Single Conjugate Adaptive Optics Research Articles

Non-modulated pyramid wavefront sensor

Context. The diffusion of adaptive optics systems in astronomical instrumentation for large ground-based telescopes is rapidly increasing and the pyramid wavefront sensor is replacing the Shack–Hartmann as the standard solution for single conjugate adaptive optics systems. The pyramid wavefront sensor is typically used with a tip-tilt modulation to increase the linearity range of the sensor, but the non-modulated case is interesting because it maximizes the sensor sensitivity. The latter case is generally avoided for the reduced linearity range that prevents robust operation in the presence of atmospheric turbulence. Aims. We aim to solve part of the issues of the non-modulated pyramid wavefront sensor by reducing the model error in the interaction matrix. We linearize the sensor response in the working conditions without extending the sensor linearity range. Methods. We developed a new calibration approach to model the response of pyramid wave front sensor in partial correction, whereby the working conditions in the presence of residual turbulence are considered. Results. We use in simulations to show how the new calibration approach allows for the pyramid wave front sensor without modulation to be used to sense and correct atmospheric turbulence and we discuss when this case is preferable over the modulated case.

Off-axis point spread function reconstruction forsingle conjugate adaptive optics.

Modern giant segmented mirror telescopes (GSMTs) such as the Extremely Large Telescope, which is currently under construction, depend heavily on adaptive optics (AO) systems to correct for atmospheric distortions. However, a residual blur always remains in the astronomical images corrected by single conjugate AO (SCAO) systems due to fitting and bandwidth errors, which can mathematically be described by a convolution of the true image with a point spread function (PSF). Due to the nature of the turbulent atmosphere and its correction, the PSF is spatially varying, which is known as an anisoplanatic effect. The PSF serves, e.g.,as a quality measure for science images and therefore needs to be known as accurately as possible. In this paper, we present an algorithm for PSF reconstruction from pupil-plane data in directions apart from the guide star direction in an SCAO system. Our algorithm is adapted to the needs of GSMTs focused on estimating the contribution of the anisoplanatic and generalized fitting error to the PSF. Results obtained in an end-to-end simulation tool show a qualitatively good reconstruction of the PSF compared to the PSF calculated directly from the simulated incoming wavefront as well as stable performance with respect to imprecise knowledge of atmospheric parameters.

Wavefront Recovery for Multiple Sun Regions in Solar SCAO Scenarios with Deep Learning Techniques

The main objective of an Adaptive Optics (AO) system is to correct the aberrations produced in the received wavefronts, caused by atmospheric turbulence. From some measures taken by ground-based telescopes, AO systems must reconstruct all the turbulence traversed by the incoming light and calculate a correction. The turbulence is characterized as a phenomenon that can be modeled as several independent, random, and constantly changing layers. In the case of Solar Single-Conjugated Adaptive Optics (Solar SCAO), the key is to reconstruct the turbulence on-axis with the direction of the observation. Previous research has shown that ANNs are a possible alternative when they have been trained in the Sun’s regions where they must make the reconstructions. Along this research, a new solution based on Artificial Intelligence (AI) is proposed to predict the atmospheric turbulence from the data obtained by the telescope sensors that can generalize recovering wavefronts in regions of the sun completely unknown previously. The presented results show the quality of the reconstructions made by this new technique based on Artificial Neural Networks (ANNs), specifically the Multi-layer Perceptron (MLP).

Research, Experiment and Validation of Adaptive Optics with a Legacy Telescope (REVOLT): First On-sky Results

The first on-sky results of the Research, Experiment and Validation of Adaptive Optics with a Legacy Telescope (REVOLT) project are presented, along with a description of the project and its purpose. The REVOLT project has so far demonstrated successful closed loop, single conjugate adaptive optics using a natural guide star at the 1.22 m McKellar telescope at the Dominion Astrophysical Observatory in Victoria, BC, Canada. In so doing, we have made the first on-sky demonstration of the Herzberg Extensible Adaptive Realtime Toolkit—based Real Time Controller, and First Light Imaging’s C-Blue One camera.

AIROPA II: modeling instrumental aberrations for off-axis point spread functions in adaptive optics

Images obtained with single-conjugate adaptive optics (AO) show spatial variation of the point spread function (PSF) due to both atmospheric anisoplanatism and instrumental aberrations. The poor knowledge of the PSF across the field of view strongly impacts the ability to take full advantage of AO capabilities. The AIROPA project aims to model these PSF variations for the NIRC2 imager at the Keck Observatory. Here, we present the characterization of the instrumental phase aberrations over the entire NIRC2 field of view and we present a new metric for quantifying the quality of the calibration, the fraction of variance unexplained (FVU). We used phase diversity measurements obtained on an artificial light source to characterize the variation of the aberrations across the field of view and their evolution with time. We find that there is a daily variation of the wavefront error (RMS of the residuals is 94~nm) common to the whole detector, but the differential aberrations across the field of view are very stable (RMS of the residuals between different epochs is 59~nm). This means that instrumental calibrations need to be monitored often only at the center of the detector, and the much more time-consuming variations across the field of view can be characterized less frequently (most likely when hardware upgrades happen). Furthermore, we tested AIROPA's instrumental model through real data of the fiber images on the detector. We find that modeling the PSF variations across the field of view improves the FVU metric by 60\% and reduces the detection of fake sources by 70\%.

Point spread function reconstruction for SOUL + LUCI LBT data

Here, we present the status of an ongoing project aimed at developing a point spread function (PSF) reconstruction software for adaptive optics (AO) observations. In particular, we test for the first time the implementation of pyramid wave-front sensor data on our algorithms. As a first step in assessing its reliability, we applied the software to bright, on-axis, point-like sources using two independent sets of observations, acquired with the single-conjugated AO upgrade for the Large Binocular Telescope. Using only telemetry data, we reconstructed the PSF by carefully calibrating the instrument response. The accuracy of the results has been first evaluated using the classical metric: specifically, the reconstructed PSFs differ from the observed ones by <2 % in Strehl ratio and 4.5% in full-width at half maximum. Moreover, the recovered encircled energy associated with the PSF core is accurate at 4% level in the worst case. The accuracy of the reconstructed PSFs has then been evaluated by considering an idealized scientific test-case consisting in the measurements of the morphological parameters of a compact galaxy. In the future, our project will include the analysis of anisoplanatism, low signal-to-noise ratio regimes, and the application to multi-conjugated AO observations.

Control oriented strategy to consider constraints of the deformable mirror M4 for the Mid-infrared ELT Imager and Spectrograph

The Mid-infrared ELT Imager and Spectrograph (METIS) will be equipped with a single conjugate adaptive optics (SCAO) system comprising the deformable mirror M4, the tip–tilt mirror M5, a wavefront sensor, and a modal controller implemented on real-time computers. To prevent any damage to M4 during operation and windup phenomena due to internal checks of M4, its absolute shape, time-discrete change of shape, and inter-actuator strokes are limited. Hence, we present a strategy to consider M4’s Cartesian constraints in the modal METIS-SCAO controller within this conceptual study. This strategy modifies the modal control error before it is fed into the SCAO controller considering the spatio-temporal and segmented characteristics of M4. Additionally, we present three different algorithms realizing this strategy. Furthermore, the presented strategy features the following characteristics, among others: add-on to a previously designed METIS-SCAO controller, no permanent trade-off between performance and constraint compliance, and application of numerically cheap approximating models. Moreover, we verify the functionality of the presented algorithms via standalone and closed loop simulations of the METIS-SCAO system. The simulations show that all presented algorithms work as intended and successfully enforce M4’s constraints. Therefore, the presented strategy and the three corresponding algorithms are applicable to the METIS-SCAO system.

Confusion in differential piston measurement with the pyramid wavefront sensor

Context. The pyramid was proven to be a highly sensitive and versatile wave-front sensor (WFS) and has been selected to be installed on the single conjugate adaptive optics (AO) systems of the extremely large telescope (ELT). The pupil of the ELT is fragmented by the secondary support spider arms, which are larger than the spatial coherence length of the atmospheric turbulence. This causes a rupture of the incoming wavefront continuity, which means that we need to be able to measure the differential pistons across the spider arms to achieve full wavefront reconstruction. Aims. We investigate the reaction of the modulated pyramid WFS to discontinuous aberrations in presence of phase residuals after AO compensation for a range of expected observing conditions at the location of the ELT. We then explore some parameters of the sensor in order to improve its sensitivity to the wavefront discontinuities, including optical gain compensation, specific sensor modulation paths, and the number of faces of the pyramidal prism. Methods. We derived sensitivity loss and modal cross-talk strength coefficients around static post-AO residual phases using the COMPASS end-to-end AO simulation software. Moreover, extensive closed-loop AO simulations let us derive two wavefront error criteria that are appropriate for a fragmented pupil geometry. We used these to assess the wavefront reconstruction performance. Results. We show that on the ELT, the pyramid experiences a drastic loss in sensitivity and also non-linear modal cross-talks. Added to the limited capture range, this makes it poorly suited for phase discontinuity measurements at visible wavelengths. The strategies we studied to increase the sensitivity and reduce the modal cross-talk provide an improvement of the reconstruction for low D/r0(λWFS) values, that is, for a K-band pyramid. In presence of a large residual wavefront variance, however, a similar sensor in visible light fails to provide the necessary trade-off to measure both the continuous modes and the wavefront discontinuities. Conclusions. The ELT instruments, designed with only visible-band pyramid WFSs, will not be able to perform a direct measurement of the wavefront discontinuities. They will have to rely on Kolmogorov statistics to restore the continuity of the atmospheric corrugated wavefront. If any other source of discontinuities arises on the ELT, instruments will need an additional, dedicated WFS.

Spatiotemporal statistics of the turbulent piston-removed phase and Zernike coefficients for two distinct beams.

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 widely used for classical adaptive optics systems. A more general framework, including both spatial and temporal statistics, can be useful for analysis of the existing systems and to support the design of future ones. In this paper, we propose an expression of the temporal cross power spectral densities of turbulent phases in two distinct beams, which is from two different sources to two different apertures. We consider the phase either as it is, without a piston, or as its decomposition on Zernike modes. The general formulas allow coverage of 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.

Advances in control of a pyramid single conjugate adaptive optics system

ABSTRACT 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 paid with increased complexity in the control. In this work, we report about advances in the adaptive optics (AO) system control obtained with SOUL at 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 Extremely Large Telescopes and the reported advances can be relevant contributions for such systems.

Direct imaging and spectroscopy of exoplanets with the ELT/HARMONI high-contrast module

Combining high-contrast imaging with medium-resolution spectroscopy has been shown to significantly boost the direct detection of exoplanets. HARMONI, one of the first-light instruments to be mounted on ESO’s future extremely large telescope (ELT), will be equipped with a single-conjugated adaptive optics system to reach the diffraction limit of the ELT in theHandKbands, a high-contrast module dedicated to exoplanet imaging, and a medium-resolution (up toR = 17 000) optical and near-infrared integral field spectrograph. When combined, these systems will provide unprecedented contrast limits at separations between 50 and 400 mas. This paper is aimed at estimating the capabilities of the HARMONI high-contrast module for the direct detection of young giant exoplanets. We use an end-to-end model of the instrument to simulate high-contrast observations performed with HARMONI, based on realistic observing scenarios and conditions. We then analyze these data with the so-called “molecule mapping” technique combined with a matched-filter approach in order to disentangle companions from the host star and tellurics and to increase the signal-to-noise ratio (S/N) of the planetary signal. We detected planets above 5σat contrasts up to 16 mag and separations down to 75 mas in several spectral configurations of the instrument. We show that molecule mapping allows for the detection of companions up to 2.5 mag fainter compared to state-of-the-art high-contrast imaging techniques based on angular differential imaging. We also demonstrate that the performance is not strongly affected by the spectral type of the host star and we show that we are able to reach close sensitivities for the best three quartiles of observing conditions at Armazones, which means that HARMONI could be used in near-critical observations during 60 to 70% of telescope time at the ELT. Finally, we simulated planets from population synthesis models to further explore the parameter space that HARMONI and its high-contrast module will open up and compare this to the current high-contrast instrumentation.

A correlation-locking adaptive filtering technique for minimum variance integral control in adaptive optics

We propose the correlation-locking optimization scheme (CLOSE), a real-time adaptive filtering technique for adaptive optics (AO) systems controlled with integrators. CLOSE leverages the temporal autocorrelation of modal signals in the controller telemetry and drives the gains of the integral command law in a closed servo-loop. This supervisory loop is configured using only a few scalar parameters and automatically controls the modal gains to closely match transfer functions achieving minimum variance control. This optimization is proven to work throughout the range of noise and seeing conditions relevant to the AO system. This technique was designed while preparing the high-order AO systems for extremely large telescopes, in particular to tackle the optical gain (OG) phenomenon. This is a sensitivity reduction induced by on-sky residuals and is a prominent issue with pyramid wavefront sensors (PWFS). CLOSE follows upon the linear modal compensation approach to OG that was previously demonstrated to substantially improve AO correction with high-order PWFS systems. Operating on modal gains through multiplicative increments, CLOSE naturally compensates for the recurring issue of unaccounted sensitivity factors throughout the AO loop. We present end-to-end simulations of the MICADO instrument single-conjugate AO to demonstrate the performances and capabilities of CLOSE. We demonstrate that a single configuration provides an efficient and versatile optimization of the modal integrator while accounting for OG compensation and while providing significant robustness to transient effects impacting the PWFS sensitivity.

Pyramid wavefront sensor optical gains compensation using a convolutional model

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.

Zonal-based high-performance control in adaptive optics systems with application to astronomy and satellite tracking.

This paper presents a model-based approach to adaptive optics (AO) control based on a zonal (i.e., pixelized) representation of the incoming atmospheric turbulence. Describing the turbulence on a zonal basis enables the encapsulation of the standard frozen-flow assumption into a control-oriented model. A multilayer zonal model is proposed for single-conjugate AO (SCAO) systems. It includes an edge compensation mechanism involving limited support, which results in a sparser model structure. To further reduce the computational complexity, new resultant zonal models localized in the telescope pupil are proposed, with AR1 or AR2 structures, that match the spatial and temporal cross-correlations of the incoming turbulence. The global performance of the resulting linear quadratic Gaussian (LQG) regulator is evaluated using end-to-end simulations and compared to several existing controllers for two different configurations: a very large telescope SCAO and low earth orbit satellite tracking. The results show the high potential of the new approach and highlight possible trade-offs between the performance and complexity.

Wavefront prediction using artificial neural networks for open-loop adaptive optics

ABSTRACT Latency in the control loop of adaptive optics (AO) systems can severely limit performance. Under the frozen flow hypothesis linear predictive control techniques can overcome this; however, identification and tracking of relevant turbulent parameters (such as wind speeds) is required for such parametric techniques. This can complicate practical implementations and introduce stability issues when encountering variable conditions. Here, we present a non-linear wavefront predictor using a long short-term memory (LSTM) artificial neural network (ANN) that assumes no prior knowledge of the atmosphere and thus requires no user input. The ANN is designed to predict the open-loop wavefront slope measurements of a Shack–Hartmann wavefront sensor (SH-WFS) one frame in advance to compensate for a single-frame delay in a simulated 7 × 7 single-conjugate adaptive optics system operating at 150 Hz. We describe how the training regime of the LSTM ANN affects prediction performance and show how the performance of the predictor varies under various guide star magnitudes. We show that the prediction remains stable when both wind speed and direction are varying. We then extend our approach to a more realistic two-frame latency system. AO system performance when using the LSTM predictor is enhanced for all simulated conditions with prediction errors within 19.9–40.0 nm RMS of a latency-free system operating under the same conditions compared to a bandwidth error of 78.3 ± 4.4 nm RMS.

Deep into the core of dense star clusters: an astrometric and photometric test case for ELT

ABSTRACT We present a novel analysis of a young star cluster in the Large Magellanic cloud, R136-like, as seen by the Extremely Large Telescope (ELT). The main aim of this study is to quantify precision and accuracy of stellar proper motion measurements in crowded field when using an ELT working at its diffraction limit. This can serve as a reference study for future development of ELT scientific cases. In particular, we investigate our future ability to detect the dynamical signature of intermediate-mass black holes (IMBHs) with mass ∼104 M⊙ through detailed measurements of stellar proper motions. We have simulated two N-body dynamical cluster models with and without an IMBH. For each model, we have chosen two snapshots temporally spaced by 5 yr. Stellar fluxes in IJHK filters and star positions have been used to create ELT mock images for both single- and multiconjugate adaptive optics observing modes following the requierements given by ESO technical specifications for the first light imager. These images have been analysed using a classical software for seeing-limited data reduction, daophot/allstar. We make accurate photometry till the very faint pre-main-sequence stars, i.e. depending on the adaptive optics (AO) mode, magnitudes down to K ∼ 24 mag (single-conjugate AO) or K ∼ 22 mag (multiconjugate AO) in a total integration time of 20 min on target. Although daophot suite of programs is not devoted to precise astrometry, the astrometric accuracy is impressive, reaching few μas yr−1 or km s−1. In these assumptions, we are able to detect the IMBH signature at the centre of the cluster.

A new temporal control approach for SCAO systems

Adaptive optics (AO) systems for ground-based telescopes use deformable mirrors to physically correct wavefront distortions induced by atmospheric turbulence. Due to time delays caused by different parts of the AO system, the process of turbulence correction becomes even more difficult since the earth’s atmosphere changes continuously. In this paper we propose a new temporal control approach for the computation of optimal mirror configurations based on the solution of a sequence of inverse problems for the wavefront sensor operator. Our mathematical formulation of the underlying problem allows the incorporation of computationally efficient wavefront reconstruction methods and a wavefront prediction step. Based on the frozen flow assumption, the prediction of a future wavefront relies on a suitable shift of the reconstructed wavefront. The performance of our temporal control algorithm is demonstrated in the context of a single conjugate adaptive optics system on a 37 meter telescope using a Shack–Hartmann wavefront sensor. Numerical results of the proposed control method are provided using OCTOPUS, the official end-to-end simulation tool of the European Southern Observatory.

A telescope-ready approach for modal compensation of pyramid wavefront sensor optical gain

The pyramid wavefront sensor (PWFS) is the currently preferred design for high-sensitivity adaptive optics (AO) systems for extremely large telescopes (ELTs). Yet, nonlinearities of the signal retrieved from the PWFS pose a significant problem for achieving the full correction potential using this sensor, a problem that will only worsen with the increasing dimension of telescopes. This paper investigates the so-called optical gain (OG) phenomenon, a sensitivity reduction and an overall modification of the sensor response induced by the residual wavefront itself, with considerable effects in standard observation conditions for ELT-sized AO systems. Through extensive numerical analysis, this work proposes a formalism to measure and minimize the first-order nonlinearity error caused by optical gain variation, which uses a modal compensation technique of the calibrated reconstructor; this enables a notable increase in performance in faint guide stars or important seeing scenarios, for example from 16 to 30% H-band Strehl ratio for a sixteenth magnitude star in r0 = 13 cm turbulence. Beyond the performance demonstrated by this compensation, a complete algorithm for realistic operation conditions is designed, which from dithering a few deformable mirror modes retrieves the optimal gains and updates the command matrix accordingly. The performance of this self-updating technique – which successfully allows automatic OG compensation regardless of the turbulent conditions, and its minimal interference with the scientific instrument are demonstrated through extensive end-to-end numerical simulations, all at the scale of an ELT instrument single-conjugate AO system.

A Multiplatform CPU-Based Architecture for Cost-Effective Adaptive Optics Systems

An adaptive optics (AO) system is composed of three key elements: a wave-front sensor (WFS) that detects the aberrations, a deformable mirror (DM) that provides the wavefront correction, and a closed-loop control system that elaborates the measurements acquired by the sensor and sends commands to the mirror. The control system can be implemented on a dedicated platform (e.g., field programmable gate array) or on general-purpose platforms (e.g., central processing unit (CPU), graphics processing unit). Dedicated hardware guarantees high performance but needs more development time and programming skills than general-purpose hardware, leading to a less maintainable system for the end user. The proposed solution aims to be a cost-effective multiplatform CPU-based flexible framework. The software, developed in C++ and using Eigen and Qt libraries, provides the tools to tune and control the AO system from wavefront measurement settings to controller parameters. A logging feature allows in-depth offline data analysis, while scripting enables execution of batch experiments. The AO system is tuned and evaluated by interfacing the WFS and DM with our software architecture. The results show that the proposed solution is able to correct the aberrations of a low- to medium-size single conjugate AO system, with a control frequency up to $\text{500}\,{\text{Hz}}$ and computational latency of $\text{40}\,\mu {\text{s}}$ , using a consumer-grade notebook.

Point spread function reconstruction for single-conjugate adaptive optics on extremely large telescopes

Modern ground-based telescopes like the planned extremely large telescope (ELT) depend heavily on adaptive optics (AO) systems to correct for atmospheric turbulence. Even though AO correction is used, the quality of astronomical images still is degraded due to the time delay stemming from the wavefront sensor integration time and temporal response of the deformable mirror(s) (DM). This results in a blur, which can be mathematically described by a convolution of the true image with the point spread function (PSF). We present an algorithm for single-conjugate adaptive optics PSF reconstruction adapted to the needs of ELTs in a storage efficient way. In particular, the classical PSF reconstruction algorithm is changed in several points to give a more accurate estimate for the post-AO PSF. Bilinear splines are used as basis functions to minimize the computational effort. Results obtained in an end-to-end simulation tool show qualitatively good reconstruction of the PSF compared with the PSF calculated directly from the simulated incoming wavefront. Furthermore, the used algorithm has a reasonable runtime and memory consumption.