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.
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.
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.
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.
KEYWORDS: Adaptive optics, Wavefront sensors, Linear filtering, Deformable mirrors, Wavefronts, Scintillation, Data modeling, Image resolution, Actuators, Control systems
Themis is a 90 cm solar telescope which undergoes a rejuvenation of its scientific instruments. In particular, it is about to be equipped with an adaptive optics (AO) system with a bandwidth of at least 1 kHz and featuring a 97 actuator deformable mirror and 10×10 Shack-Hartmann wavefront sensor. Nowadays, the computational power required by such a system can be provided by current multi-core CPU. We have therefore implemented from scratch the real-time control system in pure software using Julia,1 a new language for technical computations, and running on Linux OS. Our main motivation was to be able to exploit new advances in wavefront sensing and adaptive optics control.
With a computational cost comparable to state-of-the-art but sub-optimal methods used in solar AO, our wavefront sensing algorithm estimates the local slopes and their covariances following a maximum likelihood registration method.
Themis AO system has a modest size but can be used to assert the benefits of maximum a posteriori (MAP) wavefront sensing and control,2, 3 of accounting of the covariances of the measure and of the temporal correlation of the turbulent wavefront.
After completion of its final-design review last year, it is full steam ahead for the construction of the MOONS instrument - the next generation multi-object spectrograph for the VLT. This remarkable instrument will combine for the first time: the 8 m collecting power of the VLT, 1000 optical fibres with individual robotic positioners and both medium- and high-resolution spectral coverage acreoss the wavelength range 0.65μm - 1.8 μm. Such a facility will allow a veritable host of Galactic, Extragalactic and Cosmological questions to be addressed. In this paper we will report on the current status of the instrument, details of the early testing of key components and the major milestones towards its delivery to the telescope.
Multi-Conjugate Adaptive Optics (MCAO) systems aim at correcting for the atmospheric turbulence uniformly over wide-field observations. Compared to classical AO, this requires a tomographic reconstruction of the turbulence perturbations, that is to say a reconstruction of the atmosphere in its volume, and the control of several deformable mirrors optically conjugated to various altitudes. During the last two decades, many tomographic reconstructors have been proposed in the AO literature and some have been implemented on sky on existing MCAO systems. This paper presents an overview of MCAO reconstructors. Four categories of reconstructors are considered: i) the reconstructors based on interaction matrix; ii) the minimum-variance static reconstructors; iii) the 3-step recontructors and iv) the Kalman-based reconstructors. We discuss their relative advantages and drawbacks.
The Multi-Object Optical and Near-infrared Spectrograph (MOONS) will cover the Very Large Telescope's (VLT) field of view with 1000 fibres. The fibres will be mounted on fibre positioning units (FPU) implemented as two-DOF robot arms to ensure a homogeneous coverage of the 500 square arcmin field of view. To accurately and fast determine the position of the 1000 fibres a metrology system has been designed. This paper presents the hardware and software design and performance of the metrology system. The metrology system is based on the analysis of images taken by a circular array of 12 cameras located close to the VLTs derotator ring around the Nasmyth focus. The system includes 24 individually adjustable lamps. The fibre positions are measured through dedicated metrology targets mounted on top of the FPUs and fiducial markers connected to the FPU support plate which are imaged at the same time. A flexible pipeline based on VLT standards is used to process the images. The position accuracy was determined to ~5 μm in the central region of the images. Including the outer regions the overall positioning accuracy is ~25 μm. The MOONS metrology system is fully set up with a working prototype. The results in parts of the images are already excellent. By using upcoming hardware and improving the calibration it is expected to fulfil the accuracy requirement over the complete field of view for all metrology cameras.
We report the study and analysis of different methods to generate arbitrary patterns of sodium laser guide stars asterisms starting from a single laser beam by using continuous face-sheet deformable mirrors. Two laser beam shaping procedures based on iterative Fourier transform algorithms have been explored. Numerical simulations with realistic parameters have been carried out to highlight the requirements on the phase retrieval algorithm and on the deformable mirrors employed.
The knowledge of the atmospheric turbulence profile directly above the telescope using the telemetry from wide-field
Adaptive Optics (AO) measurements can be extremely useful for the optimization of the correction in the new
generation of AO systems. For this purpose, two techniques have been recently implemented at the Gemini South
MCAO System (GeMS); both based on the SLODAR method. The first technique uses a matrix inversion approach of
the slopes covariance matrices and the second deconvolves the cross-correlation functions between all combinations of
slopes using the auto-correlation responses.
The deconvolution approach has proved to be more reliable that the one based on matrices inversion, so we use it for
estimating the profiles from on-sky telemetry gathered over three years (2012 - 2014), obtaining statistical parameters of
the turbulence at Cerro Pachón. These results are summarized in this article.
Particular attention is paid to the occurrence of turbulence in the dome of the Gemini South telescope.
Multiple sodium laser beacons are a crucial development in multi-conjugate adaptive optics systems that offers wide-field diffraction limited adaptive optics correction to the astronomical community. This correction is strongly dependent on the laser beam power and quality, so a beam shaping concept is currently being developed to speed-up calibration and alignment of the laser before every run. A method previously reported, has now been implemented on a laboratory bench using MEMS deformable mirrors. Necessary calibration and characterization of the deformable mirrors are described and the results for experimental amplitude correction are presented.
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 C2 N and wind profile in the main turbulence layers (see e.g. Cortes et al. 20121). 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., 20132), 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.
Solar Adaptive Optics (AO) shares many issues with night-time AO, but it also has its own particularities. The wavefront sensing is performed using correlations to efficiently work on the solar granulation as a reference. The field of view for that measurement usually is around 10". A sensor collecting such a wide field of view averages wavefront information from different sky directions, and the anisoplanatism thus has a peculiar impact on the performance of solar AO and MCAO systems. Since we are entering the era of large solar telescopes (European Solar Telescope, Advanced Technology Solar Telescope) understanding this issue is crucial to evaluate its impact on the performance of future AO systems. In this paper we model the correlating wide field sensor and the way it senses the high altitude turbulence. Thanks to this improved modelling, we present an analysis of the influence of this sensing on the performance of each AO configuration, conventional AO and MCAO. In addition to the analytical study, simulations similar to the case of the EST AO systems with FRiM-3D (the Fractal Iterative Method for Atmospheric tomography) are used in order to highlight the relative influence of design parameters. In particular, results show the performance evolution when increasing the telescope diameter. We analyse the effect of high altitude turbulence correlation showing that increasing the diameter of the telescope does not degrade the performance when correcting on the same spatial and temporal scales.
Two algorithms were recently studied for C2n profiling from wide-field Adaptive Optics (AO) measurements on GeMS (Gemini Multi-Conjugate AO system). They both rely on the Slope Detection and Ranging (SLODAR) approach, using spatial covariances of the measurements issued from various wavefront sensors. The first algorithm estimates the C2n profile by applying the truncated least-squares inverse of a matrix modeling the response of slopes covariances to various turbulent layer heights. In the second method, the profile is estimated by deconvolution of these spatial cross-covariances of slopes. We compare these methods in the new configuration of ESO Adaptive Optics Facility (AOF), a high-order multiple laser system under integration. For this, we use measurements simulated by the AO cluster of ESO. The impact of the measurement noise and of the outer scale of the atmospheric turbulence is analyzed. The important influence of the outer scale on the results leads to the development of a new step for outer scale fitting included in each algorithm. This increases the reliability and robustness of the turbulence strength and profile estimations.
The European Solar Telescope (EST) will be a 4-meter diameter world-class facility, optimized for studies of the magnetic coupling between the deep photosphere and upper chromosphere. It will specialize in high spatial resolution observations and therefore it has been designed to incorporate an innovative built-in Multi-Conjugate Adaptive Optics system (MCAO). It combines a narrow field high order sensor that will provide the information to correct the ground layer and a wide field low order sensor for the high altitude mirrors used in the MCAO mode. One of the challenging particularities of solar AO is that it has to be able to correct the turbulence for a wide range of observing elevations, from zenith to almost horizon. Also, seeing is usually worse at day-time, and most science is done at visible wavelengths. Therefore, the system has to include a large number of high altitude deformable mirrors. In the case of the EST, an arrangement of 4 high altitude DMs is used. Controlling such a number of mirrors makes it necessary to use fast reconstruction algorithms to deal with such large amount of degrees of freedom. For this reason, we have studied the performance of the Fractal Iterative Method (FriM) and the Fourier Transform Reconstructor (FTR), to the EST MCAO case. Using OCTOPUS, the end-to-end simulator of the European Southern Observatory, we have performed several simulations with both algorithms, being able to reach the science requirement of a homogeneous Strehl higher that 50% all over the 1 arcmin field of view.
FrIM-3D is a novel algorithm developed for high performance in Adaptive Optics (AO) on the Extremely Large Telescopes.
It particularly solves the problem of the minimum-variance tomographic reconstruction involved in AO. Until recently
however, it was missing an optimal projection of the reconstructed atmosphere on the space of deformable mirrors, to
guarantee the best performance for every tomographic AO system. In this paper, we present a formal solution to this
projection problem. For that, a formalism based on continuous functions and modeling of the AO is chosen, in order to
clearly analyze the modeling approximations. The projector is defined as the solution of an optimization problem with
respect to AO objectives, potentially different for every wide-field AO system. After the projector derivation, we describe
a fast algorithm to apply it, and in particular how to handle the piston-removal computations. This algorithm is currently
being implemented as part of FrIM-3D.
The adaptive optics (AO) on the European Extremely Large Telescope, as well as earlier pathfinders like the
Adaptive Optics Facility, at the Very Large Telescope in 2014, will no longer be stationary systems. AO is no
longer isolated on a bench; some elements are directly in the optical train of the telescope, suffering environment
and constrains changes during the observations. To guarantee good performance at any observing time, we
investigate a self-calibration strategy. We focus here on one of the most challenging aspects: the identification
of system parameters during closed-loop observations without introducing any additional disturbance. Such
problem is known in the identification theory to be difficult to solve. We have recently presented (Béchet et al.,
AO4ELT2 Conference, 2011) an identification method for this, with promising results obtained in simulations.
To consolidate these advances, we come back in the present paper to the equations and provide a theoretical
analysis to justify the choice of the algorithm. We highlight the benefit of using incremental data and commands
to decorrelate the disturbance. We also present 2 implementations of the method, currently studied at the
European Southern Observatory.
The AOF project will transform one of the VLT UT into an adaptive telescope. This configuration presents new
challenges but also provides new opportunities for the integration of the Adaptive Optics in the global telescope control
scheme and performance improvement. In particular the Interaction Matrix between the Deformable Mirror and
Wavefront Sensor of the system cannot be measured on an artificial source, as there is no intermediate focal plane ahead
of the Deformable Mirror. The baseline for the AOF is to use a Pseudo-Pynthetic IM, i.e. computer-generated but finetuned
thanks to measured parameters of the system: Influence Functions, WFS characteristics, mis-alignments. This
paper presents the control strategy of the AOF, the simulation code that will be used to generate the PSIM for the AOF,
and the ideas for updating the Control Matrix depending on the estimation of the DM/WFS mis-registration.
The ESO Adaptive Optics Facility (AOF) consists in an evolution of one of the ESO VLT unit telescopes to a laser
driven adaptive telescope with a deformable mirror in its optical train.
The project has completed the procurement phase and several large structures have been delivered to Garching
(Germany) and are being integrated (the AO modules GRAAL and GALACSI and the ASSIST test bench). The 4LGSF
Laser (TOPTICA) has undergone final design review and a pre-production unit has been built and successfully tested.
The Deformable Secondary Mirror is fully integrated and system tests have started with the first science grade thin shell
mirror delivered by SAGEM. The integrated modules will be tested in stand-alone mode in 2012 and upon delivery of
the DSM in late 2012, the system test phase will start. A commissioning strategy has been developed and will be updated
before delivery to Paranal. A substantial effort has been spent in 2011-2012 to prepare the unit telescope to receive the
AOF by preparing the mechanical interfaces and upgrading the cooling and electrical network. This preparation will also
simplify the final installation of the facility on the telescope.
A lot of attention is given to the system calibration, how to record and correct any misalignment and control the whole
facility. A plan is being developed to efficiently operate the AOF after commissioning. This includes monitoring a
relevant set of atmospheric parameters for scheduling and a Laser Traffic control system to assist the operator during the
night and help/support the observing block preparation.
In this paper, we present simulation work done on AO systems for the E-ELT. We study the influence of the number of
Laser Guide Stars (LGS) on system performance. Then, we investigate the impact of the conjugation height of the M4
adaptive mirror on GL/LT/MC-AO. Finally, we compare the results of a Fourier code and end-to-end models on the
position of the LGS in the field of view.
The ESO Adaptive Optics Facility (AOF) consists in an evolution of one of the ESO VLT unit telescopes to a laser
driven adaptive telescope with a deformable mirror in its optical train, in this case the secondary 1.1m mirror, and four
Laser Guide Stars (LGSs). This evolution implements many challenging technologies like the Deformable Secondary
Mirror (DSM) including a thin shell mirror (1.1 m diameter and 2mm thin), the high power Na lasers (20W), the low
Read-Out Noise (RON) WaveFront Sensor (WFS) camera (< 1e-) and SPARTA the new generation of Real Time
Computers (RTC) for adaptive control. It also faces many problematic similar to any Extremely Large Telescope (ELT)
and as such, will validate many technologies and solutions needed for the European ELT (E-ELT) 42m telescope. The
AOF will offer a very large (7 arcmin) Field Of View (FOV) GLAO correction in J, H and K bands (GRAAL+Hawk-I),
a visible integral field spectrograph with a 1 arcmin GLAO corrected FOV (GALACSI-MUSE WFM) and finally a
LTAO 7.5" FOV (GALACSI-MUSE NFM). Most systems of the AOF have completed final design and are in
manufacturing phase. Specific activities are linked to the modification of the 8m telescope in order to accommodate the
new DSM and the 4 LGS Units assembled on its Center-Piece. A one year test period in Europe is planned to test and
validate all modes and their performance followed by a commissioning phase in Paranal scheduled for 2014.
A challenge of adaptive optics (AO) on Extremely Large Telescopes (ELTs) is to overcome the difficulty of solving a huge
number of equations in real time, especially when atmospheric tomography is involved. This is particularly the case for
multi-conjugate or multi-objects AO systems. In addition, the quality of the wavefront estimation is crucial to optimize the
performances of the future systems in a situation where measurements are missing and noises are correlated.
The Fractal Iterative Method has been introduced as a fast iterative algorithm for minimum variance wavefront reconstruction
and control on ELTs. This method has been successfully tested on Classical Single Conjugate AO systems on
Octopus numerical simulator at ESO. But the minimum variance approach is expected to be mostly useful with atmospheric
tomography.
We present the first results obtained with FrIM in the context of atmospheric tomography. We recall the principle of
the algorithm and we summarize the formalism used for modeling the measurements obtained from laser guide stars that
entail spot elongation and tip/tilt indetermination, mixed with low order measurements from natural guide stars. We show
the respective effects of tip/tilt indetermination, spot elongation, unseen modes on various configurations, as well as the
usefulness of priors and correct noise models in the reconstruction.
This analysis is essential for balancing the various errors that combine in a quite complex way and to optimize the
configuration of the future AO systems for specific science cases and instrument requirements.
LITpro is a software for fitting models on data obtained from various stellar optical interferometers, like the VLTI. As a
baseline, for modeling the object, it provides a set of elementary geometrical and center-to-limb darkening functions, all
combinable together. But it is also designed to make very easy the implementation of more specific models with their
own parameters, to be able to use models closer to astrophysical considerations. So LITpro only requires the modeling
functions to compute the Fourier transform of the object at given spatial frequencies, and wavelengths and time if needed.
From this, LITpro computes all the necessary quantities as needed (e.g. visibilities, spectral energy distribution, partial
derivatives of the model, map of the object model). The fitting engine, especially designed for this kind of optimization, is
based on a modified Levenberg-Marquardt algorithm and has been successfully tested on real data in a prototype version.
It includes a Trust Region Method, minimizing a heterogeneous non-linear and non-convex criterion and allows the user
to set boundaries on free parameters. From a robust local minimization algorithm and a starting points strategy, a global
optimization solution is effectively achieved. Tools have been developped to help users to find the global minimum. LITpro
is also designed for performing fitting on heterogeneous data. It will be shown, on an example, how it fits simultaneously
interferometric data and spectral energy distribution, with some benefits on the reliability of the solution and a better
estimation of errors and correlations on the parameters. That is indeed necessary since present interferometric data are
generally multi-wavelengths.
The turbulent wavefront reconstruction step in an adaptive optics system is an inverse problem. The Mean-Square Error
(MSE) assessing the reconstruction quality is made of two terms, often called bias and variance. The latter is also
commonly referred as the noise propagation. The aim of this paper is to investigate the evolution of these two error contributions
when the number of parameters to be estimated becomes of the order of 10 4. Such dimensions are expected for the
adaptive optics systems on the Extremely Large Telescopes. We provide an algebraic formalism to compare the MSE of
Maximum Likelihood and Maximum A Posteriori linear reconstructors. A Generalized Singular Value Decomposition applied
on the reconstructors theoretically enhances the differences between zonal and modal approaches, and demonstrates
the gain in using Maximum A Posteriori method. Thanks to numerical simulations, we quantitatively study the evolution
of the MSE contributions with respect to the pupil shape, to the outer scale of the turbulence, to the number of actuators
and to the signal-to-noise ratio. Simulations results are consistent with previous noise propagation studies and with our
algebraic analysis. Finally, using the Fractal Iterative Method as a Maximum A Posteriori reconstruction algorithm in
our simulations, we demonstrate a possible reduction of the MSE of a factor 2 in large adaptive optics systems, for low
signal-to-noise ratio.
The current projects of Extremely Large Telescopes rely on adaptive optics systems using several sodium laser guide
stars (LGSs). Because of the thickness of the sodium layer in the mesosphere, the subapertures of a Shack-Hartmann
wavefront sensor will see the LGS all the more elongated as its position is distant from the launching point of the laser.
This effect is significant and prompts the lasers to be launched from behind the secondary instead of from around the
telescope. The elongations increase the centroiding errors and new smarter algorithms have been designed to mitigate
this effect, but the loss of accuracy is still significant. Further, the measurement uncertainties are no more uniform across
the pupil and correlations are introduced between the two coordinates of the gradients. From numerical simulations, we
analyze the benefit of taking into account this structured correlations in wavefront reconstruction algorithms and compare
the reconstruction accuracy when using least squares, weighted least squares, or minimum variance using von Karman
turbulence priors. For a single LGS launched behind the secondary, numerical simulations show effective improvements
when using both noise correlations and priors in wavefront reconstruction. When combining the measurements from
several LGSs in a Ground Layer adaptive optics system, we show that taking into account the noise covariances yields
better reconstructions when LGSs are launched from around the telescope than from behind the secondary. Further, results
indicate that we could discard the measurements along the elongated direction where this elongation is greater than a given
threshold.
KEYWORDS: Adaptive optics, Data modeling, Turbulence, Error analysis, Monte Carlo methods, K band, Computer simulations, Iterative methods, Fractal analysis, Wavefronts
Adaptive Optics systems under study for the Extremely Large Telescopes gave rise to a new generation of algorithms for
both wavefront reconstruction and the control law. In the first place, the large number of controlled actuators impose the
use of computationally efficient methods. Secondly, the performance criterion is no longer solely based on nulling residual
measurements. Priors on turbulence must be inserted. In order to satisfy these two requirements, we suggested to associate
the Fractal Iterative Method for the estimation step with an Internal Model Control.
This combination has now been tested on an end-to-end adaptive optics numerical simulator at ESO, named Octopus.
Results are presented here and performance of our method is compared to the classical Matrix-Vector Multiplication combined
with a pure integrator. In the light of a theoretical analysis of our control algorithm, we investigate the influence
of several errors contributions on our simulations. The reconstruction error varies with the signal-to-noise ratio but is
limited by the use of priors. The ratio between the system loop delay and the wavefront coherence time also impacts on
the reachable Strehl ratio. Whereas no instabilities are observed, correction quality is obviously affected at low flux, when
subapertures extinctions are frequent. Last but not least, the simulations have demonstrated the robustness of the method
with respect to sensor modeling errors and actuators misalignments.
Adaptive optics (AO) systems under study for the future generation of telescopes have to cope with a huge number of degrees of freedom. This number N is typically 2 orders of magnitude larger than for the currently existing AO systems. An iterative method using a fractal preconditioning, has recently been suggested for a minimum-variance reconstruction in O(N) operations. We analyze the efficiency of this algorithm for both the open-loop and the closed-loop configurations. We present the formalism and illustrate the assets of this method with simulations. While the number of iterations for convergence is around 10 in open-loop, the closed-loop configuration induces a reduction of the required number of iterations by a factor of 3 typically. This analysis also enhances the importance of introducing priors to ensure an optimal command. Closed-loop simulations demonstrate the loss of performance when no temporal priors are used. Besides, we discuss the importance of an accurate model for both the system and its uncertainties, so as to ensure a stable behavior in closed-loop.
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