First on-sky SCAO validation of full LQG control with vibration mitigation on the CANARY pathfinder

Performance of the neural network-based prediction model in closed-loop adaptive optics

Adaptive optics (AO) technology is an effective means to compensate for atmospheric turbulence, but the inherent delay error of an AO system will cause the compensation phase of the deformable mirror (DM) to lag behind the actual distortion, which limits the correction performance of the AO technology. Therefore, the feed-forward prediction of atmospheric turbulence has important research value and application significance to offset the inherent time delay and improve the correction bandwidth of the AO system. However, most prediction algorithms are limited to an open-loop system, and the deployment and the application in the actual AO system are rarely reported, so its correction performance improvement has not been verified in practice. We report, to our knowledge, the first successful test of a deep learning-based spatiotemporal prediction model in an actual 3 km laser atmospheric transport AO system and compare it with the traditional closed-loop control methods, demonstrating that the AO system with the prediction model has higher correction performance.

Fractional loop delays in adaptive optics modeling and control

This paper revisits the problem of optimal (minimum variance) control for adaptive optics (AO) systems when measurement and command applications are asynchronous, resulting in a non-integer servo loop delay. When not properly accounted for, such fractional delays may severely degrade the AO performance, especially in the presence of high-frequency vibrations. We present evidence of this performance degradation thanks to in-lab experimental measurements on the Gran Telescopio Canarias Adaptive Optics (GTCAO) system controlled with standard suboptimal linear quadratic Gaussian (LQG) controllers. A constructive, easy to implement LQG control design is then proposed and validated in a simulation for vibrations affecting the tip-tilt modes. Our methodology is very interesting because it allows a performance assessment for any linear controller in terms of variance, rejection transfer functions, power spectral densities, and stability margins. We also show how the continuous-time disturbance model can be derived from standard discrete-time disturbance data-based modeling.

Highly Stable Spatio-Temporal Prediction Network of Wavefront Sensor Slopes in Adaptive Optics

Adaptive Optics (AO) technology is an effective means to compensate for wavefront distortion, but its inherent delay error will cause the compensation wavefront on the deformable mirror (DM) to lag behind the changes in the distorted wavefront. Especially when the change in the wavefront is higher than the Shack-Hartmann wavefront sensor (SHWS) sampling frequency, the multi-frame delay will seriously limit its correction performance. In this paper, a highly stable AO prediction network based on deep learning is proposed, which only uses 10 frames of prior wavefront information to obtain high-stability and high-precision open-loop predicted slopes for the next six frames. The simulation results under various distortion intensities show that the prediction accuracy of six frames decreases by no more than 15%, and the experimental results also verify that the open-loop correction accuracy of our proposed method under the sampling frequency of 500 Hz is better than that of the traditional non-predicted method under 1000 Hz.

An Optimal Integral Controller for Adaptive Optics Systems

Integral controllers are commonly employed in astronomical adaptive optics. This work presents a novel tuning procedure for integral controllers in adaptive optics systems which relies on information about the measured disturbances. This tuning procedure consists of two main steps. First, it models and identifies measured disturbances as continuous-time-damped oscillators using Whittles´s likelihood and the wavefront sensor output signal. Second, it determines the integral controller gain of the adaptive optics system by minimizing the output variance. The effectiveness of this proposed method is evaluated through theoretical examples and numerical simulations conducted using the Object-Oriented Matlab Adaptive Optics toolbox. The simulation results demonstrate that this approach accurately estimates the disturbance model and can reduce the output variance. Our proposal results in improved performance and better astronomical images even in challenging atmospheric conditions. These findings significantly contribute to adaptive optics system operations in astronomical observatories and establish our procedure as a promising tool for fine-tuning integral controllers in astronomical adaptive optics systems.

Laboratory demonstration of the prediction of wind-blown turbulence by adaptive optics at 8 kHz with use of LQG control

The low-latency adaptive optical mirror system (LLAMAS) is designed to push the limits on achievable latencies and frame rates. It has 21 subapertures across its pupil. A reformulated version of the linear quadratic Gaussian (LQG) method predictive Fourier control is implemented in LLAMAS; for all modes, it takes just 30 µs to compute. In the testbed, a turbulator mixes hot and ambient air to produce wind-blown turbulence. Wind prediction clearly improves correction when compared to an integral controller. Closed-loop telemetry shows that wind-predictive LQG removes the characteristic "butterfly" and reduces temporal error power by up to a factor of three for mid-spatial frequency modes. Strehl changes seen in focal plane images are consistent with telemetry and the system error budget.

Characterization and Analysis of Retinal Axial Motion at High Spatiotemporal Resolution and Its Implication for Real-Time Correction in Human Retinal Imaging

High-resolution ophthalmic imaging devices including spectral-domain and full-field optical coherence tomography (SDOCT and FFOCT) are adversely affected by the presence of continuous involuntary retinal axial motion. Here, we thoroughly quantify and characterize retinal axial motion with both high temporal resolution (200,000 A-scans/s) and high axial resolution (4.5 μm), recorded over a typical data acquisition duration of 3 s with an SDOCT device over 14 subjects. We demonstrate that although breath-holding can help decrease large-and-slow drifts, it increases small-and-fast fluctuations, which is not ideal when motion compensation is desired. Finally, by simulating the action of an axial motion stabilization control loop, we show that a loop rate of 1.2 kHz is ideal to achieve 100% robust clinical in-vivo retinal imaging.

Adaptive optics control with multi-agent model-free reinforcement learning

We present a novel formulation of closed-loop adaptive optics (AO) control as a multi-agent reinforcement learning (MARL) problem in which the controller is able to learn a non-linear policy and does not need a priori information on the dynamics of the atmosphere. We identify the different challenges of applying a reinforcement learning (RL) method to AO and, to solve them, propose the combination of model-free MARL for control with an autoencoder neural network to mitigate the effect of noise. Moreover, we extend current existing methods of error budget analysis to include a RL controller. The experimental results for an 8m telescope equipped with a 40x40 Shack-Hartmann system show a significant increase in performance over the integrator baseline and comparable performance to a model-based predictive approach, a linear quadratic Gaussian controller with perfect knowledge of atmospheric conditions. Finally, the error budget analysis provides evidence that the RL controller is partially compensating for bandwidth error and is helping to mitigate the propagation of aliasing.

Sparse data-driven wavefront prediction for large-scale adaptive optics

This paper presents a computationally efficient wavefront aberration prediction framework for data-driven control in large-scale adaptive optics systems. Our novel prediction algorithm splits prediction into two stages: a high-resolution and a low-resolution stage. For the former, we exploit sparsity structures in the system matrices in a data-driven Kalman filtering algorithm and constrain the identified gain to be likewise sparse; for the latter, we identify a dense Kalman gain and perform corrections to the suboptimal predictions of the former on a smaller grid. This novel prediction framework is able to retain the robustness to measurement noise of the standard Kalman filter in a much more computationally efficient manner, in both its offline and online aspects, while minimally sacrificing performance; its data-driven nature further compensates for modeling errors. As an intermediate result, we present a sparsity-exploiting data-driven Kalman filtering algorithm able to quickly estimate an approximate Kalman gain without solving the Riccati equation.

Compensation Techniques Aimed at Mitigating Vibrations in Optical Ground-Based Telescopes: A Systematic Review

The objective of this study was to evaluate the performance of the different systems and techniques aimed at suppressing vibrations on optical ground-based telescopes. We identified the studies by searching three electronic databases (Science Direct, IEEE library and Web of Science) from the year 2000 to December 2020. The studies were eligible if they proposed systems focused on mitigating the effects of vibrations in optical telescopes and brought performance data. A total of nine studies met our eligibility criteria. Current evidence confirms the feasibility of adaptative optics (AO) systems based on closed-loop control to mitigate vibrations, although variations and additions should be made depending on their nature and characteristics in order to improve the performance of the proposed techniques. This systematic review was conducted to provide a state-of-the-art of the methods and techniques that have been developed over the past two decades. The review also points out some issues that demand future research.

Performance of a U-Net-based neural network for predictive adaptive optics

We apply a U-Net-based convolutional neural network (NN) architecture to the problem of predictive adaptive optics (AO) for tracking and imaging fast-moving targets, such as satellites in low Earth orbit (LEO). We show that the fine-tuned NN is able to achieve an approximately 50% reduction in mean-squared wavefront error over non-predictive approaches while predicting up to eight frames into the future. These results were obtained when the NN, trained mostly on simulated data, tested its performance on 1 kHz Shack-Hartmann wavefront sensor data collected in open-loop at the Advanced Electro-Optical System facility at Haleakala Observatory while the telescope tracked a naturally illuminated piece of LEO space debris. We report, to our knowledge, the first successful test of a NN for the predictive AO application using on-sky data, as well as the first time such a network has been developed for the more stressing space tracking application.

Disturbance Modelling for Minimum Variance Control in Adaptive Optics Systems Using Wavefront Sensor Sampled-Data

Modern large telescopes are built based on the effectiveness of adaptive optics systems in mitigating the detrimental effects of wavefront distortions on astronomical images. In astronomical adaptive optics systems, the main sources of wavefront distortions are atmospheric turbulence and mechanical vibrations that are induced by the wind or the instrumentation systems, such as fans and cooling pumps. The mitigation of wavefront distortions is typically attained via a control law that is based on an adequate and accurate model. In this paper, we develop a modelling technique based on continuous-time damped-oscillators and on the Whittle’s likelihood method to estimate the parameters of disturbance models from wavefront sensor time-domain sampled-data. On the other hand, when the model is not accurate, the performance of the minimum variance controller is affected. We show that our modelling and identification techniques not only allow for more accurate estimates, but also for better minimum variance control performance. We illustrate the benefits of our proposal via numerical simulations.

Suppressions of vibration in the Tip-Tilt mirror control system by add-on controller

Tip-Tilt mirrors play an important role in astronomical telescopes requiring the tracking performance at the level of microradian or sub-microradian. However, the closed-loop performance suffers a lot from the low-sample rate and time delay of image sensors. Especially, this issue is under the condition of vibrations, because dynamic behaviors are complex and the models are difficult to be obtained accurately. Another challenging issue comes from the measurement of vibrations and its extraction for the closed-loop control. This paper proposes a new method based on an add-on controller of the Tip-Tilt mirror to mitigate telescope vibrations. The proposed method only uses Tip-Tilt errors from an image sensor to implement a disturbance observer, which is not being restricted by an accurate model. As a result, the closed-loop performance can be optimized by designing of a proper Q-filter. To suppress the low-frequency and high-frequency vibrations, a novel Q-filter combining a lowpass filter and a bandpass filter is proposed here. The improved control method is validated by both simulation and experiment in the tip-tilt mirror control system under the condition of vibrations.

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.

The Frequency-Domain Fusion Virtual Multi-Loop Feedback Control System with Measured Disturbance Feedforward Method in Telescopes

In the optical telescope, the stable precision of the optical path is affected by the structural vibrations. The image sensor with time delay and the micro electro-mechanical system (MEMS) accelerometer with massive drift limit the disturbance suppression performance of the closed loops. The current control methods cannot reject sufficiently vibrations due to the deficiency of the sensors, causality, and stability restrictions. In this study, the frequency-domain fusion virtual multi-loop feedback control system with measured disturbance feedforward method is proposed to suppress more structural vibrations. In spite of the deficiency of the sensors, we propose the frequency-domain fusion virtual gyroscopes (VGYR) to measure extra velocity of the system. The VGYR is estimated from the MEMS accelerometer with drift and corrected by the image sensor, and it replaces the fiber-optical gyroscopes (FOG) on the fast-stable platform because the weight of FOG is not negligible. To suppress more vibrations, the VGYR and the replaced FOG are utilized to build the virtual multi-loop feedback control system with measured disturbance feedforward, because it is not limited by the causality and stability restrictions. Therefore, the proposed method with causal ideal compensator can effectively improve stable precision and suppress much more structural vibrations in the wider frequency range. Detailed comparative experimental results adequately illustrate the advantages and effectiveness of this method.

Linear controller error budget assessment for classical adaptive optics systems

Understanding limitations of adaptive optics (AO) systems is crucial when designing new systems. In particular, analyzing the potential of different controllers is of great interest for the upcoming AO systems of the very large telescopes (VLTs) and extremely large telescopes (ELTs). This paper thus details a complete error budget assessment formalism, based on analytic formulas involving the disturbance temporal power spectral density (PSD) and the controller transfer function, and is applicable to any linear controller. This formalism is presented here for the special case of classical AO systems, but can be extended to any closed- or open-loop, single- or multi-conjugated AO configuration. Special attention is paid to the "control-dependent" errors, the importance of which is directly related to the type of control used in the AO system. The proposed method is applied to a NAOS/VLT-type single conjugated AO system, using disturbance PSD derived from a simulated turbulence trajectory or estimated from wavefront sensor measurements, enabling the construction of detailed error budgets for an integrator and different linear quadratic Gaussian controllers. Application to ELT-sized systems is discussed in the conclusion.

Vibration identification based on Levenberg-Marquardt optimization for mitigation in adaptive optics systems

When high performance is expected, vibrations are becoming a burning issue in adaptive optics systems. For mitigation of these vibrations, in this paper, we propose a method to identify the vibration model. The nonlinear least squares algorithm named the Levenberg-Marquardt method is adapted to acquire the model parameters. The experimental validation of the high performance of vibration mitigation associated with our identification method has been accomplished. Benefiting from this method, vibrations have been significantly suppressed using linear quadratic Gaussian control, where the root-mean-square of the residual vibrations has been reduced down to a portion of a microradian. Moreover, the experimental results show that with the model identified, vibrations ranging from wide low-frequency perturbation to high-frequency vibration peaks can be dramatically mitigated, which is superior to classical control strategies.

Minimum variance control for mitigation of vibrations in adaptive optics systems

In this paper, we address the design of a minimum variance controller (MVC) for the mitigation of vibrations in modern telescope adaptive optics (AO) systems. It is widely accepted that a main source of non-turbulent perturbations is the mechanical resonance induced by the wind or the instrumentation systems, such as fans and cooling pumps. To adequately mitigate vibrations, the application of frequency-based controllers has been considered in the past decade. In this work, we express the system model in terms of the tracking of a zero-input signal via the MVC. We show that the MVC is an equivalent representation of the linear quadratic Gaussian (LQG) controller for the AO system. We also show that by developing the MVC, we can obtain different expressions, in terms of transfer functions, that offer insights into the behavior and expected performance of the controller in the frequency domain. In addition, we analyze the impact of the accuracy of the system and perturbations model on the mitigation of vibrations.

High temporal resolution aberrometry in a 50-eye population and implications for adaptive optics error budget

We formed a database gathering the wavefront aberrations of 50 healthy eyes measured with an original custom-built Shack-Hartmann aberrometer at a temporal frequency of 236 Hz, with 22 lenslets across a 7-mm diameter pupil, for a duration of 20 s. With this database, we draw statistics on the spatial and temporal behavior of the dynamic aberrations of the eye. Dynamic aberrations were studied on a 5-mm diameter pupil and on a 3.4 s sequence between blinks. We noted that, on average, temporal wavefront variance exhibits a n^-2 power-law with radial order n and temporal spectra follow a f^-1.5 power-law with temporal frequency f. From these statistics, we then extract guidelines for designing an adaptive optics system. For instance, we show the residual wavefront error evolution as a function of the number of corrected modes and of the adaptive optics loop frame rate. In particular, we infer that adaptive optics performance rapidly increases with the loop frequency up to 50 Hz, with gain being more limited at higher rates.

Performance of the Gemini Planet Imager's adaptive optics system

The Gemini Planet Imager's adaptive optics (AO) subsystem was designed specifically to facilitate high-contrast imaging. A definitive description of the system's algorithms and technologies as built is given. 564 AO telemetry measurements from the Gemini Planet Imager Exoplanet Survey campaign are analyzed. The modal gain optimizer tracks changes in atmospheric conditions. Science observations show that image quality can be improved with the use of both the spatially filtered wavefront sensor and linear-quadratic-Gaussian control of vibration. The error budget indicates that for all targets and atmospheric conditions AO bandwidth error is the largest term.

Adaptive distributed Kalman filtering with wind estimation for astronomical adaptive optics

In the framework of adaptive optics (AO) for astronomy, it is a common assumption to consider the atmospheric turbulent layers as "frozen flows" sliding according to the wind velocity profile. For this reason, having knowledge of such a velocity profile is beneficial in terms of AO control system performance. In this paper we show that it is possible to exploit the phase estimate from a Kalman filter running on an AO system in order to estimate wind velocity. This allows the update of the Kalman filter itself with such knowledge, making it adaptive. We have implemented such an adaptive controller based on the distributed version of the Kalman filter, for a realistic simulation of a multi-conjugate AO system with laser guide stars on a 30 m telescope. Simulation results show that this approach is effective and promising and the additional computational cost with respect to the distributed filter is negligible. Comparisons with a previously published slope detection and ranging wind profiler are made and the impact of turbulence profile quantization is assessed. One of the main findings of the paper is that all flavors of the adaptive distributed Kalman filter are impacted more significantly by turbulence profile quantization than the static minimum mean square estimator which does not incorporate wind profile information.

Spatio-angular minimum-variance tomographic controller for multi-object adaptive-optics systems

Multi-object astronomical adaptive optics (MOAO) is now a mature wide-field observation mode to enlarge the adaptive-optics-corrected field in a few specific locations over tens of arcminutes. The work-scope provided by open-loop tomography and pupil conjugation is amenable to a spatio-angular linear-quadratic-Gaussian (SA-LQG) formulation aiming to provide enhanced correction across the field with improved performance over static reconstruction methods and less stringent computational complexity scaling laws. Starting from our previous work [J. Opt. Soc. Am. A31, 101 (2014)10.1364/JOSAA.31.000101JOAOD61084-7529], we use stochastic time-progression models coupled to approximate sparse measurement operators to outline a suitable SA-LQG formulation capable of delivering near optimal correction. Under the spatio-angular framework the wavefronts are never explicitly estimated in the volume, providing considerable computational savings on 10-m-class telescopes and beyond. We find that for Raven, a 10-m-class MOAO system with two science channels, the SA-LQG improves the limiting magnitude by two stellar magnitudes when both the Strehl ratio and the ensquared energy are used as figures of merit. The sky coverage is therefore improved by a factor of ~5.

On-sky demonstration of optimal control for adaptive optics at Palomar Observatory

High-order adaptive optics systems often suffer from significant computational latency, which ultimately limits the temporal error rejection bandwidth when classical controllers are employed. This Letter presents results from an on-sky, real-time implementation of an optimal controller on the PALM-3000 adaptive optics system at Palomar Observatory. The optimal controller is computed directly from open-loop wavefront measurements using a multichannel subspace system identification algorithm, and mitigates latency by explicitly predicting incident turbulence. Experimental results show a significant reduction in the residual wavefront error over the controlled spatial modes, illustrating the superior performance of the optimal control approach versus the nominal integral control architecture.

Linear prediction of atmospheric wave-fronts for tomographic adaptive optics systems: modelling and robustness assessment

We use a theoretical framework to analytically assess temporal prediction error functions on von-Kármán turbulence when a zonal representation of wavefronts is assumed. The linear prediction models analyzed include auto-regressive of an order up to three, bilinear interpolation functions, and a minimum mean square error predictor. This is an extension of the authors' previously published work Correia et al. [J. Opt. Soc. Am. A31, 101 (2014)JOAOD61084-752910.1364/JOSAA.31.000101], in which the efficacy of various temporal prediction models was established. Here we examine the tolerance of these algorithms to specific forms of model errors, thus defining the expected change in behavior of the previous results under less ideal conditions. Results show that ±100% wind speed error and ±50  deg are tolerable before the best linear predictor delivers poorer performance than the no-prediction case.