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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., Comment: 16 pages, 10 figures, submitted to the proceedings of SPIE Astronomical Telescopes + Instrumentation 2024, 13096-357

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 ${\lambda}/D$ as a performance criterion. The explored parameter space includes science cases, turbulence conditions, and key system parameters. 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 ${\lambda_{\mathrm{WFS}}}/D$ 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., Comment: 14 pages, 11 figures

SAXO+ is a proposed upgrade to SAXO, the AO system of the SPHERE instrument on the ESO Very Large Telescope. It will improve the capabilities of the instrument for the detection and characterization of young giant planets. It includes a second stage adaptive optics system composed of a dedicated near-infrared wavefront sensor and a deformable mirror. This second stage will remove the residual wavefront errors left by the current primary AO loop (SAXO). This paper focuses on the numerical simulations of the second stage (SAXO+) and concludes on the impact of the main AO parameters used to build the design strategy. Using an end-to-end AO simulation tool (COMPASS), we investigate the impact of several parameters on the performance of the AO system. We measure the performance in minimizing the star residuals in the coronagraphic image. The parameters that we study are : the second stage frequency, the photon flux on each WFS, the first stage gain and the DM number of actuators of the second stage. We show that the performance is improved by a factor 10 with respect to the current AO system (SAXO). The optimal second stage frequency is between 1 and 2 kHz under good observing conditions. In a red star case, the best SAXO+ performance is achieved with a low first stage gain of 0.05, which reduces the first stage rejection., Comment: 10 pages, 8 figures. Submitted to AO4ELT7 conference proceedings

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.

The advent of a new generation of Adaptive Optics systems called Wide Field AO (WFAO) mark the beginning of a new era. By using multiple Guide Stars (GSs), either Laser Guide Stars (LGSs) or Natural Guide Stars (NGSs), WFAO significantly increases the field of view of the AO-corrected images, and the fraction of the sky that can benefit from such correction. Different typologies of WFAO have been studied over the past years. They all require multiple GSs to perform a tomographic analysis of the atmospheric turbulence. One of the fundamental aspects of the new WFAO systems is the knowledge of the spatio-temporal distribution of the turbulence above the telescope. One way to get to this information is to use the telemetry data provided by the WFAO system itself. Indeed, it has been demonstrated that WFAO systems allows one to derive the Cn2 and wind profile in the main turbulence layers (see e.g. Cortes et al. 2012). This method has the evident advantage to provide information on the turbulence stratification that effectively affects the AO system, property more difficultly respected by independently vertical profilers. In this paper, we compare the wind speeds profiles of GeMS with those predicted by a non-hydrostatical mesoscale atmospherical model (Meso-NH). It has been proved (Masciadri et al., 2013), indeed, that this model is able to provide reliable wind speed profiles on the whole troposphere and stratosphere (up to 20-25 km) above top-level astronomical sites. Correlation with measurements revealed to be very satisfactory when the model performances are analyzed from a statistical point of view as well on individual nights. Such a system appears therefore as an interesting reference to be used to quantify the GeMS wind speed profiles reliability., Comment: 10 pages, 5 figures - Proceedings of the SPIE, Adaptive Optics Systems IV, 9148-236

The availability and performance of laser-based adaptive optics (AO) systems are strongly dependent on the power and quality of the laser beam before being projected to the sky. Frequent and time-consuming alignment procedures are usually required in the laser systems with free-space optics to optimize the beam. Despite these procedures, significant distortions of the laser beam have been observed during the first two years of operation of the Gemini South multi-conjugate adaptive optics system (GeMS). A beam shaping concept with two deformable mirrors is investigated in order to provide automated optimization of the laser quality for astronomical AO. This study aims at demonstrating the correction of quasi-static aberrations of the laser, in both amplitude and phase, testing a prototype of this two-deformable mirror concept on GeMS. The paper presents the results of the preparatory study before the experimental phase. An algorithm to control amplitude and phase correction, based on phase retrieval techniques, is presented with a novel unwrapping method. Its performance is assessed via numerical simulations, using aberrations measured at GeMS as reference. The results predict effective amplitude and phase correction of the laser distortions with about 120 actuators per mirror and a separation of 1.4 m between the mirrors. The spot size is estimated to be reduced by up to 15% thanks to the correction. In terms of AO noise level, this has the same benefit as increasing the photon flux by 40%., Comment: 20 pages, 12 figures

We use spatio-temporal cross-correlations of slopes from five Shack-Hartmann wavefront sensors to analyse the temporal evolution of the atmospheric turbulence layers at different altitudes. The focus is on the verification of the frozen flow assumption. The data is coming from the Gemini South Multi-Conjugate Adaptive Optics System (GeMS). First, the Cn2 and wind profiling technique is presented. This method provides useful information for the AO system operation such as the number of existing turbulence layers, their associated velocities, altitudes and strengths and also a mechanism to estimate the dome seeing contribution to the total turbulence. Next, by identifying the turbulence layers we show that it is possible to estimate the rate of decay in time of the correlation among turbulence measurements. We reduce on-sky data obtained during 2011, 2012 and 2013 campaigns and the first results suggest that the rate of temporal de-correlation can be expressed in terms of a single parameter that is independent of the layer altitude and turbulence strength. Finally, we show that the decay rate of the frozen-flow contribution increases linearly with the layer speed. The observed evolution of the decay rate confirms the potential interest of the predictive control for wide-field AO systems., Comment: 19 pages, 16 figures, accepted for publication in MNRAS