An efficient solution to the atmospheric turbulence tomography problem using Kaczmarz iteration

The planned new generation of extremely large telescopes requires highly efficient algorithms for its adaptive optics systems. We present a new reconstruction approach for multi-conjugate adaptive optics or multi-object adaptive optics that computes the mirror shapes without the use of matrix–vector multiplications. The method solves the involved subproblems—wavefront reconstruction, atmospheric tomography and determination of the mirror shapes—sequently. In this paper, we focus on highly efficient algorithms for the atmospheric tomography and the computation of the mirror shape. Finally, we estimate the complexity of the method and provide some numerical examples, including a comparison of our approach to the standard Tikhonov regularization and minimum variance reconstructors.