Context. Adaptive optics (AO) systems greatly increase the resolution of large telescopes, but produce complex point spread function (PSF) shapes, varying in time and across the field of view. The PSF must be accurately known since it provides crucial information about optical systems for design, characterization, diagnostics, and image post-processing. Aims. We develop here a model of the AO long-exposure PSF, adapted to various seeing conditions and any AO system. This model is made to match accurately both the core of the PSF and its turbulent halo.Methods. The PSF model we develop is based on a parsimonious parameterization of the phase power spectral density, with only five parameters to describe circularly symmetric PSFs and seven parameters for asymmetrical ones. Moreover, one of the parameters is the Fried parameter r 0 of the turbulence's strength. This physical parameter is an asset in the PSF model since it can be correlated with external measurements of the r 0 , such as phase slopes from the AO real time computer (RTC) or site seeing monitoring. Results. We fit our model against end-to-end simulated PSFs using the OOMAO tool, and against on-sky PSFs from the SPHERE/ZIMPOL imager and the MUSE integral field spectrometer working in AO narrow-field mode. Our model matches the shape of the AO PSF both in the core and the halo, with a relative error smaller than 1% for simulated and experimental data. We also show that we retrieve the r 0 parameter with sub-centimeter precision on simulated data. For ZIMPOL data, we show a correlation of 97% between our r 0 estimation and the RTC estimation. Finally, MUSE allows us to test the spectral dependency of the fitted r 0 parameter. It follows the theoretical λ 6/5 evolution with a standard deviation of 0.3 cm. Evolution of other PSF parameters, such as residual phase variance or aliasing, is also discussed.

Context. Here we describe a simple, efficient, and most importantly fully operational point-spread-function(PSF)-reconstruction approach for laser-assisted ground layer adaptive optics (GLAO) in the frame of the Multi Unit Spectroscopic Explorer (MUSE) Wide Field Mode. Aims. Based on clear astrophysical requirements derived by the MUSE team and using the functionality of the current ESO Adaptive Optics Facility we aim to develop an operational PSF-reconstruction (PSFR) algorithm and test it both in simulations and using on-sky data.Methods. The PSFR approach is based on a Fourier description of the GLAO correction to which the specific instrumental effects of MUSE Wide Field Mode (pixel size, internal aberrations, etc.) have been added. It was first thoroughly validated with full end-to-end simulations. Sensitivity to the main atmospheric and AO system parameters was analysed and the code was re-optimised to account for the sensitivity found. Finally, the optimised algorithm was tested and commissioned using more than one year of on-sky MUSE data. Results. We demonstrate with an on-sky data analysis that our algorithm meets all the requirements imposed by the MUSE scientists, namely an accuracy better than a few percent on the critical PSF parameters including full width at half maximum and global PSF shape through the kurtosis parameter of a Moffat function. Conclusions. The PSFR algorithm is publicly available and is used routinely to assess the MUSE image quality for each observation. It can be included in any post-processing activity which requires knowledge of the PSF.

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 on anisoplanatism signature only onto PSF: for large-field observations (20") with singleconjugated 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. 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 it is more accurate and less computationally demanding than existing models: it agrees with end-to-end physical-optics simulations to within 0.1% of PSF measurables, such as Strehl-ratio, FWHM and fraction of variance unexplained. Secondly, we study off-axis PSF modelling is with respect to C 2 n (h) profile (heights and fractional weights). For 10 m class telescope, PSF morphology is estimated at 1%-level as long as we model the atmosphere with at least 7 layers whose heights and weights are known respectively with 200m and 10%-precision. As a verification test we used the Canada's NRC-Herzberg HeNOS testbed data, featuring four lasers. We highlight capability of retrieving off-axis PSF characteristics within 10% of fraction of variance unexplained, which complies with the expected range from the sensitivity analysis. Our new off-axis PSF modelling method lays the ground-work for testing on-sky in the near future. *

In order to enhance accuracy of astrophysical estimates obtained on Adaptive-optics (AO) images, such as photometry and astrometry, we investigate a new concept to constrain the Point Spread Function (PSF) model called PSF Reconstruction and Identification for Multi-sources characterization Enhancement (PRIME), that handles jointly the science image and the AO control loop data. We present in this paper the concept of PRIME and validate it on Keck II telescope NIRC2 images. We show that by calibrating the PSF model over the scientific image, PSF reconstruction achieves 1% and 3 mas of accuracy on respectively the Strehl-ratio and the PSF full width at half maximum. We show on NIRC2 binary images that PRIME is sufficiently robust to noise to retain photometry and astrometry precision below 0.005 mag and 100µas on a mH = 14 mag object. Finally, we also validate that PRIME performs a PSF calibration on the triple system Gl569BAB which provides a separation of 66.73±1.02 and a differential photometry of 0.538±0.048, compared to the reference values obtained with the extracted PSF which are 66.76 mas ± 0.94 and 0.532 mag ± 0.041. *

Advanced adaptive optics (AO) instruments on ground-based telescopes require accurate knowledge of the atmospheric turbulence strength as a function of altitude. This information assists point spread function reconstruction, AO temporal control techniques and is required by wide-field AO systems to optimise the reconstruction of an observed wavefront. The variability of the atmosphere makes it important to have a measure of the optical turbulence profile in real-time. This measurement can be performed by fitting an analytically generated covariance matrix to the cross-covariance of Shack-Hartmann wavefront sensor (SHWFS) centroids. In this study we explore the benefits of reducing cross-covariance data points to a covariance map region of interest (ROI). A technique for using the covariance map ROI to measure and compensate for SHWFS misalignments is also introduced. We compare the accuracy of covariance matrix and map ROI optical turbulence profiling using both simulated and on-sky data from CANARY, an AO demonstrator on the 4.2 m William Herschel telescope, La Palma. On-sky CANARY results are compared to contemporaneous profiles from Stereo-SCIDAR -a dedicated high-resolution optical turbulence profiler. It is shown that the covariance map ROI optimises the accuracy of AO telemetry optical turbulence profiling. In addition, we show that the covariance map ROI reduces the fitting time for an extremely large telescope-scale system by a factor of 72. The software package we developed to collect all of the presented results is now open-source.

Context. Modeling the optical point spread function (PSF) is particularly challenging for adaptive optics (AO)-assisted observations owing to the its complex shape and spatial variations. Aims. We aim to (i) exhaustively demonstrate the accuracy of a recent analytical model from comparison with a large sample of imaged PSFs, (ii) assess the conditions for which the model is optimal, and (iii) unleash the strength of this framework to enable the joint estimation of atmospheric parameters, AO performance and static aberrations. Methods. We gathered 4812 on-sky PSFs obtained from seven AO systems and used the same fitting algorithm to test the model on various AO PSFs and diagnose AO performance from the model outputs. Finally, we highlight how this framework enables the characterization of the so-called low wind effect on the Spectro-Polarimetic High contrast imager for Exoplanets REsearch (LWE; SPHERE) instrument and piston cophasing errors on the Keck II telescope. Results. Over 4812 PSFs, the model reaches down to 4% of error on both the Strehl-ratio (SR) and full width at half maximum (FWHM). We particularly illustrate that the estimation of the Fried’s parameter, which is one of the model parameters, is consistent with known seeing statistics and follows expected trends in wavelength using the Multi Unit Spectroscopic Explorer instrument (λ6/5) and field (no variations) from Gemini South Adaptive Optics Imager images with a standard deviation of 0.4 cm. Finally, we show that we can retrieve a combination of differential piston, tip, and tilt modes introduced by the LWE that compares to ZELDA measurements, as well as segment piston errors from the Keck II telescope and particularly the stair mode that has already been revealed from previous studies. Conclusions. This model matches all types of AO PSFs at the level of 4% error and can be used for AO diagnosis, post-processing, and wavefront sensing purposes.

The Adaptive Optics (AO) performance significantly depends on the available Natural Guide Stars (NGSs) and a wide range of atmospheric conditions (seeing, Cn2, windspeed, . . . ). In order to be able to easily predict the AO performance, we have developed a fast algorithm -called TIPTOP -producing the expected AO Point Spread Function (PSF) for any of the existing AO observing modes (SCAO, LTAO, MCAO, GLAO), and any atmospheric conditions. This TIPTOP tool takes its roots in an analytical approach, where the simulations are done in the Fourier domain. This allows to reach a very fast computation time (few seconds per PSF), and efficiently explore the wide parameter space. TIPTOP has been developed in Python, taking advantage of previous work developed in different languages, and unifying them in a single framework. The TIPTOP app is available on GitHub at: https://github.com/FabioRossiArcetri/TIPTOP, and will serve as one of the bricks for the ELT Exposure Time Calculator.

Determining the PSF remains a key challenge for post adaptive-optics (AO) observations regarding the spatial, temporal and spectral variabilities of the AO PSF, as well as itx complex structure. This paper aims to provide a non-exhaustive but classified list of techniques and references that address this issue of PSF determination, with a particular scope on PSF reconstruction, or more generally pupil-plane-based approaches. We have compiled a large amount of references to synthesize the main messages and kept them at a top level. We also present applications of PSF reconstruction/models to post-processing, more especially PSF-fitting and deconvolution for which there is a fast progress in the community.