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The calibration of future wide field adaptive optics (WFAO) systems requires knowledge of the geometry of the system, in particular the alignment parameters between the sub-apertures of the wavefront sensors (WFS), pupil and deformable mirror (DM) actuator grid. Without this knowledge, closed-loop operation is not possible and the registration must be identified with an error significantly smaller than the sub-aperture size to achieve the nominal performance of the adaptive optics system. Furthermore, poor accuracy in this estimation will not only affect performance, but could also prevent the closed loop from being stable. Identification is not trivial because in a WFAO system several elements can move with respect to each other, more than in a SCAO system. For example, the pairing of the sub-aperture and the actuator grating on a DM conjugated to an altitude different from 0 can depend on the size of the pupil on the WFS, the exact conjugation of the DM, the position of the guide star and the field rotation. This is the same for each WFS/DM pair. SPRINT, System Parameters Recurrent INvasive Tracking, is a strategy for monitoring and compensating for DM/WFS mis-registrations and has been developed in the context of single conjugate adaptive optics (SCAO) systems for the ESO Extremely Large Telescope (ELT). In this work, we apply SPRINT in the context of WFAO systems with multiple WFSs and DMs, investigating the best approach for such systems, considering a simultaneous identification of all parameters or subsequent steps working on one DM at a time., Comment: 10 pages, 4 figures. Proceeding of the SPIE conference Adaptive Optics Systems IX, SPIE Astronomical Telescopes + Instrumentation 2024 (Paper No. 13097-171)

The SOUL systems at the Large Bincoular Telescope can be seen such as precursor for the ELT SCAO systems, combining together key technologies such as EMCCD, Pyramid WFS and adaptive telescopes. After the first light of the first upgraded system on September 2018, going through COVID and technical stops, we now have all the 4 systems working on-sky. Here, we report about some key control improvements and the system performance characterized during the commissioning. The upgrade allows us to correct more modes (500) in the bright end and increases the sky coverage providing SR(K)>20% with reference stars G$_{RP}$<17, opening to extragalcatic targets with NGS systems. Finally, we review the first astrophysical results, looking forward to the next generation instruments (SHARK-NIR, SHARK-Vis and iLocater), to be fed by the SOUL AO correction., Comment: 13 pages, 10 figures, Adaptive Optics for Extremely Large Telescopes 7th Edition, 25-30 Jun 2023 Avignon (France)

MORFEO (Multi-conjugate adaptive Optics Relay For ELT Observations, formerly MAORY), the MCAO system for the ELT, will provide diffraction-limited optical quality to the large field camera MICADO. MORFEO has officially passed the Preliminary Design Review and it is entering the final design phase. We present the current status of the project, with a focus on the adaptive optics system aspects and expected milestones during the next project phase.

MORFEO (Multi-conjugate adaptive Optics Relay For ELT Observation) is the future multi-conjugate adaptive optics system for the ESO ELT that will feed the instrument MICADO (Multi-AO Imaging Camera for Deep Observations). It will use the 6 laser guide stars to give a uniform correction on a field-of-view of approximately 60arcsec of diameter. Tip, tilt and slow focus measurement will be done on up to three natural guide stars that could be really faint to maximize sky coverage. The current baseline is to use the reference wavefront sensor in the visible to acquire the star and center it on the low order wavefront sensor that has a much smaller field-of-view. In this work we study this problem focusing on the estimation error of the tilt from the reference wavefront sensor as a function of star magnitude and atmospheric conditions., Comment: 9 pages, 7 figures, Adaptive Optics for Extremely Large Telescopes 7th Edition, 25-30 Jun 2023 Avignon (France)

TIPTOP is a python library that is able to quickly compute Point Spread Functions (PSF) of any kind of Adaptive Optics systems. This library has multiple objectives: support the exposure time calculators of future VLT and ELT instruments, support adaptive optics systems design activities, be part of PSF reconstruction pipelines and support the selection of the best asterism of natural guide stars for observation preparation. Here we report one of the last improvements of TIPTOP: the introduction of the error given by a single conjugated laser, commonly known as the cone effect. The Cone effect was not introduced before because it is challenging due to the non-stationarity of the phase. Laser guide stars are at a finite distance with respect to the telescope and probe beam accepted by the wavefront sensor has the shape of a cone. Given a single spatial frequency in an atmospheric layer, the cone effect arises from the apparent magnification or stretching of this frequency when it reaches the wavefront sensor. The magnification effect leads to an incorrect estimation of the spatial frequency. Therefore, we estimate the residual power by calculating the difference between two sinusoids with different periods: the nominal one and the magnified one. Replicating this for each spatial frequency we obtain the power spectrum associated with the cone effect. We compare this estimation with the one given by end-to-end simulation and we present how we plan to validate this with on-sky data., Comment: 9 pages, 8 figures, Adaptive Optics for Extremely Large Telescopes 7th Edition, 25-30 Jun 2023 Avignon (France)

Since 2005 ESO has been working with its community and industry to develop an extremely large optical/infrared telescope. ESO's Extremely Large Telescope, or ELT for short, is a revolutionary ground-based telescope that will have a 39-metre main mirror and will be the largest visible and infrared light telescope in the world. To address specific topics that are needed for the science operations and calibrations of the telescope, thirteen specific working groups were created to coordinate the effort between ESO, the instrument consortia, and the wider community. We describe here the goals of these working groups as well as their achievements so far., Comment: 8 pages, 4 figures

The future upgrade of Keck II telescope's adaptive optics system will include a pyramid wavefront sensor working in the near-infrared (J and H band). It will benefit from the recently developed avalanche photodiode arrays, specifically the SAPHIRA (Selex) array, which provides a low noise ($<$ 1 e- at high frame rates). The system will either work with a natural guide star (NGS) in a single conjugated adaptive optics system, or in a laser guide star (LGS) mode. In this case, the pyramid would be used as a low-order sensor only. We report on a study of the pyramid sensor's performance via end-to-end simulations, applied to Keck's specific case. We present the expected Strehl ratio with optimized configurations in NGS mode, and the expected residual on low orders in LGS mode. In the latter case, we also compare the pyramid to LIFT, a focal-plane sensor, demonstrating the ability of LIFT to provide a gain of about 2 magnitudes for low-order sensing.

Adaptive optics (AO) is a technique allowing to drastically improve ground-based telescopes angular resolution. The wavefront sensor (WFS) is one of the key components of such systems, driving the fundamental performance limitations. In this paper, we focus on a specific class of WFS: the Fourier-filtering wavefront sensors (FFWFS). This class is known for its extremely high sensitivity. However, a clear and comprehensive noise propagation model for any kind of FFWFS is lacking. Considering read-out noise and photon noise, we derive a simple and comprehensive model allowing to understand how these noises propagates in the phase reconstruction in the linear framework. This new noise propagation model works for any kind of FFWFS, and allows to revisit the fundamental sensitivity limit of these sensors. Furthermore, a new comparison between widely used FFWFS is held. We focus on the two main used FFWFS classes: the Zernike WFS (ZWFS) and the pyramid WFS (PWFS), bringing new understanding of their behavior.

To reach the full potential of the new generation of ground based telescopes, an extremely fine adjustment of the phase is required. Wavefront control and correction before detection has therefore become one of the cornerstones of instruments to achieve targeted performance, especially for high-contrast imaging. A crucial feature of accurate wavefront control leans on the wavefront sensor (WFS). We present a strategy to design new Fourier-Filtering WFS that encode the phase close from the fundamental photon efficiency limit. This strategy seems promising as it generates highly sensitive sensors suited for different pupil shape configurations.

The astronomical applications greatly benefit from the knowledge of the instrument PSF. We describe the PSF Reconstruction algorithm developed for the LBT LUCI instrument assisted by the SOUL SCAO module. The reconstruction procedure considers only synchronous wavefront sensor telemetry data and a few asynchronous calibrations. We do not compute the Optical Transfer Function and corresponding filters. We compute instead a temporal series of wavefront maps and for each of these the corresponding instantaneous PSF. We tested the algorithm both in laboratory arrangement and in the nighttime for different SOUL configurations, adapting it to the guide star magnitudes and seeing conditions. We nick-named it "BRUTE", Blind Reconstruction Using TElemetry, also recalling the one-to-one approach, one slope-to one instantaneous PSF the algorithm applies., Comment: 11 pages, 7 figures, Proceeding of the SPIE Conference 12185, Adaptive Optics Systems VIII, 1218540 (29 August 2022)

In the context of adaptive optics for astronomy, one can rely on the statistics of the turbulent phase to assess a part of the system's performance. Temporal statistics with one source and spatial statistics with two sources are well-known and are widely used for classical adaptive optics systems. A more general framework, including both spatial and temporal statistics, can be useful for the analysis of the existing systems and to support the design of the future ones. In this paper, we propose an expression of the temporal cross power spectral densities of the turbulent phases in two distinct beams, that is from two different sources to two different apertures. We either consider the phase as it is, without piston, or as its decomposition on Zernike modes. The general formulas allow to cover a wide variety of configurations, from single-aperture to interferometric telescopes equipped with adaptive optics, with the possibility to consider apertures of different sizes and/or sources at a finite distance. The presented approach should lead to similar results with respect to existing methods in the Fourier domain, but it is focused on temporal frequencies rather than spatial ones, which might be convenient for some aspects such as control optimization. To illustrate this framework with a simple application, we demonstrate that the wavefront residual due to the anisoplanatism error in a single-conjugated adaptive optics system is overestimated when it is computed from covariances without taking into account the temporal filtering of the adaptive optics loop. We also show this overestimation in the case of a small-baseline interferometer, for which the two beams are significantly correlated., Comment: \c{opyright} 2021 Optica Publishing Group. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved

A new era of ground-based observations, either in the infrared with the next-generation of 25-40m extremely large telescopes or in the visible with the 8m Very Large Telescope, is going to be assisted by multi-conjugate adaptive optics (MCAO) to restore the unprecedented resolutions potentially available for these systems in absence of atmospheric turbulence. Astrometry is one of the main science drivers, as MCAO can provide good quality and uniform correction over wide field of views ($\sim$ 1 arcmin) and offer a large number of reference sources with high image quality. The requirements have been set to very high precisions on the differential astrometry (e.g. 50$\mu$as for MICADO/MORFEO - formerly known as MAORY - at the Extremely Large Telescope) and an accurate analysis of the astrometric error budget is needed. In this context, we present an analysis of the impact of MCAO atmospheric tip-tilt residuals on relative astrometry. We focus on the effects of the scientific integration time on tip-tilt residuals, that we model through the temporal transfer function of the exposure. We define intra- and inter-exposure tip-tilt residuals that we use in the estimation of the centroiding error and the differential tilt jitter error within the astrometric error budget. As a case study, we apply our results in the context of the MORFEO astrometric error budget.

Multi-conjugate adaptive optics (MCAO) will assist a new era of ground-based astronomical observations with the extremely large telescopes and the Very Large Telescope. High precision relative astrometry is among the main science drivers of these systems and challenging requirements have been set for the astrometric measurements. A clear understanding of the astrometric error budget is needed and the impact of the MCAO correction has to be taken into account. In this context, we propose an analytical formulation to estimate the residual phase produced by an MCAO correction in any direction of the scientific field of view. The residual phase, computed in the temporal frequency domain, allows to consider the temporal filtering of the turbulent phase from the MCAO loop and to extract the temporal spectrum of the residuals, as well as to include other temporal effects such as the scientific integration time. The formulation is kept general and allows to consider specific frameworks by setting the telescope diameter, the turbulence profile, the guide stars constellation, the deformable mirrors configuration, the modes sensed and corrected and the tomographic reconstruction algorithm. The formalism is presented for both a closed loop and a pseudo-open loop control. We use our results to investigate the effect of tip-tilt residuals on MCAO-assisted astrometric observations. We derive an expression for the differential tilt jitter power spectrum that also includes the dependence on the scientific exposure time. Finally, we investigate the contribution of the differential tilt jitter error on the future astrometric observations with MAVIS and MAORY.

The MCAO Assisted Visible Imager and Spectrograph (MAVIS) is a new visible instrument for ESO Very Large Telescope (VLT). Its Adaptive Optics Module (AOM) must provide extreme adaptive optics correction level at low galactic latitude and high sky coverage at the galactic pole on the FoV of 30arcsec of its 4k x 4k optical imager and on its monolithic Integral Field Unit, thanks to 3 deformable mirrors (DM), 8 Laser Guide Stars (LGS), up to 3 Natural Guide Stars (NGS) and 11 Wave Front Sensors (WFS). A careful performance estimation is required to drive the design of this module and to assess the fulfillment of the system and subsystems requirements. Here we present the work done on this topic during the last year: we updated the system parameters to account for the phase B design and for more realistic conditions, and we produced a set of results from analytical and end-to-end simulations that should give a as complete as possible view on the performance of the system., Comment: 13 pages, 16 figures, 2 tables, SPIE Astronomical Telescopes + Instrumentation, 2022, Montreal, Canada

Laser Guide Star (LGS) Shack-Hartmann (SH) wavefront sensors for next generation Extremely Large Telescopes (ELTs) require low-noise, large format (about 1Mpx), fast detectors to match the need for a large number of subapertures and a good sampling of the very elongated spots. One path envisaged to fulfill this need has been the adoption of CMOS detectors with a rolling shutter read-out scheme, that allows low read-out noise and fast readout time at the cost of image distortion due to the detector rows exposed in different moments. In this work we analyze the impact of the rolling shutter read-out scheme when used for LGS SH wavefront sensing of the Multiconjugate adaptive Optic Relay For ELT Observations (MORFEO, formerly known as MAORY) for ESO ELT; in particular, we focus on the impact on the adaptive optics correction of the distortion-induced aberrations created by the rolling exposure in the case of fast varying aberrations, like the ones coming from the LGS tilt jitter due to the up-link propagation of laser beams. We show that the LGS jitter-induced aberration for MORFEO can be as large as 100nm rms and we discuss possible mitigation strategies., Comment: 8 pages, 6 figures, SPIE Astronomical Telescopes + Instrumentation, 2022, Montreal, Canada

The Multiconjugate adaptive Optic Relay For ELT Observations (MORFEO, formerly known as MAORY) is the adaptive optics (AO) module for the Extremely Large Telescope (ELT) aimed at providing a 1 arcmin corrected field to the Multi-AO Imaging CamerA for Deep Observations (MICADO) and to a future client instrument. It should provide resolution close to the diffraction limit on a large portion of the sky and in a wide range of atmospheric conditions. Its ability to provide a flat wavefront must face the known aspect of the atmospheric turbulence and telescope environment, but also the final characteristic of a telescope still to be fully developed and built. In this work we focused on issues related to the segmentation of the telescope pupil (like low wind effect, residual phasing error at handover and control related issues), that could limit the system performance. MORFEO currently does not foresee a dedicated sensor to measure the phase step between adjacent mirror segments: in this work we study the possibility to use the low order wavefront sensors designed to sense and correct tip-tilt and focus as phasing sensors thanks to the linearized focal-plane technique (LIFT)., Comment: 8 pages, 7 figures, SPIE Astronomical Telescopes + Instrumentation, 2022, Montreal, Canada

Laser guide star (LGS) wave-front sensing (LGSWFS) is a key element of tomographic adaptive optics system. However, when considering Extremely Large Telescope (ELT) scales, the LGS spot elongation becomes so large that it challenges the standard recipes to design LGSWFS. For classical Shack-Hartmann wave-front sensor (SHWFS), which is the current baseline for all ELT LGS-assisted instruments, a trade-off between the pupil spatial sampling [number of sub-apertures (SAs)], the SA field-of-view (FoV) and the pixel sampling within each SA is required. For ELT scales, this trade-off is also driven by strong technical constraints, especially concerning the available detectors and in particular their number of pixels. For SHWFS, a larger field of view per SA allows mitigating the LGS spot truncation, which represents a severe loss of performance due to measurement biases. For a given number of available detectors pixels, the SA FoV is competing with the proper sampling of the LGS spots, and/or the total number of SAs. We proposed a sensitivity analysis, and we explore how these parameters impacts the final performance. In particular, we introduce the concept of super resolution, which allows one to reduce the pupil sampling per WFS and opens an opportunity to propose potential LGSWFS designs providing the best performance for ELT scales., Comment: 21 pages, 11 figures, 1 table, part of the 2022 JATIS Special Section on Extremely Large Telescopes

Adaptive optics systems are an essential technology for the modern astronomy for ground based telescopes. One of the most recent revolution in the field is the introduction of the pyramid wavefront sensor. The higher performance of this device is payed with increased complexity in the control. In this work we report about advances in the AO system control obtained with SOULat the Large Binocular Telescope. The first is an improved Tip/Tilt temporal control able to recover the nominal correction even in presence of high temporal frequency resonances. The second one is a modal gain optimization that has been successfully tested on sky for the first time. Pyramid wavefront sensors are the key technology for the first light AO systems of all ELTs and the reported advances can be relevant contributions for such systems., Comment: 12 pages, 13 figures. Fixed typos in footnote 2 and in equation 13

Accurate astrometry is a key deliverable for the next generation of multi-conjugate adaptive optics (MCAO) systems. The MCAO Visible Imager and Spectrograph (MAVIS) is being designed for the Very Large Telescope Adaptive Optics Facility and must achieve 150 $\mu$as astrometric precision (50 $\mu$as goal). To test this before going on-sky, we have created MAVISIM, a tool to simulate MAVIS images. MAVISIM accounts for three major sources of astrometric error, high- and low-order point spread function (PSF) spatial variability, tip-tilt residual error and static field distortion. When exploring the impact of these three error terms alone, we recover an astrometric accuracy of 50 $\mu$as for all stars brighter than $m=19$ in a 30s integration using PSF-fitting photometry. We also assess the feasibility of MAVIS detecting an intermediate mass black hole (IMBH) in a Milky Way globular cluster. We use an N-body simulation of an NGC 3201-like cluster with a central 1500 M$_{\odot}$ IMBH as input to MAVISIM and recover the velocity dispersion profile from proper motion measurements. Under favourable astrometric conditions, the dynamical signature of the IMBH is detected with a precision of ~0.20 km/s in the inner ~4" of the cluster where HST is confusion-limited. This precision is comparable to measurements made by Gaia, HST and MUSE in the outer ~60" of the cluster. This study is the first step towards building a science-driven astrometric error budget for an MCAO system and a prediction of what MAVIS could do once on sky., Comment: 17 pages, 13 figures, accepted for publication in MNRAS, main result is shown in Figure 12. Fixed typo in introduction

MAORY is the adaptive optics module for ELT providing two gravity invariant ports with the same optical quality for two different client instruments. It enable high angular resolution observations in the near infrared over a large field of view (~1 arcmin2 ) by real time compensation of the wavefront distortions due to atmospheric turbulence. Wavefront sensing is performed by laser and natural guide stars while the wavefront sensor compensation is performed by an adaptive deformable mirror in MAORY which works together with the telescope's adaptive and tip tilt mirrors M4 and M5 respectively., Comment: 4 pages, 4 figures

The SOUL project is upgrading the 4 SCAO systems of LBT, pushing the current guide star limits of about 2 magnitudes fainter thanks to Electron Multiplied CCD detector. This improvement will open the NGS SCAO correction to a wider number of scientific cases from high contrast imaging in the visible to extra-galactic source in the NIR. The SOUL systems are today the unique case where pyramid WFS, adaptive secondary and EMCCD are used together. This makes SOUL a pathfinder for most of the ELT SCAO systems like the one of GMT, MICADO and HARMONI of E-ELT, where the same key technologies will be employed. Today we have 3 SOUL systems installed on the telescope in commissioning phase. The 4th system will be installed in a few months. We will present here the results achieved during daytime testing and commissioning nights up to the present date., Comment: 11 pages, 9 figures, 1 table. AO4ELT6 proceedings

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., Comment: Proceeding of SPIE 2020

MAORY is the Multi-conjugate Adaptive Optics RelaY for the European ELT aimed at providing a 1 arcmin corrected field to MICADO, a near-infrared spectro-imager with a focus on astrometry. In this paper we re-view the main requirements and analysis that justify the current adaptive optics architecture and subsystem requirements. We discuss the wavefront error budget allocation focusing on the worst offenders terms and on a statistical analysis of their dependence on atmospheric and sodium profiles. We present an updated revision of the trade-off studies on the main AO parameters that, along with considerations coming from optical and mechanical subsystems, are used to define the preliminary design of the instrument., Comment: 10 pages, 8 figures. AO4ELT6 proceedings

Electro-Multiplying CCDs offer a unique combination of speed, sub-electron noise and quantum efficiency. These features make them extremely attractive for astronomical adaptive optics. The SOUL project selected the Ocam2k from FLI as camera upgrade for the pyramid wavefront sensor of the LBT SCAO systems. Here we present results from the laboratory characterization of the 3 of the custom Ocam2k cameras for the SOUL project. The cameras showed very good noise ($0.4e^-$ and $0.4-0.7e^-$ for binned modes) and dark current values ($1.5e^-$). We measured the camera gain and identified the dependency on power cycle and frame rate. Finally, we estimated the impact of these gain variation in the SOUL adaptive optics system. The impact on the SOUL performance resulted to be negligible., Comment: 9 pages, 3 figures, 7 tables. SPIE Astronomical Telescopes + Instrumentation, 2018, Austin, Texas, United States

The MCAO Assisted Visible Imager and Spectrograph (MAVIS) Adaptive Optics Module has very demanding goals to support science in the optical: providing 15% SR in V band on a large FoV of 30arcsec diameter in standard atmospheric conditions at Paranal. It will be able to work in closed loop on up to three natural guide stars down to H=19, providing a sky coverage larger than 50% in the south galactic pole. Such goals and the exploration of a large MCAO system parameters space have required a combination of analytical and end- to-end simulations to assess performance, sky coverage and drive the design. In this work we report baseline performance, statistical sky coverage and parameters sensitivity analysis done in the phase-A instrument study., Comment: 12 pages, 9 figures, 7 tables. SPIE conference Astronomical Telescopes and Instrumentation, 14 - 18 December 2020, digital forum

The Multi-conjugate Adaptive Optics RelaY (MAORY) should provide 30% SR in K band (50% goal) on half of the sky at the South Galactic Pole. Assessing its performance and the sensitivity to parameter variations during the design phase is a fundamental step for the engineering of such a complex system. This step, centered on numerical simulations, is the connection between the performance requirements and the Adaptive Optics system configuration. In this work we present MAORY configuration and performance and we justify theAdaptive Optics system design choices., Comment: 9 pages, 7 figures, 1 table. SPIE conference Astronomical Telescopes and Instrumentation, 14 - 18 December 2020, digital forum