Abstract
The SPHERE instrument, dedicated to high contrast imaging on VLT, has been routinely operated for more than 3 years, over a large range of conditions and producing observations from visible to NIR. A central part of the instrument is the high order adaptive optics system, named SAXO, designed to deliver high Strehl image quality with a balanced performance budget for bright stars up to magnitude R=9. We take benefit now from the very large set of observations to revisit the assumptions and analysis made at the time of the design phase: We compare the actual AO behavior as a function of expectations. The data set consists of the science detector data, for both coronagraphic images and non-coronagraphic PSF calibrations, but also of AO internal data from the high frequency sensors and statistics computations from the real-time computer which are systematically archived, and finally of environmental data, monitored at VLT level. This work is supported and made possible by the SPHERE Data Center infrastructure hosted at Grenoble which provides an efficient access and the capability for the homogeneous analysis of this large and statistically-relevant data set. We review in a statistical manner the actual AO performance as a function of external conditions for different regimes and we discuss the possible performance metrics, either derived from AO internal data or directly from the high contrast images. We quantify the dependency of the actual performance on the most relevant environmental parameters. By comparison to earlier expectations, we conclude on the reliability of the usual AO modeling. We propose some practical criteria to optimize the queue scheduling and the expression of observer requirements; finally, we revisit what could be the most important AO specifications for future high contrast imagers as a function of the primary science goals, the targets and the turbulence properties.

Abstract
Scientific exploitation in ground-based astronomy is improved thanks to adaptive optics (AO) that restore diffraction-limit angular resolution. Besides, the ultimate data interpretation is delivered by post-processing techniques that usually relies on a Point spread function (PSF) model. Nevertheless, existing methods to constrain this model based on standard pipeline encounter the spatial and time variations of the AO PSF. In order to improve accuracy on key science observables, such as photometry and astrometry, alternative methods are investigated, such as PSF reconstruction (PSF-R), designed to estimate the PSF from AO control-loop data and key atmosphere and system parameters. We aim in this paper at retrieving directly these relevant inputs we need to reconstruct the PSF using an hybrid approach, that couples AO telemetry with focal plane images, named as Focal plane profiling and reconstruction (FPPR). It adjusts atmosphere parameters (the C2n (h) profile) and optical gains in the system. We describe the FPPR method that is applied to on-sky Keck images in engineering mode operated with either natural or laser guide star and show we get 1% of accuracy on respectively the Strehl-ratio and the PSF FWHM reconstruction.

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.