The SAXO+ upgrade of the VLT/SPHERE adaptive optics system introduces a second-stage near-infrared pyramid wavefront sensor to improve high-contrast imaging, making accurate calibration of non-common path aberrations (NCPAs) essential to fully exploit its performance. This work refines the expected level of NCPAs in SAXO+ and presents the calibration procedures developed for static NCPA compensation and focal-plane dark-hole control. Monte Carlo simulations based on an updated Zemax optical model were used to estimate the NCPA error budget. These simulations are in good agreement with previous measurements on SPHERE and with the assumptions adopted in earlier performance studies. We also propose a calibration strategy that offloads most static aberration correction to the first-stage deformable mirror while preserving the second-stage mirror stroke for high-speed adaptive optics correction. These results validate the expected SAXO+ optical quality and establish the calibration framework required for efficient NCPA compensation and focal-plane wavefront control during future on-sky operations.

The interaction matrix models the effects of deformable mirror (DM) commands as perceived by the wavefront sensor (WFS) and is the cornerstone of the Adaptive Optics (AO) control. Difficulties to calibrate this matrix arise due to the number of degrees of freedom, the non-linearity, and temporal evolution of the AO system. An affine approximation of the unknown mapping between the DM commands and the WFS measurements is considered. Optimal estimators of the parameters of this affine model are obtained by fitting, in the weighted least squares sense, WFS data acquired with random probe commands sent to the DM. Several calibration methods are being considered depending on whether the model is directly fit to the WFS data or to the differences between successive WFS data. We derive closed-form expressions of the estimators of the components of the model. The proposed calibration methods can be applied under different conditions: before observing, on an internal source, or on-sky in open- or closed-loop. By introducing forgetting factors to reduce the weight of data as they age, we show that the model can be learned continuously using simple recurrence rules. The low computational complexity of these rules makes them suitable for real-time at the same frequency as the AO loop. We derive simple expressions for the mean squared errors (MSE) of the proposed estimators. We apply the proposed calibration methods to real telemetry data from the AO system of the THEMIS solar telescope. Our results show that the simple differences method is the method of choice: not only does it produce estimators with the least MSE, but it is also very simple to implement compared to the push-pull method which is widely used in AO systems.

In order to address new science objectives in exoplanet imaging, the SAXO+ technical development project has been undertaken for the SPHERE instrument at ESO's VLT. As a part of this, the AO system will be completed by adding a second, faster stage of correction. We present simulation results obtained by implementing an optimal predictive linear quadratic Gaussian controller for the 2nd stage. The prediction relies on a stochastic state-space disturbance model fully identified from closed-loop measurements. In addition, we also investigate a disentangled cascade AO (dCAO) mode where the model represents the full incoming disturbance and is identified using in addition the 1st stage commands.

SPHERE, operating at the VLT since 2014, is currently one of the high-contrast instruments with a higher performance. Its adaptive optics system, known as SAXO, will be upgraded to SAXO+, which features the addition of a second stage of adaptive optics. This stage will use a near-infrared pyramid wavefront sensor to record images of fainter exoplanets around redder stars. In this work, we compare the performance of SAXO and SAXO+. We look for the optimal values of the key system parameters of SAXO+ for various science cases and turbulence conditions. We performed numerical simulations using COMPASS, an end-to-end adaptive optics simulation tool. We simulated perfect coronagraph images of an on-axis point source, and we minimized the residual starlight intensity between 3 and $5\ / D$ as a performance criterion. The explored parameter space includes science cases (described by magnitude in G and J bands), turbulence conditions (seeing and coherence time), and key system parameters (first and second stage gains, first and second stage frequencies, pyramid modulation radius, pyramid modal gains optimization). In every science case and turbulence condition, SAXO+ reduces the residual starlight intensity inside the correction zone of the second stage by a factor of ten compared to SAXO. The optimal first stage gain is lower for SAXO+ than for SAXO alone. We quantified the gain in performance of SAXO+ when changing the second stage frequency from 2\,kHz to 3\,kHz, and we conclude that 2\,kHz may be sufficient for most realistic conditions. We give the optimal first stage gain as well as the first and second stage frequencies for every seeing, coherence time, and science case. Finally, we find that a $2\ WFS / D$ pyramid modulation radius is a good trade-off between performance and robustness against varying turbulence conditions. This study shows that the future SAXO+ system will outperform the current SAXO system in all studied cases.

This study introduces a novel frequency-based data-driven controller for adaptive optics, using power spectral density for optimization while ensuring stability criteria. It addresses disturbance rejection, command amplitude constraints and system transfer functions through convex optimization to obtain an optimal control in an infinite input response filter form. Evaluated within the SAXO+ project, it demonstrates efficacy under diverse atmospheric conditions and operational scenarios. The proposed controller is tested in both standard and disentangled adaptive optics schemes, showcasing its adaptability and performance. Experimental validation is conducted using the COMPASS simulation tool, affirming the controller's promise for enhancing adaptive optics systems in real-world applications.

SAXO+ is a planned enhancement of the existing SAXO, the VLT/ SPHERE adaptive optics system, deployed on ESO's Very Large Telescope. This upgrade is designed to significantly enhance the instrument's capacity to detect and analyze young Jupiter-like planets. The pivotal addition in SAXO+ is a second-stage adaptive optics system featuring a dedicated near-infrared pyramid wavefront sensor and a second deformable mirror. This secondary stage is strategically integrated to address any residual wavefront errors persisting after the initial correction performed by the current primary AO loop, SAXO. However, several recent studies clearly showed that in good conditions, even in the current system SAXO, non-common path aberrations (NCPAs) are the limiting factor of the final normalized intensity in focal plane, which is the final metric for ground-based high-contrast instruments. This is likely to be even more so the case with the new AO system, with which the AO residuals will be minimized. Several techniques have already been extensively tested on SPHERE in internal source and/or on-sky and will be presented in this paper. However, the use of a new type of sensor for the second stage, a pyramid wavefront sensor, will likely complicate the correction of these aberrations. Using an end-to-end AO simulation tool, we conducted simulations to gauge the effect of measured SPHERE NCPAs in the coronagraphic image on the second loop system and their correction using focal plane wavefront sensing systems. We finally analyzed how the chosen position of SAXO+ in the beam will impact the evolution of the NCPAs in the new instrument.

SAXO+ is the upgrade of SAXO, the adaptive optics system used by the SPHERE instrument on ESO's Very Large Telescope. SAXO+ consists of a second stage adaptive optics downstream of the first stage, SAXO, to improve wavefront correction, achieve deeper contrast in the coronagraphic images and observe fainter and redder stars. Using the COMPASS end-to-end simulation tool, we assess the SAXO+ improved correction compared to SAXO in multiple science cases and turbulence conditions. The adaptive optics performance criterion is the starlight residual intensity in the coronagraph image : the lower the better. We show that SAXO+ improves the performance of the adaptive optics system by a factor of 10 in all simulated observing conditions. We specifically study the impact of the second stage frequenc and we conclude that a 2 kHz second stage is a reasonable trade-off between performance and technical constraints on the real-time system.

VERMILION is a VLTI visitor instrument project intended to extend the sensitivity and the spectral coverage of Optical Long Baseline Interferometry (OLBIn). It is based on a new concept of Fringe Tracker (VERMILIONFT) combined with a J band spectro-interferometer (VERMILION-J). The Fringe Tracker is the Adaptive Optics module specific to OLBIn that measures and corrects in real time the Optical Path Difference (OPD) perturbations introduced by the atmosphere and the interferometer, by providing a sensitivity gain of 2 to 3 magnitudes over all other state of the art fringe trackers. The J band spectro-interferometer will provide all interferometric measurements as a function of wavelength. In addition to a possible synergy with MATISSE, VERMILION-J, by observing at high spectral resolution many strong lines in J (Paβ-γ, HeII, TiO and other metallic monoxides), will cover several scientific topics, e.g. Exoplanets, YSOs, Binaries, Active Hot, Evolved stars, Asteroseismology, and also AGNs.

Accurate positioning of opto-mechanical elements in the focal plane of large telescopes is a challenging requirements for many state of the art observational scientific applications. In particular high multiplexing multi object spectroscopy requires precise metrology tools for performing efficient observations and calibrations of the instruments. We have developed a metrology system based on modified commercial off-the-shelf components to reach high performances with a cost effective solution. Our system is based on the photogrammetry technique and on a number of fixed off-axis cameras. The cameras acquire images of the focal plane where metrology targets and references are located. The acquisition is based on Odroid-XU4, a single-board computer running on GNU/Linux. No moving parts in the setup ensures an extremely fast acquisition of the data. The calibration and metrology data processing is based on the computer vision library OpenCV. We present a prototype system and results of the camera calibrations and metrology tests obtained in our laboratory.

Laser-based adaptive optics telemetry contains information about the atmospheric vertical profiles of turbulence strength (C2n), outer scale (L0) and wind speeds. Various techniques in the literature already process laser-based Shack-Hartmann telemetry and estimate the profiles out of cross-covariance maps from the slopes data. Building local derivative estimates out of the data (i.e. curvatures or even higher-order derivative estimates) is a possible mean to remove the large uncertainties existing on low-order modes in laser-based systems. The present study analyses this filtering strategies in a unified formalism. The modified shapes of the cross-covariance peaks are studied and compared. It explains how the sensitivity to the outer scale is strongly reduced by using such higher- order derivative estimates than slopes. The sharpened covariance peaks also simplify the layer detection problem in atmospheric profiling and may improve vertical resolution of SLODAR-based techniques. As a first application of this analysis, an automated algorithm for turbulence profiling is presented with results on simulated data and also on on-sky registered data from the Adaptive Optics Facility at Paranal Observatory.

SPHERE+ is a proposed upgrade of the SPHERE instrument at the VLT, which is intended to boost the current performances of detection and characterization for exoplanets and disks. SPHERE+ will also serve as a demonstrator for the future planet finder (PCS) of the European ELT. The main science drivers for SPHERE+ are 1/ to access the bulk of the young giant planet population down to the snow line (3 − 10 au), to bridge the gap with complementary techniques (radial velocity, astrometry); 2/ to observe fainter and redder targets in the youngest (1 − 10 Myr) associations compared to those observed with SPHERE to directly study the formation of giant planets in their birth environment; 3/ to improve the level of characterization of exoplanetary atmospheres by increasing the spectral resolution in order to break degeneracies in giant planet atmosphere models. Achieving these objectives requires to increase the bandwidth of the xAO system (from ~1 to 3 kHz) as well as the sensitivity in the infrared (2 to 3 mag). These features will be brought by a second stage AO system optimized in the infrared with a pyramid wavefront sensor. As a new science instrument, a medium resolution integral field spectrograph will provide a spectral resolution from 1000 to 5000 in the J and H bands. This paper gives an overview of the science drivers, requirements and key instrumental tradeoff that were done for SPHERE+ to reach the final selected baseline concept.

An adaptive optics system with a single deformable mirror is being implemented on the THEMIS 90cm solar telescope. This system is designed to operate in the visible and is required to be as robust as possible in order to deliver the best possible correction in any atmospheric conditions, even if wavefronts are sensed on some low-contrast solar granulation. In extreme conditions, the images given by the subapertures of the Shack-Hartmann wavefront sensor get randomly blurred in space, in the set of subapertures, and the distribution of blurred images is rapidly changing in time, some of them possibly fading away. The algorithms we have developed for such harsh conditions rely on inverse problem approach. As an example, with the gradients of the wavefronts, the wavefront sensor also estimates their errors, including their covariance. This information allows the control loop to promptly optimize itself to the fast varying conditions, both in space (wavefront reconstruction) and in time. A major constraint is to fit the calculations in a low-cost multi-core CPU. An overview of the algorithms in charge of implementing this strategy is presented, focusing on wavefront sensing.

MOONS is the new Multi-Object Optical and Near-infrared Spectrograph currently under construction for the Very Large Telescope (VLT) at ESO. This remarkable instrument combines, for the first time, the collecting power of an 8-m telescope, 1000 fibres with individual robotic positioners, and both low- and high-resolution simultaneous spectral coverage across the 0.64–1.8 μm wavelength range. This facility will provide the astronomical community with a powerful, world-leading instrument able to serve a wide range of Galactic, extragalactic and cosmological studies. Construction is now proceeding full steam ahead and this overview article presents some of the science goals and the technical description of the MOONS instrument. More detailed information on the MOONS surveys is provided in the other dedicated articles in this Messenger issue.

The Multi Object Optical and Near-infrared Spectrograph (MOONS) instrument is the next generation multi-object spectrograph for the VLT. This powerful instrument will combine for the first time: the large collecting power of the VLT with a high multipexing capability offered by 1000 optical fibres moved with individual robotic positioners and a novel, very fast spectrograph able to provide both low- and high-resolution spectroscopy simultaneously across the wavelength range 0.64 mu m - 1.8 mu m. Such a facility will provide the astronomical community with a powerful, world-leading instrument able to serve a wide range of Galactic, Extragalactic and Cosmological studies. The final assembly, integration and verification phase of the instrument is now about to start performance testing.

We propose an optically efficient active beam-shaping system which consists of two continuous-surface deformable mirrors correcting for both phase and amplitude distortions to improve the beam quality of a laser. We present the results obtained with simulations and we validate next the technique using an experimental setup with two Boston micromachines MEMS deformable mirrors of 12 x 12 actuators each.