Towards analytical model optimization in atmospheric tomography

Modern ground-based telescopes rely on a technology called adaptive optics in order to compensate for the loss of angular resolution caused by atmospheric turbulence. Next-generation adaptive optics systems designed for a wide field of view require a stable and high-resolution reconstruction of the turbulent atmosphere. By introducing a novel Bayesian method, we address the problem via reconstructing the atmospheric turbulence strength profile and the turbulent layers simultaneously, where we only use wavefrontmeasurements of incoming light from guide stars. Most importantly, we demonstrate how this method can be used for model optimization as well. We propose two different algorithms for solving the maximum a posteriori estimate: the first approach is based on alternating minimization and has the advantage of integrability into existing atmospheric tomography methods. In the second approach, we formulate a convex non-differentiable optimization problem, which is solved by an iterative thresholding method. This approach clearly illustrates the underlying sparsity-enforcing mechanism for the strength profile. By introducing a tuning/regularization parameter, an automated model reduction of the layer structure of the atmosphere is achieved. Using numerical simulations, we demonstrate the performance of our method in practice. Copyright (C) 2016 JohnWiley & Sons, Ltd.