Wide field adaptive optics laboratory demonstration with closed-loop tomographic control

Multi-line-of-sight Hartmann-Shack wavefront sensing based on image segmentation and K-means sorting

Multi-line-of-sight wavefront sensing, crucial for next-generation astronomy and laser applications, often increases system complexity by adding sensors. This research introduces, to the best of our knowledge, a novel method for multi-line-of-sight Hartmann-Shack wavefront sensing by using a single sensor, addressing challenges in centroid estimation and classification under atmospheric turbulence. This method contrasts with existing techniques that rely on multiple sensors, thereby reducing system complexity. Innovations include combining edge detection and peak extraction for precise centroid calculation, improved k-means clustering for robust centroid classification, and a centroid filling algorithm for subapertures with light loss. The method's effectiveness was confirmed through simulations for a five-line-of-sight system and experimental setup for two-line and three-line-of-sight systems, demonstrating its potential in real atmospheric aberration correction conditions. Experimental findings indicate that, when implemented in a closed-loop configuration, the method significantly reduces wavefront residuals from 1 λ to 0.1 λ under authentic atmospheric turbulence conditions. Correspondingly, the quality of the far-field spot is enhanced by a factor of 2 to 4. These outcomes collectively highlight the method's robust capability in enhancing optical system performance in environments characterized by genuine atmospheric turbulence.

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

Adaptive optics provides real time correction of wavefront disturbances on ground based telescopes. Optimizing control and performance is a key issue for ever more demanding instruments on ever larger telescopes affected not only by atmospheric turbulence, but also by vibrations, windshake and tracking errors. Linear Quadratic Gaussian control achieves optimal correction when provided with a temporal model of the disturbance. We present in this paper the first on-sky results of a Kalman filter based LQG control with vibration mitigation on the CANARY instrument at the Nasmyth platform of the 4.2-m William Herschel Telescope. The results demonstrate a clear improvement of performance for full LQG compared with standard integrator control, and assess the additional improvement brought by vibration filtering with a tip-tilt model identified from on-sky data, thus validating the strategy retained on the instrument SPHERE at the VLT.

Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).

Laser tomography adaptive optics: a performance study

We present an analytical derivation of the on-axis performance of adaptive optics systems using a given number of guide stars of arbitrary altitude, distributed at arbitrary angular positions in the sky. The expressions of the residual error are given for cases of both continuous and discrete turbulent atmospheric profiles. Assuming Shack-Hartmann wavefront sensing with circular apertures, we demonstrate that the error is formally described by integrals of products of three Bessel functions. We compare the performance of adaptive optics correction when using natural, sodium, or Rayleigh laser guide stars. For small diameter class telescopes (≲5 m), we show that a small number of Rayleigh beacons can provide similar performance to that of a single sodium laser, for a lower overall cost of the instrument. For bigger apertures, using Rayleigh stars may not be such a suitable alternative because of the too severe cone effect that drastically degrades the quality of the correction.

Fast computation of an optimal controller for large-scale adaptive optics

The linear quadratic Gaussian regulator provides the minimum-variance control solution for a linear time-invariant system. For adaptive optics (AO) applications, under the hypothesis of a deformable mirror with instantaneous response, such a controller boils down to a minimum-variance phase estimator (a Kalman filter) and a projection onto the mirror space. The Kalman filter gain can be computed by solving an algebraic Riccati matrix equation, whose computational complexity grows very quickly with the size of the telescope aperture. This "curse of dimensionality" makes the standard solvers for Riccati equations very slow in the case of extremely large telescopes. In this article, we propose a way of computing the Kalman gain for AO systems by means of an approximation that considers the turbulence phase screen as the cropped version of an infinite-size screen. We demonstrate the advantages of the methods for both off- and on-line computational time, and we evaluate its performance for classical AO as well as for wide-field tomographic AO with multiple natural guide stars. Simulation results are reported.

Generalized aliasing and its implications in modal gain optimization for multi-conjugate adaptive optics

The error of generalized aliasing associated with the limited sampling of the atmospheric turbulence volume due to the finite number of wavefront sensing directions in wide-field-of-view adaptive optics is formally defined. Following a modal approach, we extend the direct problem formulation of star-oriented multi-conjugate adaptive optics (MCAO) to model and quantify this error analytically. We show that the turbulence estimation with the least-squares reconstructor is subject to strong generalized aliasing, in particular affecting the badly seen modes, whereas with the minimum-mean-square-error reconstructor the estimation is little affected. Finally, we show that the application of modal gain optimization techniques in closed-loop MCAO systems is jeopardized by the generalized aliasing error.