Adaptive optics control using model-based reinforcement learning.

Reinforcement learning (RL) presents a new approach for controlling adaptive optics (AO) systems for Astronomy. It promises to effectively cope with some aspects often hampering AO performance such as temporal delay or calibration errors. We formulate the AO control loop as a model-based RL problem (MBRL) and apply it in numerical simulations to a simple Shack-Hartmann Sensor (SHS) based AO system with 24 resolution elements across the aperture. The simulations show that MBRL controlled AO predicts the temporal evolution of turbulence and adjusts to mis-registration between deformable mirror and SHS which is a typical calibration issue in AO. The method learns continuously on timescales of some seconds and is therefore capable of automatically adjusting to changing conditions.

Comparison of methods for the reduction of reconstructed layers in atmospheric tomography.

For the new generation of extremely large telescopes (ELTs), the computational effort for adaptive optics (AO) systems is demanding even for fast reconstruction algorithms. In wide-field AO, atmospheric tomography, i.e., the reconstruction of turbulent atmospheric layers from wavefront sensor data in several directions of view, is the crucial step for an overall reconstruction. Along with the number of deformable mirrors, wavefront sensors and their resolution, as well as the guide star separation, the number of reconstruction layers contributes significantly to the numerical effort. To reduce the computational cost, a sparse reconstruction profile which still yields good reconstruction quality is needed. In this paper, we analyze existing methods and present new approaches to determine optimal layer heights and turbulence weights for the tomographic reconstruction. Two classes of methods are discussed. On the one hand, we have compression methods that downsample a given input profile to fewer layers. Among other methods, a new compression method based on discrete optimization of collecting atmospheric layers to subgroups and the compression by means of conserving turbulence moments is presented. On the other hand, we take a look at a joint optimization of tomographic reconstruction and reconstruction profile during atmospheric tomography, which is independent of any a priori information on the underlying input profile. We analyze and study the qualitative performance of these methods for different input profiles and varying fields of view in an ELT-sized multi-object AO setting on the European Southern Observatory end-to-end simulation tool OCTOPUS.

Efficient reconstruction method for ground layer adaptive optics with mixed natural and laser guide stars.

The imaging quality of modern ground-based telescopes such as the planned European Extremely Large Telescope is affected by atmospheric turbulence. In consequence, they heavily depend on stable and high-performance adaptive optics (AO) systems. Using measurements of incoming light from guide stars, an AO system compensates for the effects of turbulence by adjusting so-called deformable mirror(s) (DMs) in real time. In this paper, we introduce a novel reconstruction method for ground layer adaptive optics. In the literature, a common approach to this problem is to use Bayesian inference in order to model the specific noise structure appearing due to spot elongation. This approach leads to large coupled systems with high computational effort. Recently, fast solvers of linear order, i.e., with computational complexity O(n), where n is the number of DM actuators, have emerged. However, the quality of such methods typically degrades in low flux conditions. Our key contribution is to achieve the high quality of the standard Bayesian approach while at the same time maintaining the linear order speed of the recent solvers. Our method is based on performing a separate preprocessing step before applying the cumulative reconstructor (CuReD). The efficiency and performance of the new reconstructor are demonstrated using the OCTOPUS, the official end-to-end simulation environment of the ESO for extremely large telescopes. For more specific simulations we also use the MOST toolbox.

Finite element-wavelet hybrid algorithm for atmospheric tomography.

Reconstruction of the refractive index fluctuations in the atmosphere, or atmospheric tomography, is an underlying problem of many next generation adaptive optics (AO) systems, such as the multiconjugate adaptive optics or multiobject adaptive optics (MOAO). The dimension of the problem for the extremely large telescopes, such as the European Extremely Large Telescope (E-ELT), suggests the use of iterative schemes as an alternative to the matrix-vector multiply (MVM) methods. Recently, an algorithm based on the wavelet representation of the turbulence has been introduced in [Inverse Probl.29, 085003 (2013)] by the authors to solve the atmospheric tomography using the conjugate gradient iteration. The authors also developed an efficient frequency-dependent preconditioner for the wavelet method in a later work. In this paper we study the computational aspects of the wavelet algorithm. We introduce three new techniques, the dual domain discretization strategy, a scale-dependent preconditioner, and a ground layer multiscale method, to derive a method that is globally O(n), parallelizable, and compact with respect to memory. We present the computational cost estimates and compare the theoretical numerical performance of the resulting finite element-wavelet hybrid algorithm with the MVM. The quality of the method is evaluated in terms of an MOAO simulation for the E-ELT on the European Southern Observatory (ESO) end-to-end simulation system OCTOPUS. The method is compared to the ESO version of the Fractal Iterative Method [Proc. SPIE7736, 77360X (2010)] in terms of quality.