Fast iterative tomographic wavefront estimation with recursive Toeplitz reconstructor structure for large-scale systems.

Tomographic wavefront reconstruction is the main computational bottleneck to realize real-time correction for turbulence-induced wavefront aberrations in future laser-assisted tomographic adaptive-optics (AO) systems for ground-based giant segmented mirror telescopes because of its unprecedented number of degrees of freedom, N, i.e., the number of measurements from wavefront sensors. In this paper, we provide an efficient implementation of the minimum-mean-square error (MMSE) tomographic wavefront reconstruction, which is mainly useful for some classes of AO systems not requiring multi-conjugation, such as laser-tomographic AO, multi-object AO, and ground-layer AO systems, but is also applicable to multi-conjugate AO systems. This work expands that by Conan [Proc. SPIE9148, 91480R (2014)PSISDG0277-786X10.1117/12.2054472] to the multi-wavefront tomographic case using natural and laser guide stars. The new implementation exploits the Toeplitz structure of covariance matrices used in an MMSE reconstructor, which leads to an overall O(N log N) real-time complexity compared with O(N2) of the original implementation using straight vector-matrix multiplication. We show that the Toeplitz-based algorithm leads to 60 nm rms wavefront error improvement for the European Extremely Large Telescope laser-tomography AO system over a well-known sparse-based tomographic reconstruction; however, the number of iterations required for suitable performance is still beyond what a real-time system can accommodate to keep up with the time-varying turbulence.

Modeling astronomical adaptive optics performance with temporally filtered Wiener reconstruction of slope data.

We build on a long-standing tradition in astronomical adaptive optics (AO) of specifying performance metrics and error budgets using linear systems modeling in the spatial-frequency domain. Our goal is to provide a comprehensive tool for the calculation of error budgets in terms of residual temporally filtered phase power spectral densities and variances. In addition, the fast simulation of AO-corrected point spread functions (PSFs) provided by this method can be used as inputs for simulations of science observations with next-generation instruments and telescopes, in particular to predict post-coronagraphic contrast improvements for planet finder systems. We extend the previous results presented in Correia and Teixeira [J. Opt. Soc. Am. A31, 2763 (2014)JOAOD60740-323210.1364/JOSAA.31.002763] to the closed-loop case with predictive controllers and generalize the analytical modeling of Rigaut et al. [Proc. SPIE3353, 1038 (1998)PSISDG0277-786X10.1117/12.321649], Flicker [Technical Report (W. M. Keck Observatory, 2007)], and Jolissaint [J. Eur. Opt. Soc.5, 10055 (2010)1990-257310.2971/jeos.2010.10055]. We follow closely the developments of Ellerbroek [J. Opt. Soc. Am. A22, 310 (2005)JOAOD60740-323210.1364/JOSAA.22.000310] and propose the synthesis of a distributed Kalman filter to mitigate both aniso-servo-lag and aliasing errors while minimizing the overall residual variance. We discuss applications to (i) analytic AO-corrected PSF modeling in the spatial-frequency domain, (ii) post-coronagraphic contrast enhancement, (iii) filter optimization for real-time wavefront reconstruction, and (iv) PSF reconstruction from system telemetry. Under perfect knowledge of wind velocities, we show that ∼60 nm rms error reduction can be achieved with the distributed Kalman filter embodying antialiasing reconstructors on 10 m class high-order AO systems, leading to contrast improvement factors of up to three orders of magnitude at few λ/D separations (∼1-5λ/D) for a 0 magnitude star and reaching close to one order of magnitude for a 12 magnitude star.

Random generation of the turbulence slopes of a Shack-Hartmann wavefront sensor.

A method to generate the turbulence measurements of a Shack-Hartmann wavefront sensor is presented. Numerical simulations demonstrate that the spatial and temporal statistic properties of the slopes are respected, allowing us to generate the turbulence wavefront gradient corresponding to both natural and laser guide stars, as well as time series in accordance with the frozen flow model.

Open-loop control demonstration of micro-electro-mechanical-system MEMS deformable mirror.

New astronomical challenges revolve around the observation of faint galaxies, nearby star-forming regions and the direct imaging of exoplanets. The technologies required to progress in these fields of research rely on the development of custom Adaptive Optics (AO) instruments such as Multi-Object AO (MOAO) or Extreme AO (ExAO). Many obstacles remain in the development of these new technologies. A major barrier to the implementation of MOAO is the utilisation of deformable mirrors (DMs) in an open-loop control system. Micro-Electro-Mechanical-System (MEMS) DMs show promise for application in both MOAO and ExAO. Despite recent encouraging laboratory results, it remains an immature technology which has yet to be demonstrated on a fully operational on-sky AO system. Much of the research in this area focuses on the development of an accurate model of the MEMS DMs. In this paper, a thorough characterization process of a MEMS DM is performed, with the goal of developing an open-loop control strategy free of computationally heavy modelling (such as the use of plate equations). Instead, a simpler approach, based on the additivity of the influence functions, is chosen. The actuator stroke-voltage relationship and the actuator influence functions are carefully calibrated. For 100 initial phase screens with a mean rms of 97 nm (computer generated following a Von Karman statistic), the resulting mean residual open-loop rms error is 16.5 nm, the mean fitting error rms is 13.3 nm and the mean DM error rms is 10.8 nm (error reflecting the performances of the model under test in this paper). This corresponds to 11% of residual DM error.

Closed-loop control of a woofer-tweeter adaptive optics system using wavelet-based phase reconstruction.

A novel closed-loop control technique for adaptive optics (AO) systems based on a wavelet-based phase reconstruction technique and a woofer-tweeter controller is presented. The wavelet-based reconstruction technique is based on obtaining a Haar decomposition of the phase screen directly from gradient measurements and has been extended here with the use of a Poisson solver to improve performance. This method is O(N) (i.e., a linear computation cost as number of actuators increases) and is the fastest of the known O(N) reconstruction techniques. The controller configuration is based on the woofer-tweeter controller to control low- and high-spatial-frequency aberrations, respectively. The separation of the woofer and tweeter signals is done using a computationally efficient method that is based on the availability of a low-spatial-resolution reconstruction during the wavelet synthesis process. The performance of the proposed technique is evaluated using a simulated AO system and phase screens generated to reflect atmospheric turbulence with various dynamic characteristics. Results indicate that the combination of the wavelet-based phase reconstruction and woofer-tweeter controller leads to very good results with respect to speed and accuracy.

Modeling and parameter estimation for point-actuated continuous-facesheet deformable mirrors.

We present a variant of the model introduced by Vogel and Yang [J. Opt. Soc. Am. A23, 1074 (2006)] for point-actuated deformable mirrors (DMs) with continuous facesheets, and we describe a robust efficient regularized- output least-squares computational scheme to estimate the parameters in the model, given noisy discrete observations of the DM response to known actuation. We demonstrate the effectiveness of this approach with experimental data obtained from a pair of DMs--a piezo-actuated prototype DM built by CILAS for the Thirty Meter Telescope Project and an electrostatically actuated commercial micro-electro-mechanical systems (MEMS) DM produced by Boston Micromachines Corporation.

A laser guide star wavefront sensor bench demonstrator for TMT.

Sodium laser guide stars (LGSs) allow, in theory, Adaptive Optics (AO) systems to reach a full sky coverage, but they have their own limitations. The artificial star is elongated due to the sodium layer thickness, and the temporal and spatial variability of the sodium atom density induces changing errors on wavefront measurements, especially with Extremely Large Telescopes (ELTs) for which the LGS elongation is larger. In the framework of the Thirty-Meter-Telescope project (TMT), the AO-Lab of the University of Victoria (UVic) has built an LGS-simulator test bed in order to assess the performance of new centroiding algorithms for LGS Shack-Hartmann wavefront sensors (SH-WFS). The design of the LGS-bench is presented, as well as laboratory SH-WFS images featuring 29x29 radially elongated spots, simulated for a 30-m pupil. The errors induced by the LGS variations, such as focus and spherical aberrations, are characterized and discussed. This bench is not limited to SH-WFS and can serve as an LGS-simulator test bed to any other LGS-AO projects for which sodium layer fluctuations are an issue.

Evaluation of a MEMS deformable mirror for an adaptive optics test bench.

An adaptive optics (AO) test bed has been designed and implemented to evaluate the effectiveness of the next generation of AO components and their associated control system. The optical design presented herein incorporates a turbulence generator, tip-tilt mirror, 140-actuator micro-electro-mechanical-system (MEMS) deformable mirror, Shack-Hartmann wave front sensor, and a science camera. This system has been operated in a closed AO loop at a 261 Hz sample rate. This paper focuses on the performance of the MEMS DM. It was examined using an interferometer to determine the influence functions, response time, and the quadratic relationship of displacement of the actuators to an applied voltage.

Experimental assessment of the matched filter for laser guide star wavefront sensing.

Laser guide star wavefront sensing comes with several limitations. When imaged with a Shack-Hartmann wavefront sensor, the laser guide star is seen as extended sources elongated in the directions given by the lenslet locations and the laser axis. A test bed has been built in the Adaptive Optics Laboratory of the University of Victoria that reproduces this effect as seen on extremely large telescopes. A new wavefront sensing algorithm, the matched filter, has been implemented and its performance assessed with the test bed. Its ability to mitigate laser guide star aberrations by tracking the sodium layer fluctuations in a closed loop adaptive optics system is shown.

Mean-square residual error of a wavefront after propagation through atmospheric turbulence and after correction with Zernike polynomials.

The root-mean-square (rms) of the residual wavefront, after propagation through atmospheric turbulence and corrected from Zernike polynomials, has been derived for the von Kármán turbulence model. The rms for any location in the telescope pupil and the pupil average rms have been calculated. It is shown that the residual rms on the edge of the pupil can be up to 35% larger than the pupil average residual rms. The results are useful to estimate the required rms stroke of deformable mirror (DM) actuators when they are used as a second stage of correction either in a tip-tilt, single-DM configuration or in a tip-tilt, two-DM (woofer-tweeter) setup.

Self-characterization of linear and nonlinear adaptive optics systems.

We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM.

Comparison between a model-based and a conventional pyramid sensor reconstructor.

A model of a non-modulated pyramid wavefront sensor (P-WFS) based on Fourier optics has been presented. Linearizations of the model represented as Jacobian matrices are used to improve the P-WFS phase estimates. It has been shown in simulations that a linear approximation of the P-WFS is sufficient in closed-loop adaptive optics. Also a method to compute model-based synthetic P-WFS command matrices is shown, and its performance is compared to the conventional calibration. It was observed that in poor visibility the new calibration is better than the conventional.

Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach.

End-to-end simulation of adaptive optics (AO) systems allows high-fidelity modeling of system performance, but at the cost of long computation time. Analytical modeling, on the other hand, can provide much faster first-order performance estimates for a rapid exploration of the AO parameter space. In this paper, we present the foundations of a modeling method for the AO optical transfer function, based on an analytical description of the residual phase spatial power spectrum. The method has been implemented in an IDL-based code, PAOLA, and comparison with end-to-end simulations demonstrates the validity of the analytical approach.