Abstract
We build on a long-standing tradition in astronomical adaptive optics (AO) of specifying performance metrics and error budgets using linear systems modeling in the spatial-frequency domain. Our goal is to provide a comprehensive tool for the calculation of error budgets in terms of residual temporally filtered phase power spectral densities and variances. In addition, the fast simulation of AO-corrected point spread functions (PSFs) provided by this method can be used as inputs for simulations of science observations with next-generation instruments and telescopes, in particular to predict post-coronagraphic contrast improvements for planet finder systems. We extend the previous results presented in Correia and Teixeira [J. Opt. Soc. Am. A 31, 2763 (2014)] to the closed-loop case with predictive controllers and generalize the analytical modeling of Rigaut et al. [Proc. SPIE 3353, 1038 (1998)], Flicker [Technical Report (W. M. Keck Observatory, 2007)], and Jolissaint [J. Eur. Opt. Soc. 5, 10055 (2010)]. We follow closely the developments of Ellerbroek [J. Opt. Soc. Am. A 22, 310 (2005)] and propose the synthesis of a distributed Kalman filter to mitigate both aniso-servo-lag and aliasing errors while minimizing the overall residual variance. We discuss applications to (i) analytic AO-corrected PSF modeling in the spatial-frequency domain, (ii) post-coronagraphic contrast enhancement, (iii) filter optimization for real-time wavefront reconstruction, and (iv) PSF reconstruction from system telemetry. Under perfect knowledge of wind velocities, we show that ~60 nm rms error reduction can be achieved with the distributed Kalman filter embodying antialiasing reconstructors on 10 m class high-order AO systems, leading to contrast improvement factors of up to three orders of magnitude at few ?/D separations (~1 - 5?/D) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.

Abstract
Knowledge of the atmospheric turbulence in the telescope line-of-sight is crucial for widefield observations assisted by adaptive optics (AO), particularly tomodel how the point spread function (PSF) elongates across the field of view(FOV) owing to the anisoplanatism effect. The extraction of key astronomical parameters accounts on an accurate representation of the PSF, which call for an accurate anisoplanatism characterisation . This one is, however, a function of the Cn2(h) profile, which is not directly accessible from single-conjugate AO telemetry. It is possible to rely on external profilers, but recent studies have highlighted discrepancies of more than 10 per cent with AO internal measurements, while we aim at better than 1 per cent accuracy for PSF modelling. In order to tackle this limitation, we present focal-plane profiling (FPP) as a Cn2(h) profiling method that relies on post-AO focal-plane images.We demonstrate that such an approach complies with a 1 per cent level of accuracy on the Cn2(h) estimation and establish how this accuracy varies regarding the calibration star magnitudes and their positions in the field. We highlight the fact that photometry and astrometry errors caused by PSF mis-modelling reach respectively 1 per cent and 50 µas using FPP on a Keck baseline, with a preliminary calibration using a star of magnitude H = 14 at 20 arcsec. We validate this concept using Canada's NRC-Herzberg HeNOS testbed images by comparing FPP retrieval with alternative Cn2 (h) measurements on HeNOS. The FPP approach allows the Cn2(h) to be profiled using the SCAO systems and significantly improves the PSF characterization. Such a methodology is also ELT-size-compliant and will be extrapolated to tomographic systems in the near future.

Abstract

Abstract
Tomographic wavefront reconstruction is the main computational bottleneck to realize real-time correction for turbulence-induced wavefront aberrations in future laser-assisted tomographic adaptive-optics (AO) systems for ground-based giant segmented mirror telescopes because of its unprecedented number of degrees of freedom, N, i.e., the number of measurements from wavefront sensors. In this paper, we provide an efficient implementation of the minimum-mean-square error (MMSE) tomographic wavefront reconstruction, which is mainly useful for some classes of AO systems not requiring multi-conjugation, such as laser-tomographic AO, multi-object AO, and ground-layer AO systems, but is also applicable to multi-conjugate AO systems. This work expands that by Conan [Proc. SPIE 9148, 91480R (2014)] to the multi-wavefront tomographic case using natural and laser guide stars. The new implementation exploits the Toeplitz structure of covariance matrices used in an MMSE reconstructor, which leads to an overall ON log N real-time complexity compared with ON2 of the original implementation using straight vector-matrix multiplication. We show that the Toeplitz-based algorithm leads to 60 nm rms wavefront error improvement for the European Extremely Large Telescope laser-tomography AO system over a well-known sparse-based tomographic reconstruction; however, the number of iterations required for suitable performance is still beyond what a real-time system can accommodate to keep up with the time-varying turbulence.

Abstract
Adaptive optics (AO) restore the angular resolution of ground-based telescopes, but at the cost of delivering a time- and space-varying point spread function (PSF) with a complex shape. PSF knowledge is crucial for breaking existing limits on the measured accuracy of photometry and astrometry in science observations. In this paper, we concentrate our analyses of the anisoplanatism signature only on to the PSF. For large-field observations (20 arcmin) with single-conjugated AO, PSFs are strongly elongated due to anisoplanatism that manifests itself as three different terms for laser guide star (LGS) systems: angular, focal and tilt anisoplanatism. First, we propose a generalized model that relies on a point-wise decomposition of the phase and encompasses the non-stationarity of LGS systems. We demonstrate that it is more accurate and less computationally demanding than existing models: it agrees with end-to-end physical-optics simulations to within 0.1 per cent of PSF measurables, such as the Strehl ratio, FWHM and the fraction of variance unexplained (FVU). Secondly, we study off-axis PSF modelling with respect to the Cn2(h) profile (heights and fractional weights). For 10-mclass telescopes, PSF morphology is estimated at the 1 per cent level as long as we model the atmosphere with at least seven layers, whose heights and weights are known with precisions of 200 m and 10 per cent, respectively. As a verification test, we used the Canada's National Research Council - Herzberg NFIRAOS Optical Simulator (HeNOS) testbed data, featuring four lasers. We highlight the capability of retrieving off-axis PSF characteristics within 10 per cent of the FVU, which complies with the expected range from the sensitivity analysis. Our new off-axis PSF modelling method lays the groundwork for testing on-sky in the near future.

Abstract
The latest generation of high-contrast instruments dedicated to exoplanets and circumstellar disk imaging are equipped with extreme adaptive optics and coronagraphs to reach contrasts of up to 10 -4 at a few tenths of arcseconds in the near-infrared. The resulting image shows faint features, only revealed with this combination, such as the wind driven halo. The wind driven halo is due to the lag between the adaptive optics correction and the turbulence speed over the telescope pupil. However, we observe an asymmetry of this wind driven halo that was not expected when the instrument was designed. In this letter, we describe and demonstrate the physical origin of this asymmetry and support our explanation by simulating the asymmetry with an end-To-end approach. From this work, we find that the observed asymmetry is explained by the interference between the AO-lag error and scintillation effects, mainly originating from the fast jet stream layer located at about 12 km in altitude. Now identified and interpreted, this effect can be taken into account for further design of high-contrast imaging simulators, next generation or upgrade of high-contrast instruments, predictive control algorithms for adaptive optics, or image post-processing techniques.