformable mirror and the WFS geometry. This can occur during observations and therefore degrade the adaptive optics (AO) correction. To relax the need of frequent painful calibrations and to prevent a loss of performance due to misregistrations, we investigate how to track the evolution of the interaction matrix errors in closed-loop without introducing any degradation in the observations. This is done thanks to identification methods and optimization theory.

First, we formally describe the problem and the difficulties of such an identification in closed-loop configuration. Then, we present 2 solutions, based on the optimization of the error of estimates of the WFS slopes, at the output of the closed-loop AO. The performance of the methods and their limitations are discussed formally and thanks to numerical simulations of a high order AO system. We finally explore to which extent these methods currently studied for the Adaptive Optics Facility (AOF) at the VLT can be applied to the E-ELT.