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.     

Adaptive control of a micromachined continuous-membrane deformable mirror for aberration compensation

The nonlinear response and strong coupling of control channels in micromachined membrane deformable mirror (MMDM) devices make it difficult for one to control the MMDM to obtain the desired mirror surface shapes. A closed-loop adaptive control algorithm is developed for a continuous-surface MMDM used for aberration compensation. The algorithm iteratively adjusts the control voltages of all electrodes to reduce the variance of the optical wave front measured with a Hartmann-Shack wave-front sensor. Zernike polynomials are used to represent the mirror surface shape as well as the optical wave front. An adaptive experimental system to compensate for the wave-front aberrations of a model eye has been built in which the developed adaptive mirror-control algorithm is used to control a deformable mirror with 19 active channels. The experimental results show that the algorithm can adaptively update control voltages to generate an optimum continuous mirror surface profile, compensating for the aberrations within the operating range of the deformable mirror.     

压电倾斜镜迟滞非线性建模及逆补偿控制

自适应光学系统中的压电倾斜镜通常是用来实时校正大气湍流引起的波前畸变,但压电倾斜镜的响应都有较大的非线性迟滞效应,大大降低了倾斜镜的到位精度,并且影响系统稳定性,制约了倾斜校正系统的带宽,因此需要对迟滞现象进行建模,通过建立的模型进行补偿。本文通过引入迟滞算子,使用贝叶斯正则化训练算法训练BP神经网络来构建压电倾斜镜迟滞模型,以中国科学院光电技术研究所自主研制的压电倾斜镜为对象开展了实验研究。最后的实验结果表明,通过BP神经网络构建的压电倾斜镜迟滞模型具有较准确的辨识能力,其中,X方向的迟滞大小由6.5%降低到了1.3%,Y方向的迟滞大小由7.1%降低到了1.6%。     

Optimum control of the laser beam intensity profile with a deformable mirror

A new deformable mirror control system is developed. This system consists of a deformable mirror, a CCD camera, an image processor, a computer, and actuator drive power supplies. A genetic algorithm is adopted as a control algorithm to obtain an optimum surface profile of the deformable mirror. A circular cross-sectional Gaussian beam was transformed into a beam with a rectangular contour using this system. Although the transfer function of this system is complicated and unknown, this system can be used to obtain the optimum beam profile within the achievable limits of a deformable mirror.     

Hexapod control for an active secondary mirror: general concept and test results

Active control of the secondary mirror, mainly for correction of the decentering coma, is an essential tool for an active-optics telescope. The Italian Telescopio Nazionale Galileo is equipped with a secondary mirror supported by an hexapod mechanical structure, providing a positioning control with six degrees of freedom. The hexapod system has been built and tested to characterize its performance. The results show that the errors in the positioning of the secondary mirror lead to an aberration image well below the diffraction figure of the telescope.     

Optical control of the Advanced Technology Solar Telescope

The Advanced Technology Solar Telescope (ATST) is an off-axis Gregorian astronomical telescope design. The ATST is expected to be subject to thermal and gravitational effects that result in misalignments of its mirrors and warping of its primary mirror. These effects require active, closed-loop correction to maintain its as-designed diffraction-limited optical performance. The simulation and modeling of the ATST with a closed-loop correction strategy are presented. The correction strategy is derived from the linear mathematical properties of two Jacobian, or influence, matrices that map the ATST rigid-body (RB) misalignments and primary mirror figure errors to wavefront sensor (WFS) measurements. The two Jacobian matrices also quantify the sensitivities of the ATST to RB and primary mirror figure perturbations. The modeled active correction strategy results in a decrease of the rms wavefront error averaged over the field of view (FOV) from 500 to 19 nm, subject to 10 nm rms WFS noise. This result is obtained utilizing nine WFSs distributed in the FOV with a 300 nm rms astigmatism figure error on the primary mirror. Correction of the ATST RB perturbations is demonstrated for an optimum subset of three WFSs with corrections improving the ATST rms wavefront error from 340 to 17.8 nm. In addition to the active correction of the ATST, an analytically robust sensitivity analysis that can be generally extended to a wider class of optical systems is presented.     

Modeling, simulation, and open-loop control of a continuous facesheet MEMS deformable mirror

We introduce a coupled system of nonlinear partial differential equations (PDEs) to model a particular microelectromechanical systems (MEMS) deformable mirror consisting of a continuous facesheet coupled with electrostatic plate-driven actuators. To make the problem computationally tractable, we reduced the system to a single linear PDE for the facesheet coupled with nonlinear algebraic constraints for each of the actuators. We also introduce a nonlinearly constrained quadratic optimization problem for open-loop control of the MEMS mirror. Numerical simulation and control results are presented, and shortcomings of the model are discussed.     

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.     

Properties of a phase-conjugate etalon mirror and its application to laser resonator spatial-mode control

The concept of a phase-conjugate etalon mirror consisting of one flat and one aspheric surface is introduced. This new element can be used as an end mirror of a conventional resonator to promote spatial-mode selection and mode shaping. A phase-conjugate etalon designed for the fundamental Gaussian mode is experimentally implemented and tested with a single-mode He-Ne laser.     

大口径压电倾斜镜模型辨识与控制

本文提出了一种基于随机梯度优化算法的倾斜镜模型辨识方法,实现对大口径压电倾斜镜的复杂频率响应规律的辨识与控制带宽提高。文章介绍了压电倾斜镜原理和数学模型,描述了随机梯度优化算法在模型辨识的应用过程,并通过实验验证的方式检验了算法辨识模型的准确性以及在提高系统控制带宽方面的能力;最后,利用随机梯度下降算法本文还开展了对抖动输入频谱的辨识,结合倾斜镜模型的辨识结果,获得了对特定频谱区域更高抑制能力的控制效果。

     

音圈电机驱动的快速控制反射镜高带宽控制

分析一种音圈电机驱动的快速控制反射镜(FSM)的机械结构,由此建立其数学模型。依据模型,以不完全微分PID控制算法来消除结构谐振的不稳定影响,采用线性功率放大驱动方式,可使控制带宽超过其结构谐振频率,实现高带宽控制。实验表明,该方法应用于结构谐振频率分别为90Hz和20Hz的两种快速控制反射镜,系统的抑制带宽能分别达到315Hz和240Hz,而且该方法简单可行,通用性强。     

Adaptive optics: wave-front correction by use of adaptive filtering and control

A class of adaptive-optics problems is described in which phase distortions caused by atmospheric turbulence are corrected by adaptive wave-front reconstruction with a deformable mirror, i.e., the control loop that drives the mirror adapts in real time to time-varying atmospheric conditions, as opposed to the linear time-invariant control loops used in conventional adaptive optics. The basic problem is posed as an adaptive disturbance-rejection problem with many channels. The solution given is an adaptive feedforward control loop built around a multichannel adaptive lattice filter. Simulation results are presented for a 1-m telescope with both one-layer and two-layer atmospheric turbulence profiles. These results demonstrate the significant improvement in imaging resolution produced by the adaptive control loop compared with a classical linear time-invariant control loop.     

Reflection-wavelength control method for layer-by-layer controlled x-ray multilayer mirrors

A reflection-wavelength control method for a layer-by-layer controlled x-ray multilayer mirror without interface roughness is proposed. The reflection wavelength of the multiperiodic mirror is found to be simply determined by a combination ratio of periodic layers. Multiperiodic x-ray mirrors with reflectance wavelengths at 3.374 nm (C VI 1s-2p) and 3.950 nm (Ca XVIII 3d-5f) are successfully designed.     

Laboratory demonstration of accurate and efficient nanometer-level wavefront control for extreme adaptive optics

A 32 x 32 microelectricalmechanical systems mirror is controlled in a closed-loop adaptive optics test bed with a spatially filtered wavefront sensor (WFS), Fourier transform wavefront reconstruction, and calibration of references with a high-precision interferometer. When correcting the inherent aberration of the mirror, 0.7 nm rms phase error in the controllable band is achieved. When correcting an etched phase plate with atmospheric statistics, a dark hole 10(3) deeper than the uncontrollable phase is produced in the phase power spectral density. Compensation of the mirror's influence function is done with a Fourier filter, which results in improved loop convergence. Use of the spatial filter is shown to reduce the gain variability of the WFS in a quadcell configuration.     

Adaptive Control of a Micromachined Continuous Membrane Deformable Mirror for Aberration Compensation

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Beam-divergence control of excimers with plane-parallel Gaussian cavities

Plane-parallel cavities with Gaussian-reflectivity-profile mirrors as full reflectors were applied to a XeCl laser, and the near- and the far-field characteristics of the laser radiation were analyzed. It is shown that excimer lasers fitted with plane-parallel Gaussian cavities deliver laser radiation with a beam-quality factor M(2) that is more than 50% smaller than that of laser beams delivered by conventional plane-parallel cavities. The effect of the Gaussian mirror spot size on M(2) was also investigated, and it is shown that the narrowing of the Gaussian mirror spot size reduces the beam-quality-factor value.     

Characterization of an active control system for holographic setup stabilization

We report on the realization and characterization of an active control system of the optical holographic setup used for fabrication of holographic gratings in liquid-crystalline composite materials. The system exploits a reference diffraction grating and a piezomirror in closed-loop feedback. The piezoelectric mirror exhibits a hysteresis that depends not only on the applied voltage, but also on the history of the mirror motion. In an open-loop configuration, the hysteresis can be reduced by adjusting the delay time between the application of two different control voltage values; in a closed-loop operation, it is possible to eliminate the residual hysteresis. By testing the system in different conditions, it has been shown that residual fluctuations are comparable to the resolution of the piezomirror operation.     

变形反射镜薄膜应力与元件变形有限元研究

残余应力是变形反射镜面临的一个重要问题。考虑薄膜中残余应力的起源,利用有限元软件建立了变形反射镜有限元模型。基于所建立的有限元模型,计算变形镜各部分受薄膜残余应力作用后的变形与应力分布。与试验测量结果进行对比,计算结果表明,建立的模型是合理的,薄膜产生的残余应力为张应力,氟化物薄膜产生的张应力大于ZnS薄膜产生的压应力,残余应力主要集中在变形反射镜镜面上,基本呈放射状分布,外圈驱动器受到应力较大。     

Sparse matrix approximation method for an active optical control system

We develop a sparse matrix approximation method to decompose a wave front into a basis set of actuator influence functions for an active optical system consisting of a deformable mirror and a segmented primary mirror. The wave front used is constructed by Zernike polynomials to simulate the output of a phase-retrieval algorithm. Results of a Monte Carlo simulation of the optical control loop are compared with the standard, nonsparse approach in terms of accuracy and precision, as well as computational speed and memory. The sparse matrix approximation method can yield more than a 50-fold increase in the speed and a 20-fold reduction in matrix size and a commensurate decrease in required memory, with less than 10% degradation in solution accuracy. Our method is also shown to be better than when elements are selected for the sparse matrix on a magnitude basis alone. We show that the method developed is a viable alternative to use of the full control matrix in a phase-retrieval-based active optical control system.     

Preparation and characterization of a reference aluminum mirror

The preparation and characterization of a reference mirror of protected aluminum (Al) is reported. The mirror is made of 50-60-nm-thick Al film, coated with several-nanometer-thick A12O5 and 30-nm-thick film of AIN. The mirror characterization is based on reliable and precise reflectance measurements relative to a silicon- (Si-) wafer reference mirror. The simple phenomenological Drude-Lorentz model is applied for modeling the dispersion relations n(lambda) and k(lambda) of the Al film. The reflection of the protected Al mirror is determined in the 400-800-nm spectral range with accuracy better than 0.01 for p- and s-polarized light at angles of incidence from 0 degrees to 70 degrees. The accuracy has been confirmed with an evaporated thin silver film with known n(lambda), k(lambda), and d derived by photometric measurements at normal light incidence.