Beyond FRiM, ASAP: a family of sparse approximation for covariance matrices and preconditioners

The FRiM fractal operator belongs to a family of operators, called ASAP, defined by an ordered selection of nearest neighbors. This generalization provides means to improve upon the good properties of FRiM. We propose a fast algorithm to build an ASAP operator mimicking the fractal structure of FRiM for pupils of any size and geometry and to learn the sparse coefficients from empirical data. We empirically show the good approximation by ASAP of correlated statistics and the benefits of ASAP for solving phase restoration problems

Closing the loop as an inverse problem: the real-time control of THEMIS adaptive optics

We have taken advantage of the implementation of an adaptive optics system on the Themis solar telescope to implement innovative strategies based on an inverse problem formulation for the control loop. Such an approach encompassing the whole system implies the estimation of the pixel variances of the Shack-Hartmann wavefront sensor, a novel real-time method to extract the wavefront slopes as well as their associated noise covariance, and the computation of pseudo-open loop data. The optimal commands are computed by iteratively solving a regularized inverse problem with spatio-temporal constraints including Kolmogorov statistics. The latency of the dedicated real-time control software with conventional CPU is shorter than 300 $\mu$s from the acquisition of the raw 400 x 400 pixel wavefront sensor image to the sending of the commands

Development of an ELT XAO testbed using a self referenced Mach-Zehnder wavefront sensor

Extreme adaptive optics (XAO) has severe difficulties meeting the high speed (>1kHz), accuracy and photon efficiency requirements for future extremely large telescopes. An innovative high order adaptive optics system using a self-referenced Mach-Zehnder wavefront sensor (MZWFS) allows counteracting these limitations. In addition to its very high accuracy, this WFS is the most robust alternative to segments gaps and telescope spiders which can result in strong wavefront artifacts. In particular in XAO systems when the size of these gaps in the wavefront measurement is comparable to the sub aperture size, loss in performance can be very high. The MZWFS estimates the wavefront phase by measuring intensity differences between two outputs, with a λ/4 path length difference between its two legs, but is limited in dynamic range. During the past few years, such an XAO system has been studied by our team in the framework of 8-meter class telescopes. In this paper, we report on our latest results with the XAO testbed recently installed in CRAL laboratory, and dedicated to high contrast imaging with 30m-class telescopes (such as the E-ELT or the TMT). A woofer-tweeter architecture is used in order to deliver the required high Strehl ratio (>95%). It consists of a 12x12 deformable mirror (DM) and a 512x512 Spatial Light Modulator (SLM) characterized both using monochromatic and polychromatic light. We present our latest experimental results, including components characterization, close loop performances and sensitivity to calibration errors. This work is carried out in synergy with the validation of fast iterative wavefront reconstruction algorithms and the optimal treatment of phase ambiguities in order to mitigate the dynamical range limitation of such a wavefront sensor

LITpro: a model fitting software for optical interferometry

9 pagesInternational audienceLITpro is a software for fitting models on data obtained from various stellar optical interferometers, like the VLTI. As a baseline, for modeling the object, it provides a set of elementary geometrical and center-to-limb darkening functions, all combinable together. But it is also designed to make very easy the implementation of more specific models with their own parameters, to be able to use models closer to astrophysical considerations. So LITpro only requires the modeling functions to compute the Fourier transform of the object at given spatial frequencies, and wavelengths and time if needed. From this, LITpro computes all the necessary quantities as needed (e.g. visibilities, spectral energy distribution, partial derivatives of the model, map of the object model). The fitting engine, especially designed for this kind of optimization, is based on a modified Levenberg-Marquardt algorithm and has been successfully tested on real data in a prototype version. It includes a Trust Region Method, minimizing a heterogeneous non-linear and non-convex criterion and allows the user to set boundaries on free parameters. From a robust local minimization algorithm and a starting points strategy, a global optimization solution is effectively achieved. Tools have been developped to help users to find the global minimum. LITpro is also designed for performing fitting on heterogeneous data. It will be shown, on an example, how it fits simultaneously interferometric data and spectral energy distribution, with some benefits on the reliability of the solution and a better estimation of errors and correlations on the parameters. That is indeed necessary since present interferometric data are generally multi-wavelengths

Fast minimum variance wavefront reconstruction for extremely large telescopes

We present a new algorithm, FRiM (FRactal Iterative Method), aiming at the reconstruction of the optical wavefront from measurements provided by a wavefront sensor. As our application is adaptive optics on extremely large telescopes, our algorithm was designed with speed and best quality in mind. The latter is achieved thanks to a regularization which enforces prior statistics. To solve the regularized problem, we use the conjugate gradient method which takes advantage of the sparsity of the wavefront sensor model matrix and avoids the storage and inversion of a huge matrix. The prior covariance matrix is however non-sparse and we derive a fractal approximation to the Karhunen-Loeve basis thanks to which the regularization by Kolmogorov statistics can be computed in O(N) operations, N being the number of phase samples to estimate. Finally, we propose an effective preconditioning which also scales as O(N) and yields the solution in 5-10 conjugate gradient iterations for any N. The resulting algorithm is therefore O(N). As an example, for a 128 x 128 Shack-Hartmann wavefront sensor, FRiM appears to be more than 100 times faster than the classical vector-matrix multiplication method.Comment: to appear in the Journal of the Optical Society of America

Simulations of Adaptive Optics Systems for the E-ELT

ABSTRACT In this paper, we present simulation work done on AO systems for the E-ELT. We study the influence of the number of Laser Guide Stars (LGS) on system performance. Then, we investigate the impact of the conjugation height of the M4 adaptive mirror on GL/LT/MC-AO. Finally, we compare the results of a Fourier code and end-to-end models on the position of the LGS in the field of view