Sparse calibration of an extreme Adaptive Optics system

Adaptive optics systems are extensively used in astronomy to obtain high resolution pictures of stars and galaxies with ground telescopes. The crucial point is to shape deformable mirrors in order to compensate for the incoming wave distorted by the atmospheric turbulence. The calibration of the system is the cornerstone to obtain good performance. The next generation of adaptive optics system, eXtreme Adaptive Optics (XAO), will have a very large number of actuators and sensors (~ 10^4) in order to guarantee high Strehl ratio and contrast levels; as such computational burden could become a serious bottleneck. For this reason several iterative methods have been proposed in the last decade. Since convergence and computational complexity of these methods depend on the sparsity of the interaction matrix (matrix projecting commands into measurements), the problem of calibrating an XAO system forcing the interaction matrix to be as sparse as possible is clearly important. In this paper we propose a method based on the LASSO regression algorithm that solves efficiently this problem.