Fast calibration of high-order adaptive optics systems

We present a new method of calibrating adaptive optics systems that greatly reduces the required calibration time or, equivalently, improves the signal-to-noise ratio. The method uses an optimized actuation scheme with Hadamard patterns and does not scale with the number of actuators for a given noise level in the wavefront sensor channels. It is therefore highly desirable for high-order systems and/or adaptive secondary systems on a telescope without a Gregorian focal plane. In the latter case, the measurement noise is increased by the effects of the turbulent atmosphere when one is calibrating on a natural guide star.     

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.     

Dynamic eye model for adaptive optics testing

An artificial dynamic eye model is proposed. The prototype enabled us to introduce temporal variations in defocus and spherical aberration, resembling those typically found in the human eye. The eye model consisted of a meniscus lens together with a modal liquid crystal lens with controllable focus. A diffuser placed at a fixed distance from the lenses acted as the artificial retina. Developed software allowed the user to precisely control the dynamic generation of aberrations. In addition, different refractive errors could simultaneously be emulated by varying the distance between the components of the model. The artificial eye was first used as a dynamic generator of both spherical aberration and defocus, imitating the behavior of a real eye. The artificial eye was implemented in an adaptive optics system designed for the human eye. The system incorporated an electrostatic deformable mirror and a Hartmann-Shack wavefront sensor. Results with and without real time closed-loop aberration correction were obtained. The use of the dynamic artificial eye could be quite useful for testing and evaluating adaptive optics instruments for ophthalmic applications.     

Advanced vibration suppression algorithms in adaptive optics systems

Vibration suppression in astronomical adaptive optics (AO) systems has gathered great attention in the context of next-generation instrumentation for current telescopes and future Extremely Large Telescopes. Laser tomographic AO systems require natural guide stars to measure the low-order modes such as tip-tilt (TT) and TT-anisoplanatism. To increase the sky coverage, the guide stars are often faint, thus requiring lower temporal sampling frequencies to work on a more favorable signal-to-noise regime. Such sampling frequencies can be of the order of, or even lower than, the range of frequencies where vibrations are likely to appear. Ideally, vibrations affecting the low-order modes could be corrected at the higher laser loop frame rate using an upsampling procedure. This paper compares the most relevant solutions proposed hitherto to a novel multirate algorithm using the linear-quadratic-Gaussian (LQG) approach capable of upsampling the correction to further reduce the impact of vibrations. Results from numerical Monte Carlo simulations span a large range of parameters from pure sinusoids to relatively broad peak vibrations, covering the likely-to-be signals in a realistic AO system. The improvement is shown at sampling frequencies from 20 to 800 Hz, including below the vibration itself, in the example of 29.5 Hz on a Thirty Meter Telescope-like scenario. The multirate LQG ensures the least residual for both faint and bright stars for all the peak widths considered based on telemetry from the Keck Observatory.     

Wavefront correction with high-order curvature adaptive optics systems

We demonstrate the existence of higher-order curvature adaptive optics (AO) systems and compare their performance with the current 85-element system being built at the Institute for Astronomy at the University of Hawaii. Simulation results show that systems with in excess of 500 actuators are possible with actuator patterns that are simple extensions of the 85-element design. The attenuation of residual phase error within the Nyquist frequency of the deformable mirror (DM) satisfies the (-5/6) power law. A high-order system is also analyzed in which the pattern of wavefront sensor is synthesized from square pixels and the curvature actuators of the DM are also rectangular. The Strehl performance is approximately 2% worse than its annular analog.     

Minimum-variance control for woofer-tweeter systems in adaptive optics

The woofer-tweeter concept in adaptive optics consists in correcting for the turbulent wavefront disturbance with a combination of two deformable mirrors (DMs). The woofer corrects for temporally slow-evolving, spatially low-frequency, large-amplitude disturbances, whereas the tweeter is generally its complement, i.e., corrects for faster higher-order modes with lower amplitude. A special feature is that in general both are able to engender a common correction space. In this contribution a minimum-variance solution for the double stage woofer-tweeter concept in adaptive optics systems is addressed using a linear-quadratic-Gaussian approach. An analytical model is built upon previous developments on a single DM with temporal dynamics that accommodates a double-stage woofer-tweeter DM. Monte Carlo simulations are run for a system featuring an 8×8 actuator DM (considered infinitely fast), mounted on a steering tip/tilt platform (considered slow). Results show that it is essential to take into account temporal dynamics on the estimation step. Besides, unlike the other control strategies considered, the optimal solution is always stable.     

Minimum variance control structure for adaptive optics systems

The adaptive optics minimum variance control problem is formulated as a linear-quadratic-Gaussian optimization. The formulation incorporates the wavefront sensor frame integration in discrete-time models of the deformable mirror and incident wavefront. It shows that, under nearly ideal conditions, the resulting minimum variance controller approaches the integral controller commonly used in adaptive optics systems. The inputs to the controller dynamics are obtained from a reconstructor with the maximum a posteriori structure that uses the estimation error covariance of the wavefront error. The ideal conditions assumed to obtain the integral controller are as follows; isotropic first-order (but nonstationary) temporal atmospheric aberrations, no computational loop delay, and no deformable mirror dynamics. The effects of variations in these conditions are examined.     

Comparison of vibration mitigation controllers for adaptive optics systems

Vibrations are detrimental to the performance of modern adaptive optics (AO) systems. In this paper, we describe new methods tested to mitigate the vibrations encountered in some of the instruments of the Gemini South telescope. By implementing a spectral analysis of the slope measurements from several wavefront sensors and an imager, we can determine the frequencies and magnitude of these vibrations. We found a persistent vibration at 55 Hz with others occurring occasionally at 14 and 100 Hz. Two types of AO controllers were designed and implemented, Kalman and H∞, in the multiconjugate AO tip-tilt loop. The first results show a similar performance for these advanced controllers and a clear improvement in vibration rejection and overall performance over the classical integrator scheme. It is shown that the reduction in the standard deviation of the residual slopes (as measured by wavefront sensors) is highly dependent on turbulence, wind speed, and vibration conditions, ranging--in terms of slopes RMS value--from an almost negligible reduction for high speed wind to a factor of 5 for a combination of low wind and strong vibrations.     

Adaptive control in an adaptive optics experiment

This paper presents results from an adaptive optics experiment in which an adaptive control loop augments a classical adaptive optics feedback loop. Closed-loop wavefront errors measured by a self-referencing interferometer are fed back to the control loops, which drive a membrane deformable mirror to correct the wavefront. The paper introduces new frequency-weighted deformable mirror modes used as the control channels and new wavefront sensor modes for analyzing the performance of the control loops. The corrected laser beam also is imaged by a diagnostic target camera. The experimental results show reduced closed-loop wavefront errors and correspondingly sharper diagnostic target images produced by the adaptive control loop as compared with the classical AO loop.     

天文学自适应光学成像望远镜的模拟

为分析天文学自适应光学(AO)望远镜中AO系统的校正性能,利用Matlab仿真其成像过程。采用正交基为Zernike多项式的自相关法产生符合大气统计特性的大气相位屏,仿真平行光通过大气后的瞬时畸变波前相位;采用快速傅里叶变换仿真哈特曼-夏克波前传感器的成像光斑,根据实际成像与参考平面波成像的质心坐标之差,计算波前传感器子孔径内的平均波前斜率。模拟比较了1.2m望远镜两种AO系统布局的校正性能,结果表明,子孔径为正六边形AO系统的校正性能略优于子孔径为正方形AO系统的校正性能,两种AO系统的SR比(StrechlRatio)分别为0.872和0.859。     

Linear systems modeling of adaptive optics in the spatial-frequency domain

Spatial-frequency domain techniques have traditionally been applied to obtain estimates for the independent effects of a variety of individual error sources in adaptive optics (AO). Overall system performance is sometimes estimated by introducing the approximation that these individual error terms are statistically independent, so that their magnitudes may be summed in quadrature. More accurate evaluation methods that account for the correlations between the individual error sources have required Monte Carlo simulations or large matrix calculations that can take much longer to compute, particularly as the order of the AO system increases beyond a few hundred degrees of freedom. We describe an approach to evaluating AO system performance in the spatial-frequency domain that is relatively computationally efficient but still accounts for many of the interactions between the fundamental error sources in AO. We exploit the fact that (in the limits of an infinite aperture and geometrical optics) all the basic wave-front propagation, sensing, and correction processes that describe the behavior of an AO system are spatial-filtering operations in the Fourier domain. Essentially all classical wave-front control algorithms and evaluation formulas are expressed in terms of these filters and may therefore be evaluated one spatial-frequency component at a time. Performance estimates for very-high-order AO systems may be obtained in 1 to 2 orders of magnitude less time than needed when detailed simulations or analytical models in the spatial domain are used, with a relative discrepancy of 5% to 10% for typical sample problems.     

Robust control of a bimorph mirror for adaptive optics systems

We apply robust control techniques to an adaptive optics system including a dynamic model of the deformable mirror. The dynamic model of the mirror is a modification of the usual plate equation. We propose also a state-space approach to model the turbulent phase. A continuous time control of our model is suggested, taking into account the frequential behavior of the turbulent phase. An H(infinity) controller is designed in an infinite-dimensional setting. Because of the multivariable nature of the control problem involved in adaptive optics systems, a significant improvement is obtained with respect to traditional single input-single output methods.     

Bulk wind estimation and prediction for adaptive optics control systems

We present a wind-predictive controller for astronomical adaptive optics (AO) systems that is able to predict the motion of a single windblown layer in the presence of other, more slowly varying phase aberrations. This controller relies on fast, gradient-based optical flow estimation to identify the velocity of the translating layer and a recursive mean estimator to account for turbulence that varies on a time scale much slower than the operating speed of the AO loop. We derive the Cramer-Rao lower bound for the wind estimation problem and show that the proposed estimator is very close to achieving theoretical minimum-variance performance. We also present simulations using on-sky data that show significant Strehl increases from using this controller in realistic atmospheric conditions.     

Discrete-time dynamic shaping systems

The equations and the output series are examined for discrete-time dynamic generating systems producing input simulations for testing digital data-acquisition systems.Translated from Izmeritelnaya Tekhnika, No. 12, pp. 3–8, December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Time-sharing wave-front-sensing adaptive optics

Based on the concept of common-path/common-mode adaptive optics, the time-sharing wave-front-sensing adaptive optics system contains only one Hartmann-Shack (H-S) wave-front sensor, which detects two aberrations in the beam path alternately. After data fusion of the two aberrations, the actuator voltage of the deformable mirror (DM) is obtained. How the disturbances of the slope data and the response matrix influence the DM's actuator voltage in the data fusion methods is discussed, and the effective upper limits are given. Feasible data fusion methods are tested, and experiments verify that the performance of the system is good. The time-sharing technique is limited in sampling rate and is suitable only for corrections of slowly changing phases, because the H-S wave-front sensor's sampling frequency must be adequate for the alternate detection of two aberrations.     

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.     

Impact of sodium laser guide star fratricide on multi-conjugate adaptive optics systems

Laser beams projected from the ground to form sodium layer laser guide stars (LGSs) for adaptive optics (AO) systems experience scattering and absorption that reduce their intensity as they propagate upward through the atmosphere. Some fraction of the scattered light will be collected by the other wavefront sensors and causes additional background in parts of the pupil. This cross-talk between different LGS wavefront sensors is referred to as the fratricide effect. In this paper we quantify the magnitude of four different sources of scattering/absorption and backscattering, and we evaluate their impact on performance with various zenith angles and turbulence profiles for one particular AO system. The resulting wavefront error for the Thirty Meter Telescope (TMT) multi-conjugate AO (MCAO) system, NFIRAOS, is on the order of 5 to 20 nm RMS, provided that the mean background from the fratricide effect can be calibrated and subtracted with an accuracy of 80%. We also present the impact on system performance of momentary variations in LGS signal levels due to variations in cirrus absorption or laser power, and we show that this affects the performance more than does an equal variation in the level of the fratricide.     

太阳自适应光学技术进展

对太阳大气进行大视场高分辨力光学成像观测是开展太阳物理、空间天气等基础与应用研究的重要前提。对于地基太阳望远镜而言,为了消除地球大气湍流对光学系统的影响,自适应光学是高分辨力成像观测必备的技术手段,与此同时,为了突破大气非等晕性对传统自适应光学校正视场的限制,近年来多层共轭自适应光学技术等大视场自适应光学得到极大发展。本文首先梳理国外太阳自适应光学系统研制情况,重点介绍国内太阳自适应光学技术发展及应用情况,并进一步介绍了后续大视场太阳自适应光学技术发展情况以及目前所取得的成果。

     

自适应光学发展综述

自适应光学(AO)是校正动态光学波前误差的技术。本文概述了近50年来AO的发展历程,包括发展初期,“星球大战”期间美国的发展,以及在地基高分辨力成像望远镜,激光系统(特别是惯性约束聚变)以及眼科等方面的应用,此外还给出AO的发展趋势。通过引用每一项技术发展,首创者的首篇文献,给出了比较清晰的发展脉络。

     

Sky coverage estimates for adaptive optics systems from computations in Zernike space

A sky coverage model for laser guide star adaptive optics systems is proposed. The atmosphere is considered to consist of a finite number of phase screens, which are defined by Zernike basis polynomials, located at different altitudes. These phase screens are transformed to the aperture plane, where they are converted to laser and natural guide star wavefront sensing measurements. These transformations incorporate the cone effect due to guide stars at finite heights, anisoplanatism due to guide stars off axis with respect to the science object, and adaptive optics systems with multiple guide stars. The wavefront error is calculated tomographically with minimum variance estimators derived from the transformation matrices and the known statistical properties of the atmosphere. This sky coverage model provides fast Monte Carlo simulations over random natural guide star configurations, irrespective of telescope diameter. The Monte Carlo simulations outlined show that inclusion of a finite outer scale for the atmosphere significantly reduces the median wavefront error, that increasing the number of laser guide stars in the asterism reduces the median wavefront error, and that a larger natural guide star patrol field provides a smaller median wavefront error when there is a low star density in the field.