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Technological advances and the ever-growing human quest for improving the resolution of telescope observations are motivating the design of larger and larger ground telescopes: indeed, the larger is the telescope lens diameter, the better is the diffraction limited resolution of the telescope. Unfortunately, the terrestrial atmospheric turbulence, if not properly compensated, negatively affects the telescope observations, limiting its real resolution. Adaptive Optics (AO) systems are used in large ground telescopes in order to compensate the effect of the atmosphere, and hence to make the real telescope resolution be determined by the diffraction properties of the lens.

Technological advances and the ever-growing human quest for improving the resolution of telescope observations are motivating the design of larger and larger ground telescopes: indeed, the larger is the telescope lens diameter, the better is the diffraction limited resolution of the telescope. Unfortunately, the terrestrial atmospheric turbulence, if not properly compensated, negatively affects the telescope observations, limiting its real resolution. Adaptive Optics (AO) systems are used in large ground telescopes in order to compensate the effect of the atmosphere, and hence to make the real telescope resolution be determined by the diffraction properties of the lens. AO systems exploit the measurements of wavefront sensors to estimate the current values of the atmospheric turbulence, and compensate its effect by properly adapting the shape of a set of deformable mirrors. As the size of the telescope lenses is increasing, then the size of the AO system (e.g. the number of deformable mirror actuators and the size of the wavefront sensor) is increasing as well. This causes the increase of the computational burden needed to compute a proper compensation of the effect of the atmosphere. Consequently, as the potential telescope resolution increases, the task of the AO systems becomes more challenging. Motivated by the need of providing AO solutions useful for the next generations of ground telescopes, then a number of efficient algorithms have been recently considered in the literature to solve the problems related to the AO system. This paper considers the combination of a recently proposed very efficient phase reconstruction method, namely the CuRe, with a properly defined Kalman filter in order to obtain a dynamic compensation of the atmospheric turbulence. The performance of the proposed approach is investigated in some simulations.

Turbulence simulation methods are of fundamental importance for evaluating the performance of control strategies for Adaptive Optics (AO) systems. In order to obtain a reliable evaluation of the performance a statistically accurate turbulence simulation method has to be used. This work generalizes a previously proposed method for turbulence simulation based on the use of a multiscale stochastic model. The main contributions of this work are: first, a multiresolution local PCA representation is considered. In typical operating conditions, the computational load for turbulence simulation is reduced approximately by a factor of 4, with respect to the previously proposed method, by means of this PCA representation. Second, thanks to a different low resolution method, based on a moving average model, the wind velocity can be in any direction (not necessarily that of the spatial axes). Finally, this paper extends the simulation procedure to generate, if needed, turbulence samples by using a more general model than that of the frozen flow hypothesis.

Models typically used to simulate the influence of atmospheric turbulence on ground telescope observations are usually based on the frozen flow hypothesis. However, the frozen flow model of the atmosphere is valid at time scales of the order of tens/hundreds of milliseconds. This paper generalizes a previous model for turbulence simulation to ensure reliable tests of AO system performance in realistic working conditions. The proposed method relies on the use of two simulation models: First, the part of turbulence that shows a coherent flow at short time scales is simulated by means of a multiscale autoregressive-moving average model, which allows to efficiently simulate (with computational complexity O(n)) the coherent evolution of the turbulence. Secondly, an approach similar to that considered for dynamic textures, is used to simulate aberrations caused by processes that evolve on much longer time scales. The proposed procedure is tested on simulations.

Motivated by the increasing importance of Adap- tive Optics (AO) systems for improving the real resolution of large ground telescopes, and by the need of testing the AO system performance in realistic working conditions, in this paper we address the problem of simulating the turbulence effect on ground telescope observations at high resolution. The multiscale approach presented here generalizes that in [3]: First, a relevant computational time reduction is obtained by exploiting a local spatial principal component analysis (PCA) representation of the turbulence. Furthermore, differently from [3], the turbulence at low resolution is modeled as a moving average (MA) process. While in [3] the wind velocity was restricted to be directed along one of the two spatial axes, the approach proposed here allows to evolve the turbulence indifferently in all the directions. In our simulations the pro- posed procedure reproduces with good accuracy the theoretical statistical characteristics of the turbulent phase.

Motivated by the increasing importance of adaptive optics (AO) systems for improving the real resolution of large ground telescopes, and by the need of testing the AO system performance in realistic working conditions, in this paper we address the problem of simulating the turbulence effect on ground telescope observations at high resolution. The procedure presented here generalizes the multiscale stochastic approach introduced in our earlier paper [Appl. Opt. 50, 4124 (2011)], with respect to the previous solution, a relevant computational time reduction is obtained by exploiting a local spatial principal component analysis (PCA) representation of the turbulence. Furthermore, the turbulence at low resolution is modeled as a moving average (MA) process, while previously [Appl. Opt. 50, 4124 (2011)] the wind velocity was restricted to be directed along one of the two spatial axes, the use of such MA model allows the turbulence to evolve indifferently in all the directions. In our simulations, the proposed procedure reproduces the theoretical statistical characteristics of the turbulent phase with good accuracy.

In large ground telescopes the Adaptive Optics (AO) system aims at compensating the atmosphere effect on telescope measurements, and, the use of optimal filtering is fundamental for such task. This work is motivated by two important characteristics of new AO systems: on one hand, because of the request of very high measurement resolutions, the size of new telescopes, and of their sensors, is quickly increasing in the last decades, thus imposing to the AO systems the analysis of larger amount of data. On the other hand, the optimal filter has to be periodically updated according to temporal changes in atmosphere characteristics. Hence, it is of fundamental importance the use of computationally efficient algorithms for the update of the optimal filter gain.
This paper proposes some changes to a recently presented method for the efficient computation, in the frequency domain, of the Kalman gain for large AO systems [15]. The proposed changes, which mainly aim at correcting some issues due to the conversion spatial–frequency domain, and viceversa, allow to compute a better approximation of the optimal Kalman gain, and, consequently, significantly improve the performance of the AO system.

In current and next generation of ground tele- scopes, Adaptive Optics (AO) are employed to overcome the detrimental effects induced by the presence of atmospheric turbulence, that strongly affects the quality of data transmission and limits the actual resolution of the overall system. The analysis as well as the prediction of the turbulent phase affecting the light wavefront is therefore of paramount importance to guarantee the effective performance of the AO solution.
In this work, a layered model of turbulence is proposed, based on the definition of a Markov-Random-Field whose pa- rameters are determined according to the turbulence statistics. The problem of turbulence estimation is formalized within the stochastic framework and conditions for the identifiability of the turbulence structure (numbers of layers, energies and velocities) are stated. Finally, an algorithm to allow the layer detection and characterization from measurements is designed. Numerical simulations are used to assess the proposed procedure and validate the results, confirming the validity of the approach and the accuracy of the detection.

Measurements of large ground telescopes are af- fected by the presence of the terrestrial atmospheric turbulence: local changes of the atmospheric refraction index (e.g. due to wind and temperature variations) cause a non flat surface of the wavefront of light beams incoming on the telescope, thus degrading the quality of the observed images. Adaptive Optics (AO) systems are of fundamental importance to reduce such atmospheric influence on ground telescopes and thus to obtain high resolution observations. The goal of the AO system is that of estimating and compensating the atmospheric turbulence effect by properly commanding a set of deformable mirrors.
Because of delays in the closed loop system, the Kalman filter plays an important role in ensuring an effective control perfor- mance by providing good atmosphere predictions. However, the need of periodically updating the Kalman filter gain because of changes in the atmosphere characteristics, the increase of telescopes and sensors resolutions and the high sampling rate impose quite strict restrictions to the computational load for computing the Kalman gain.
Motivated by the above considerations, some strategies have been recently considered in the system theory and astronomical communities for the efficient computation of the Kalman gain for large AO systems. Specifically, this paper presents some changes to a recently proposed procedure: the proposed approach, which exploits some results in the control theory of distributed systems, computes an approximation of the optimal gain in the frequency domain exploiting the spatial homogeneity of the system. Then, the control strategy takes advantage of some information on the turbulent phase dynamic, that is estimated from the turbulence measurements. Performances of the proposed method are investigated in some simulations.

This paper considers the problem of simulating the turbulence effect on ground telescope observations. The approach presented here is an evolution of a recently proposed approach [3]. The main contributions with respect to [3] are: First, the Haar transform at the basis of the multiscale model in [3] is shown to be equivalent to a local PCA representation. This equivalence allows to reduce the computational complexity of the simulation algorithm by neglecting the components in the signal with lower energy. Furthermore, the simulation of nonstationary turbulence is obtained by properly changing the values of the multiscale model: Such change is eased by the invariance of the PCA spatial basis with respect to the change of turbulence statistical characteristics. The proposed approach is validated by means of some simulations.

Nowadays, the adaptive optics (AO) system is of fundamental importance to reduce the effect of atmospheric turbulence on the images formed on large ground telescopes. In this paper the AO system takes advantage of the knowledge of the current turbulence characteristics, that are estimated by data, to properly control the deformable mirrors. The turbulence model considered in this paper is based on two assumptions: considering the turbulence as formed by a discrete set of layers moving over the telescope lens, and each layer is modeled as a Markov-Random-Field. The proposed Markov-Random-Field approach is exploited for estimating the layers’ characteristics. Then, a linear predictor of the turbulent phase, based on the computed information on the turbulence layers, is constructed. Since scalability and low computational complexity of the control algorithms are important requirements for real AO systems, the computational complexity properties of the proposed model are investigated. Interestingly, the proposed model shows a good scalability and an almost linear computational complexity thanks to its block diagonal structure. Performances of the proposed method are investigated by means of some simulations.

Simulating the turbulence effect on ground telescope observations is of fundamental importance for the design and test of suitable control algorithms for adaptive optics systems. In this paper we propose a multiscale approach for efficiently synthesizing turbulent phases at very high resolution. First, the turbulence is simulated at low resolution, taking advantage of a previously developed method for generating phase screens. Then, high-resolution phase screens are obtained as the output of a multiscale linear stochastic system. The multiscale approach significantly improves the computational efficiency of turbulence simulation with respect to recently developed methods. Furthermore, the proposed procedure ensures good accuracy in reproducing the statistical characteristics of the turbulent phase.