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

Characterizing turbulence profile layers through celestial single-source observations

Future spacecraft missions aim to communicate with the Earth using near-infrared lasers. The possible bit rate of free-space optical communication (FSOC) is orders of magnitude greater when compared to current radio frequency transmissions. The challenge of ground-space FSOC is that atmospheric turbulence perturbs optical wavefront propagation. These wavefront aberrations can be measured using a Shack-Hartmann wavefront sensor (SHWFS). A ground-based adaptive optics (AO) system can mitigate these aberrations along the optical path by translating wavefront measurements into deformable mirror commands. However, errors result from atmospheric turbulence continuously evolving, and there are unavoidable delays during AO wavefront correction. The length of an acceptable delay is referred to as the coherence time-a parameter dependent on the strength of turbulence profile layers and their corresponding wind-driven velocity. This study introduces a novel technique, to the best of our knowledge, for using SHWFS single-source observations, e.g., the downlink signal from a geostationary satellite, to measure the strength and velocity of turbulence profile layers. This work builds upon previous research and demonstrates that single-source observations can disentangle turbulence profile layers through studying the cross-covariance of temporally offset SHWFS centroid measurements. Simulated data are used to verify that the technique can recover the coherence time. The expected and measured results have a correlation coefficient of 0.95.

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.

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.

Impact of time-variant turbulence behavior on prediction for adaptive optics systems

For high-contrast imaging systems, the time delay is one of the major limiting factors for the performance of the extreme adaptive optics (AO) sub-system and, in turn, the final contrast. The time delay is due to the finite time needed to measure the incoming disturbance and then apply the correction. By predicting the behavior of the atmospheric disturbance over the time delay we can in principle achieve a better AO performance. Atmospheric turbulence parameters, which determine wavefront phase fluctuations, have time-varying behavior. We present a stochastic model for wind speed and model time-variant atmospheric turbulence effects using varying wind speeds. We test a low-order, data-driven predictor, the linear minimum mean square error predictor, for a near-infrared AO system under varying conditions. Our results show varying wind can have a significant impact on the performance of wavefront prediction, preventing it from reaching optimal performance. The impact depends on the strength of wind fluctuations with the greatest loss in expected performance being for high wind speeds.

Tensor-based predictive control for extremely large-scale single conjugate adaptive optics

In this paper we propose a data-driven predictive control algorithm for large-scale single conjugate adaptive optics systems. At each time sample, the Shack-Hartmann wavefront sensor signal sampled on a spatial grid of size N×N is reshuffled into a d-dimensional tensor. Its spatial-temporal dynamics are modeled with a d-dimensional autoregressive model of temporal order p, where each tensor storing past data undergoes a multilinear transformation by factor matrices of small sizes. Equivalently, the vector form of this autoregressive model features coefficient matrices parametrized with a sum of Kronecker products between d-factor matrices. We propose an Alternating Least Squares algorithm for identifying the factor matrices from open-loop sensor data. When modeling each coefficient matrix with a sum of r terms, the computational complexity for updating the sensor prediction online reduces from O(pN⁴) in the unstructured matrix case to O(prd N^2(d+1)d). Most importantly, this model structure breaks away from assuming any prior spatial-temporal coupling as it is discovered from the data. The algorithm is validated on a laboratory testbed that demonstrates the ability to accurately decompose the coefficient matrices of large-scale autoregressive models with a tensor-based representation, hence achieving high data compression rates and reducing the temporal error especially for a large Greenwood per sample frequency ratio.

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.