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Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (⁠|$r_0$|⁠) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope's MUSE instrument. Two approaches were analysed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (⁠|$r_0$|⁠) and residual AO variance (⁠|$\sigma _{AO}^2$|⁠). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations. [ABSTRACT FROM AUTHOR]

Context. Upcoming giant segmented mirror telescopes will use laser guide stars (LGS) for their adaptive optics (AO) systems. Two options of wavefront sensors (WFSs) are the Shack-Hartmann wavefront sensor (SHWFS) and the pyramid wavefront sensor (PWFS). Aims. In this paper, we compare the noise performance of the PWFS and the SHWFS. We aim to identify which of the two is best to use in the context of a single or tomographic configuration. Methods. To compute the noise performance, we extended a noise model developed for the PWFS to be used with the SHWFS. To do this, we expressed the centroiding algorithm of the SHWFS as a matrix-vector multiplication, which allowed us to use the statistics of noise to compute its propagation through the AO loop. We validated the noise model with end-to-end simulations for telescopes of 8 and 16 m in diameter. Results. For an AO system with only one WFS, we found that given the same number of subapertures, the PWFS outperforms the SHWFS. For a 40 m telescope, the limiting magnitude of the PWFS is around one magnitude higher than the SHWFS. When using multiple WFS and a generalized least-squares estimator to combine the signal, our model predicts that in a tomographic system, the SHWFS performs better than the PWFS (with a limiting magnitude that is higher by a 0.3 magnitude. When using sub-electron RON detectors for the PWFS, the performance quality is almost identical for the two WFSs. Conclusions. We find that when using a single WFS with LGS, PWFS is a better alternative than the SH. For a tomographic system, both sensors would give roughly the same performance. [ABSTRACT FROM AUTHOR]

Context. Extremely large telescopes are overwhelmingly equipped with pyramid wavefront sensors (PyWFS) over the more widely used Shack–Hartmann wavefront sensor to perform their single-conjugate adaptive optics (SCAO) mode. The PyWFS, a sensor based on Fourier filtering, has proven to be highly successful in many astronomy applications. However, this sensor exhibits non-linear behaviours that lead to a reduction of the sensitivity of the instrument when working with non-zero residual wavefronts. This so-called optical gains (OG) effect, degrades the closed-loop performance of SCAO systems and prevents accurate correction of non-common path aberrations (NCPA). Aims. In this paper, we aim to compute the OG using a fast and agile strategy to control PyWFS measurements in adaptive optics closed-loop systems. Methods. Using a novel theoretical description of PyWFS, which is based on a convolutional model, we are able to analytically predict the behaviour of the PyWFS in closed-loop operation. This model enables us to explore the impact of residual wavefront errors on particular aspects such as sensitivity and associated OG. The proposed method relies on the knowledge of the residual wavefront statistics and enables automatic estimation of the current OG. End-to-end numerical simulations are used to validate our predictions and test the relevance of our approach. Results. We demonstrate, using on non-invasive strategy, that our method provides an accurate estimation of the OG. The model itself only requires adaptive optics telemetry data to derive statistical information on atmospheric turbulence. Furthermore, we show that by only using an estimation of the current Fried parameter r0 and the basic system-level characteristics, OGs can be estimated with an accuracy of less than 10%. Finally, we highlight the importance of OG estimation in the case of NCPA compensation. The proposed method is applied to the PyWFS. However, it remains valid for any wavefront sensor based on Fourier filtering subject from OG variations. [ABSTRACT FROM AUTHOR]

Point-spread function (PSF) reconstruction (PSF-R) is a well-established technique to determine the PSF reliably and accurately from adaptive optics (AO) control-loop data. We have successfully applied this technique to improve the precision of photometry and astrometry for observations of NGC 6121 obtained with the Spectro Polarimetric High-contrast Exoplanet REsearch (SPHERE)/Zurich IMaging POLarimeter (ZIMPOL), which will be presented in a forthcoming Letter. First, we present the methodology we followed to reconstruct the PSF by combining pupil-plane and focal-plane measurements using our PSF-R method PRIME (PSF Reconstruction and Identification for Multiple-source characterization Enhancement), with upgrades of both the model and best-fitting steps compared with previous articles. Secondly, we highlight that PRIME allows us to maintain the PSF fitting residual below 0.2 per cent over 2 hours of observation and using only 30 s of AO telemetry, which may have important consequences for telemetry storage for PSF-R purposes on future 30–40 m class telescopes. Finally, we deploy PRIME in a more realistic regime using faint stars, so as to identify the precision needed on the initial-guess parameters to ensure convergence towards the optimal solution. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

For extremely large telescopes, adaptive optics will be required to correct the Earth's turbulent atmosphere. The performance of tomographic adaptive optics is strongly dependent on the vertical distribution (profile) of this turbulence. An important way in which this manifests is the tomographic error, arising from imperfect measurement and reconstruction of the turbulent phase at altitude. Conventionally, a small number of reference profiles are used to obtain this error in simulation; however these profiles are not constructed to be representative in terms of tomographic error. It is therefore unknown whether these simulations are providing realistic performance estimates. Here, we employ analytical adaptive optics simulation that drastically reduces computation times to compute tomographic error for 10 691 measurements of the turbulence profile gathered by the Stereo-SCIDAR instrument at ESO Paranal. We assess for the first time the impact of the profile on tomographic error in a statistical manner. We find, in agreement with previous work, that the tomographic error is most directly linked with the distribution of turbulence into discrete, stratified layers. Reference profiles are found to provide mostly higher tomographic error than expected, which we attribute to the fact that these profiles are primarily composed of averages of many measurements resulting in unrealistic, continuous distributions of turbulence. We propose that a representative profile should be defined with respect to a particular system, and that as such simulations with a large statistical sample of profiles must be an important step in the design process. [ABSTRACT FROM AUTHOR]

In order to enhance the scientific exploitation of adaptive optics (AO)-assisted observations, we investigate a novel hybrid concept to improve the parametric estimation of point spread function (PSF) called PSF Reconstruction and Identification for Multiple-source characterization Enhancement (PRIME). PRIME uses both focal and pupil-plane measurements to estimate jointly the model parameters related to the atmosphere [ |$C_n^2(h)$|⁠ , seeing] and the AO system (e.g. optical gains and residual low-order errors). Photometry and astrometry are provided as by-products. The parametric model in use is flexible enough to be scaled with field location and wavelength, making it a proper choice for optimized on-axis and off-axis data-reduction across the spectrum. Here, we present the methodology and validate PRIME on engineering and binary Keck II telescope NIRC2 images. We also present applications of PSF model parameters retrieval using PRIME: (i) calibrate the PSF model for observations void of stars on the acquired images, i.e. optimize the PSF reconstruction process, (ii) update the AO error breakdown mutually constrained by the telemetry and the images in order to speculate on the origin of the missing error terms and evaluate their magnitude, and (iii) measure photometry and astrometry with an application to the triple system Gl569 images. [ABSTRACT FROM AUTHOR]

Several telescopes include large deformable mirrors (DM) located directly inside the telescope. These adaptive telescopes trigger new constraints for the calibration of the adaptive optics (AO) systems as they usually offer no access to an artificial calibration source for the interaction matrix measurement. Moreover, the optical propagation between the DM and the wavefront sensor (WFS) may evolve during the operation, resulting in misregistrations that highly affect the AO performance and thus the scientific observation. They have to be measured and compensated, for instance by updating the calibration. A new strategy consists of estimating the misregistrations and injecting them into synthetic models to generate noise-free interaction matrices. This pseudo-synthetic approach is the baseline for the adaptive optics facility working with a Shack–Hartmann WFS and seems particularly suited for the future Extremely Large Telescope as the calibration will have to be regularly updated, for a large numbers of actuators. In this paper, the feasibility of a pseudo-synthetic calibration with pyramid WFS at the Large Binocular Telescope (LBT) is investigated. A synthetic model of the LBT AO systems is developed, and the procedure to adjust the misregistrations parameters is introduced, extracting them from an experimental interaction matrix. We successfully tested an interaction matrix generated from the model on the real system in high-order AO mode. We recorded a slightly better performance with respect to the experimental one. This work demonstrates that a high-accuracy calibration can be obtained using the pseudo-synthetic approach with pyramid WFS. [ABSTRACT FROM AUTHOR]

Knowledge of the atmospheric turbulence in the telescope line-of-sight is crucial for wide-field observations assisted by adaptive optics (AO), particularly tomodel how the point spread function (PSF) elongates across the field of view (FOV) owing to the anisoplanatism effect. The extraction of key astronomical parameters accounts on an accurate representation of the PSF, which call for an accurate anisoplanatism characterisation. This one is, however, a function of the |$C_n^2(h)$| profile, which is not directly accessible from single-conjugate AO telemetry. It is possible to rely on external profilers, but recent studies have highlighted discrepancies of more than 10 per cent with AO internal measurements, while we aim at better than 1 per cent accuracy for PSF modelling. In order to tackle this limitation, we present focal-plane profiling (FPP) as a |$C_n^2(h)$| profiling method that relies on post-AO focal-plane images. We demonstrate that such an approach complies with a 1 per cent level of accuracy on the |$C_n^2(h)$| estimation and establish how this accuracy varies regarding the calibration star magnitudes and their positions in the field. We highlight the fact that photometry and astrometry errors caused by PSF mis-modelling reach respectively 1 per cent and 50 μas using FPP on a Keck baseline, with a preliminary calibration using a star of magnitude H = 14 at 20 arcsec. We validate this concept using Canada's NRC–Herzberg HeNOS testbed images by comparing FPP retrieval with alternative |$C_n^2(h)$| measurements on HeNOS. The FPP approach allows the |$C_n^2(h)$| to be profiled using the SCAO systems and significantly improves the PSF characterization. Such a methodology is also ELT-size-compliant and will be extrapolated to tomographic systems in the near future. [ABSTRACT FROM AUTHOR]

We present detailed simulations of integral field spectroscopic observations of a supernova in a host galaxy at z  ∼ 3, as observed by the HARMONI spectrograph on the Extremely Large Telescope, assisted by laser tomographic adaptive optics. The goal of the simulations, using the HSIM simulation tool, is to determine whether HARMONI can discern the supernova type from spectral features in the supernova spectrum. We find that in a 3 h observation, covering the near-infrared H and K bands, at a spectral resolving power of ∼3000, and using the 20 × 20 mas spaxel scale, we can classify Type Ia supernovae and their redshift robustly up to 80 d past maximum light (20 d in the supernova rest frame). We show that HARMONI will provide spectra at z  ∼ 3, which are of comparable (or better) quality to the best spectra we can currently obtain at z  ∼ 1, thus allowing studies of cosmic expansion rates to be pushed to substantially higher redshifts. [ABSTRACT FROM AUTHOR]

Wide Field Adaptive Optics (WFAO) systems are among the most sophisticated adaptive optics (AO) systems available today on large telescopes. Knowledge of the vertical spatio-temporal distribution of wind speed (WS) and direction (WD) is fundamental to optimize the performance of such systems. Previous studies already proved that the Gemini Multi-Conjugated AO system (GeMS) is able to retrieve measurements of the WS and WD stratification using the SLOpe Detection And Ranging (SLODAR) technique and to store measurements in the telemetry data. In order to assess the reliability of these estimates and of the SLODAR technique applied to such complex AO systems, in this study we compared WS and WD values retrieved from GeMS with those obtained with the atmospheric model Meso-NH on a rich statistical sample of nights. It has previously been proved that the latter technique provided excellent agreement with a large sample of radiosoundings, both in statistical terms and on individual flights. It can be considered, therefore, as an independent reference. The excellent agreement between GeMS measurements and the model that we find in this study proves the robustness of the SLODAR approach. To bypass the complex procedures necessary to achieve automatic measurements of the wind with GeMS, we propose a simple automatic method to monitor nightly WS and WD using Meso-NH model estimates. Such a method can be applied to whatever present or new-generation facilities are supported byWFAO systems. The interest of this study is, therefore, well beyond the optimization of GeMS performance. [ABSTRACT FROM AUTHOR]

Whether ground based or space based, any optical instrument suffers from some amount of optical geometric distortion. Recently, the diffraction-limited image quality afforded by spacebased telescopes and by instruments corrected with adaptive optics on ground-based telescope has increased the relative importance of the error terms induced by optical distortions. In particular, the variable distortion in multi-conjugate adaptive optics (MCAO) data limits the astrometric and photometric accuracy of such high-resolution instruments. These phenomena have become a critical issue for high-precision studies. We present in this paper an optimal method of distortion correction for high-angular-resolution images. Based on prior knowledge of the static distortion, the method aims to correct the dynamic distortion for each observation set and each frame. The method follows an inverse problem approach based on the work by Gratadour, Mugnier & Rouan on image re-centring, and we aim to generalize this to any kind of distortion mode. The complete formalism of a weighted least-squares minimization as well as a detailed characterization of the error budget are presented. In particular, we study the influence of different parameters such as the number of frames, the density of the field (sparse or crowed images), the noise level and the aliasing effect. Finally, we show the first application of the method on real observations collected with the Gemini MCAO instrument, GeMS/GSAOI. The performance of as well as the gain brought by this method are presented. [ABSTRACT FROM AUTHOR]

We describe an onlinemethod to estimate thewavefront outer scale profile, L0(h), for very large and future extremely large telescopes. The stratified information on this parameter impacts the estimation of the main turbulence parameters [turbulence strength, Cn²(h); Fried's parameter, r0; isoplanatic angle, τ0; and coherence time, t0) and determines the performance of widefield adaptive optics (AO) systems. This technique estimates L0(h) using data from the AO loop available at the facility instruments by constructing the cross-correlation functions of the slopes between two or more wavefront sensors, which are later fitted to a linear combination of the simulated theoretical layers having different altitudes and outer scale values. We analyse some limitations found in the estimation process: (i) its insensitivity to large values of L0(h) as the telescope becomes blind to outer scales larger than its diameter; (ii) the maximum number of observable layers given the limited number of independent inputs that the cross-correlation functions provide and (iii) the minimum length of data required for a satisfactory convergence of the turbulence parameters without breaking the assumption of statistical stationarity of the turbulence. The method is applied to the Gemini South multiconjugate AO system that comprises five wavefront sensors and two deformable mirrors. Statistics of L0(h) at Cerro Pach'on from data acquired during 3 yr of campaigns show interesting resemblance to other independent results in the literature. A final analysis suggests that the impact of error sources will be substantially reduced in instruments of the next generation of giant telescopes. [ABSTRACT FROM AUTHOR]

The Adaptive Optics Facility (AOF) project envisages transforming one of theVLT units into an adaptive telescope and providing its ESO (European Southern Observatory) second generation instruments with turbulence-corrected wavefronts. For MUSE and HAWK-I this correction will be achieved through the GALACSI and GRAALAOmodulesworking in conjunction with a 1170 actuators deformable secondary mirror (DSM) and the new Laser Guide Star Facility (4LGSF). Multiple wavefront sensors will enable GLAO (ground layer adaptive optics) and LTAO (laser tomography adaptive optics) capabilities, whose performance can greatly benefit from a knowledge about the stratification of the turbulence in the atmosphere. This work, totally based on end-to-end simulations, describes the validation tests conducted on a C²n profiler adapted for the AOF specifications. Because an absolute profile calibration is strongly dependent on a reliable knowledge of turbulence parameters r0 and L0, the tests presented here refer only to normalized output profiles. Uncertainties in the input parameters inherent to the code are tested as well as the profiler response to different turbulence distributions. It adopts a correction for the unseen turbulence, critical for the GRAAL mode, and highlights the effects of masking out parts of the corrected wavefront on the results. Simulations of data with typical turbulence profiles from Paranal were input to the profiler, showing that it is possible to identify reliably the input features for all the AOF modes. [ABSTRACT FROM AUTHOR]

Detailed knowledge of the mesospheric sodium layer characteristics is crucial to estimate and optimize the performance of laser guide star (LGS) assisted adaptive optics (AO) systems. In this paper, we present an analysis of two sets of data on the mesospheric sodium layer. The first set comes from a laser experiment that was carried out at Cerro Tololo to monitor the abundance and altitude of the mesospheric sodium in 2001, during six runs covering a period of one year. These data are used to derive the mesospheric sodium column density, the sodium layer thickness and the temporal behaviour of the sodium layer mean altitude. The second set of data was gathered during the first year of the Gemini Multi-Conjugate Adaptive Optics (MCAO) System (GeMS) commissioning and operations. GeMS uses five LGSs to measure and compensate for atmospheric distortions. Analysis of the LGS wavefront sensor (WFS) data provides information about the sodium photon return and the spot elongation seen by the WFS. All these parameters show large variations on a yearly, nightly and hourly basis, affecting the LGS brightness, shape and mean altitude. The sodium photon return varies by a factor of 3–4 over a year, and can change by a factor of 2 over a night. In addition, the comparison of the photon returns obtained in 2001 with those measured a decade later using GeMS shows a significant difference in laser format efficiencies. We find that the temporal power spectrum of the sodium mean altitude follows a linear trend, in good agreement with the results reported by Pfrommer & Hickson. [ABSTRACT FROM AUTHOR]

One of the main scientific goals of the future European Extremely Large Telescope (E-ELT) will be to understand the mass assembly process in galaxies as a function of cosmic time. To this aim, a multi-object, adaptive optics (AO)-assisted integral field spectrograph will be required to map the physical and chemical properties of very distant galaxies. In this paper, we examine the ability of such an instrument to obtain spatially resolved spectroscopy of a large sample of massive galaxies at , selected from future large area optical–near-IR surveys. We produced a set of about 1000 numerical simulations of 3D observations using reasonable assumptions about the site, telescope and instrument and about the physics of distant galaxies. These data cubes were analysed as real data to produce realistic kinematic measurements of very distant galaxies. We then studied how sensitive the scientific goals are to the observational (i.e. site-, telescope- and instrument-related) and physical (i.e. galaxy-related) parameters. We specifically investigated the impact of AO performance on the scientific goals. We did not identify any breaking points with respect to the parameters (e.g. the telescope diameter), with the exception of the telescope thermal background, which strongly limits the performance in the highest redshift bin. We find that a survey of galaxies that fulfil the range of scientific goals can be achieved with an ∼90-night programme on the E-ELT, provided a multiplex capability . [ABSTRACT FROM AUTHOR]

Elucidating the processes that governed the assembly and evolution of galaxies over cosmic time is one of the main objectives of all of the proposed Extremely Large Telescopes (ELT). To make a leap forward in our understanding of these processes, an ELT will want to take advantage of Multi-Objects Adaptive Optics (MOAO) systems, which can substantially improve the natural seeing over a wide field of view. We have developed an end-to-end simulation to specify the science requirements of a MOAO-fed integral field spectrograph on either an 8-m or 42-m telescope. Our simulations rescale observations of local galaxies or results from numerical simulations of disc or interacting galaxies. The code is flexible in that it allows us to explore a wide range of instrumental parameters such as ensquared energy (EE), pixel size, spectral resolution, etc. For the current analysis, we limit ourselves to a local disc galaxy which exhibits simple rotation and a simulation of a merger. While the number of simulations is limited, we have attempted to generalize our results by introducing the simple concepts of ‘point spread function (PSF) contrast’ which is the amount of light polluting adjacent spectra which we find drives the smallest EE at a given spatial scale. The choice of the spatial sampling is driven by the ‘scale-coupling’. By scale-coupling we mean the relationship between the integral field unit (IFU) pixel scale and the size of the features that need to be recovered by 3D spectroscopy in order to understand the nature of the galaxy and its substructure. Because the dynamical nature of galaxies is mostly reflected in their large-scale motions, a relatively coarse spatial resolution is enough to distinguish between a rotating disc and a major merger. Although we used a limited number of morphokinematic cases, our simulations suggest that, on a 42-m telescope, the choice of an IFU pixel scale of 50–75 mas seems to be sufficient. Such a coarse sampling has the benefit of lowering the exposure time to reach a specific signal-to-noise ratio as well as relaxing the performance of the MOAO system. On the other hand, recovering the full 2D kinematics of galaxies requires high signal-to-noise ratio and at least an EE of 34 per cent in 150 mas (2 pixels of 75 mas). Finally, we carried out a similar study for a hypothetical galaxy/merger at with a MOAO-fed spectrograph for an 8 m, and find that at least an EE of 30 per cent at 0.25 arcsec spatial sampling is required to understand the nature of discs and mergers. [ABSTRACT FROM AUTHOR]

In this paper, we describe Fourier-based wave-front sensors (WFSs) as linear integral operators, characterized by their kernel. In the first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil geometry, filtering mask, and tip/tilt modulation. In the second part, we focus the study on the special case of convolutional kernels. The assumptions required to be in such a regime are described. We then show that these convolutional kernels allow to drastically simplify the WFS model by summarizing its behavior in a concise and comprehensive quantity called the WFS impulse response. We explain in particular how it allows to compute the sensor's sensitivity with respect to spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In the third part, we develop the impact of the residual phases on the sensor's impulse response, and show that the convolutional model remains valid. Finally, a section dedicated to the pyramid WFS concludes this work and illustrates how the slope maps are easily handled by the convolutional model.

Tomographic wavefront reconstruction is the main computational bottleneck to realize real-time correction for turbulence-induced wavefront aberrations in future laser-assisted tomographic adaptive-optics (AO) systems for ground-based giant segmented mirror telescopes because of its unprecedented number of degrees of freedom, N, i.e., the number of measurements from wavefront sensors. In this paper, we provide an efficient implementation of the minimum-mean-square error (MMSE) tomographic wavefront reconstruction, which is mainly useful for some classes of AO systems not requiring multi-conjugation, such as laser-tomographic AO, multi-object AO, and ground-layer AO systems, but is also applicable to multi-conjugate AO systems. This work expands that by Conan [Proc. SPIE9148, 91480R (2014)PSISDG0277-786X10.1117/12.2054472] to the multi-wavefront tomographic case using natural and laser guide stars. The new implementation exploits the Toeplitz structure of covariance matrices used in an MMSE reconstructor, which leads to an overall O(N log N) real-time complexity compared with O(N 2 ) of the original implementation using straight vector-matrix multiplication. We show that the Toeplitz-based algorithm leads to 60 nm rms wavefront error improvement for the European Extremely Large Telescope laser-tomography AO system over a well-known sparse-based tomographic reconstruction; however, the number of iterations required for suitable performance is still beyond what a real-time system can accommodate to keep up with the time-varying turbulence.

The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data set which conform to specific boundary requirements, whereas wave-front sensor data is typically defined over a circular domain (the telescope pupil). Here we present an iterative Gerchberg routine modified for the purposes of discrete wave-front reconstruction which adapts the measurement data (wave-front sensor slopes) for Fourier analysis, fulfilling the requirements of the fast Fourier transform (FFT) and providing accurate reconstruction. The routine is used in the adaptation step only and can be coupled to any other Wiener-like or least-squares method. We compare simulations using this method with previous Fourier methods and show an increase in performance in terms of Strehl ratio and a reduction in noise propagation for a 40×40 SPHERE-like adaptive optics system. For closed loop operation with minimal iterations the Gerchberg method provides an improvement in Strehl, from 95.4% to 96.9% in K-band. This corresponds to ~ 40 nm improvement in rms, and avoids the high spatial frequency errors present in other methods, providing an increase in contrast towards the edge of the correctable band.

The continuous membrane stiffness of a deformable mirror propagates the deformation of the actuators beyond their neighbors. When phase-retrieval algorithms are used to determine the desired shape of these mirrors, this cross-coupling-also known as influence function (IF)-is generally disregarded. We study this problem via simulations and bench tests for different target shapes to gain further insight into the phenomenon. Sound modeling of the IF effect is achieved as highlighted by the concurrence between the modeled and experimental results. In addition, we observe that the actuators IF is a key parameter that determines the accuracy of the output light pattern. Finally, it is shown that in some cases it is possible to achieve better shaping by modifying the input irradiance of the phase-retrieval algorithm. The results obtained from this analysis open the door to further improvements in this type of beam-shaping systems.

We propose a new type of wave-front sensor (WFS) derived from the pyramid WFS (PWFS). This new WFS, called the flattened pyramid-WFS (FPWFS), has a reduced pyramid angle in order to optically overlap the four pupil images into an unique intensity. This map is then used to derive the phase information. In this Letter, this new WFS is compared to three existing WFSs, namely the PWFS, the modulated PWFS (MPWFS), and the Zernike WFS (ZWFS) following tests about sensitivity, linearity range, and low-photon-flux behavior. The FPWFS turns out to be more linear than a modulated pyramid for the high-spatial order aberrations, but it provides an improved sensitivity compared to the non-modulated pyramid. The noise propagation may even be as low as the ZWFS for some given radial orders. Furthermore, the pixel arrangement being more efficient than for the PWFS, the FPWFS seems particularly well suited for high-contrast applications.

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%.

We describe a new technique to reduce tip and tilt vibrations via the design of adaptive optics controllers in a frequency framework. The method synthesizes controllers by minimizing an H2 norm of the tip and tilt residuals. In this approach, open loop slopes (pseudo-open-loop) are reconstructed from on-sky data and input into off-line simulations of the adaptive optics system. The proposed procedure executes a sequence of off-line closed-loop runs with increasing controller complexity and searches for the controller that minimizes the variance of residuals. Although the method avoids any identification of the vibration and turbulence models during the controller synthesis, the actual models are indirectly constructed as a by-product of the H2 norm minimization. The technique has been implemented on and tested with two operational instruments, namely Paranal's NACO and Gemini-South's GeMS, showing an effective rejection of the main vibrations in the loop and also improving the overall performance of the system over varying turbulence conditions. It is shown that a superior performance is obtained when compared to the standard integrator controller.

Vibrations are detrimental to the performance of modern adaptive optics (AO) systems. In this paper, we describe new methods tested to mitigate the vibrations encountered in some of the instruments of the Gemini South telescope. By implementing a spectral analysis of the slope measurements from several wavefront sensors and an imager, we can determine the frequencies and magnitude of these vibrations. We found a persistent vibration at 55 Hz with others occurring occasionally at 14 and 100 Hz. Two types of AO controllers were designed and implemented, Kalman and H∞, in the multiconjugate AO tip-tilt loop. The first results show a similar performance for these advanced controllers and a clear improvement in vibration rejection and overall performance over the classical integrator scheme. It is shown that the reduction in the standard deviation of the residual slopes (as measured by wavefront sensors) is highly dependent on turbulence, wind speed, and vibration conditions, ranging--in terms of slopes RMS value--from an almost negligible reduction for high speed wind to a factor of 5 for a combination of low wind and strong vibrations.

Several wide-field-of-view adaptive optics (WFAO) concepts such as multi-conjugate AO (MCAO), multi-object AO (MOAO), and ground-layer AO (GLAO) are currently being studied for the next generation of Extremely Large Telescopes (ELTs). All these concepts will use atmospheric tomography to reconstruct the turbulent-phase volume. In this paper, we explore different reconstruction algorithms and their fundamental limitations, conducting this analysis in the Fourier domain. This approach allows us to derive simple analytical formulations for the different configurations and brings a comprehensive view of WFAO limitations. We then investigate model and statistical errors and their effect on the phase reconstruction. Finally, we show some examples of different WFAO systems and their expected performance on a 42 m telescope case.