Abstract
Using Fourier methods to reconstruct the phase measured by a wavefront sensor (WFS) can significantly re- duce the number of computations required, as well as easily enable predictive reconstruction methods based on knowledge of the adaptive optics system, atmospheric turbulence and wind profile. Previous work on Fourier re- construction has focused on the Shack-Hartmann WFS. With increasing interest in the highly sensitive Pyramid WFS we present the development of Fourier reconstruction tools tailored to the Pyramid sensor. We include the development of the Fourier model, it's use for formulating error budgets and a laboratory demonstration of Fourier reconstruction with a Pyramid WFS.

Abstract
SLODAR (SLOpe Detection And Ranging) methods recover the atmospheric turbulence profile from cross-correlations of wavefront sensor (WFS) measurements, based on known turbulence models. Our work grows out of several experiments showing that turbulence statistics can deviate significantly from the classical Kolmogorov/ von Kármán models, especially close to the ground. We present a novel SLODAR-type method which simultaneously recovers both the turbulence profile in the atmosphere and the turbulence statistics at the ground layer - namely the slope of the spatial frequency power law. We consider its application to outer scale (L0)- reconstruction and investigate the limits of the joint estimation of such parameters.

Abstract
While deep learning has led to breakthroughs in many areas of computer science, its power has yet to be fully exploited in the area of adaptive optics (AO) and astronomy as a whole. In this paper we describe the first steps taken to apply deep, convolutional neural networks to the problem of wavefront reconstruction and prediction and demonstrate their feasibility of use in simulation. Our preliminary results show we are able to reconstruct wavefronts comparably well to current state of the art methods. We further demonstrate the ability to predict future wavefronts up to five simulation steps with under 1nm RMS wavefront error.

Abstract
The performance of an Adaptive Optics (AO) System relies on the accuracy of its Interaction Matrix which defines the opto-geometrical link between the Deformable Mirror (DM) and the Wave Front Sensor (WFS). Any mis-registrations (relative shifts, rotation, magnification or higher order pupil distortion) will strongly impact the performance, especially for high orders AO systems. Adaptive Telescopes provide a constraining environment for the AO calibration with large number of actuators DM, located inside the telescope with often no access to a calibration source and with a high accuracy required. The future Extremely Large Telescope (ELT) will take these constraints to another level with a longer calibration time required, no artificial calibration source and most of all, frequent updates of the calibration during the operation. To overcome these constraints, new calibration strategies have to be developed either doing it on-sky or working with synthetic models. The most promising approach seems to be the Pseudo-Synthetic Calibration. The principle is to generate the Interaction Matrix of the system in simulator, injecting the correct model alignment parameters identified from on-sky Measurements. It is currently the baseline for the Adaptive Optics Facility (AOF) at the Very Large Telescope (VLT) working with a Shack-Hartmann WFS but it remains to be investigated in the case of the Pyramid WFS.

Abstract
Geared by the increasing need for enhanced performance, both optical and computational, new dynamic control laws have been researched in recent years for next generation adaptive optics systems on current 10 m-class and extremely large telescopes up to 40 m. We provide an overview of these developments and point out prospects to making such controllers drive actual systems on-sky.

Abstract
Shack-Hartmann wavefront sensing relies on accurate spot centre measurement. Several algorithms were developed with this aim, mostly focused on precision, i.e. minimizing random errors. In the solar and extended scene community, the importance of the accuracy (bias error due to peak-locking, quantization, or sampling) of the centroid determination was identified and solutions proposed. But these solutions only allow partial bias corrections. To date, no systematic study of the bias error was conducted. This article bridges the gap by quantifying the bias error for different correlation peak-finding algorithms and types of sub-aperture images and by proposing a practical solution to minimize its effects. Four classes of sub-aperture images (point source, elongated laser guide star, crowded field, and solar extended scene) together with five types of peak-finding algorithms (1D parabola, the centre of gravity, Gaussian, 2D quadratic polynomial, and pyramid) are considered, in a variety of signal-to-noise conditions. The best performing peak-finding algorithm depends on the sub-aperture image type, but none is satisfactory to both bias and random errors. A practical solution is proposed that relies on the antisymmetric response of the bias to the sub-pixel position of the true centre. The solution decreases the bias by a factor of similar to 7 to values of less than or similar to 0.02 pix. The computational cost is typically twice of current cross-correlation algorithms.