Application of eigenmode in the adaptive optics system based on a micromachined membrane deformable mirror

The construction process and characteristics of a deformable mirror eigenmode are introduced. The eigenmode of a 37-element micromachined membrane deformable mirror (MMDM) from OKO, Ltd. is analyzed. The Gaussian-Seidel low-order aberrations are fitted with eigenmodes as basic functions. An experimental adaptive optics (AO) system is constructed with the MMDM as the wavefront corrector, a deformable mirror eigenmode as the wavefront control algorithm, and a Shack-Hartmann wavefront sensor as the wavefront detector. The experimental results demonstrate that the deformable mirror eigenmode can act as the wavefront control algorithm for the AO system based on the MMDM.     

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.     

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.     

基于MEMS技术的自适应光学系统的研究

用自适应光学系统来校正由大气湍流等产生的波前畸变,能够得到很好的效果.通过对自适应光学系统的工作原理进行研究,提出了一种基于MEMS技术的微小型自适应光学系统校正波前畸变的方法,将MEMS技术应用于变形反射镜,并构建了具体的实验平台,用来校正一种人为产生的波前畸变,且阐述了具体的实验过程.实验结果表明,基于MEMS技术的自适应光学系统能够很好地闭环校正波前畸变,且其体积小、质量轻、校正性能稳定,为自适应光学技术在星载相机上的应用提供了依据.     

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.     

The influence of high-frequency phase and correction distance on the phase correction effect

By studying the propagation characteristics of the wavefront phase of laser beams in adaptive optics systems, the influence of the high-frequency phase on the correction effect has been analyzed and the variations of correction effect with the position of optical deformable mirror have been analyzed quantitatively. The results show that the beam quality of the corrected beam in far field obviously degrades with an increase of high-frequency phase in a distorted wavefront, and the correction effect becomes worse and worse. In addition, the correction effect is related to the position of the deformable mirror; with an increase of the distance between the deformable mirror and the output mirror of the laser the correction effect is better. For a deformable mirror with a given unit size, when the distance of correction is more than 20?m the correction effect is perfect.     

Multiconjugate adaptive optics results from the laboratory for adaptive optics MCAO/MOAO testbed

We report on the development of wavefront reconstruction and control algorithms for multiconjugate adaptive optics (MCAO) and the results of testing them in the laboratory under conditions that simulate an 8 meter class telescope. The University of California Observatories (UCO) Lick Observatory Laboratory for Adaptive Optics multiconjugate testbed allows us to test wide-field-of-view adaptive optics systems as they might be instantiated in the near future on giant telescopes. In particular, we have been investigating the performance of MCAO using five laser beacons for wavefront sensing and a minimum-variance algorithm for control of two conjugate deformable mirrors. We have demonstrated improved Strehl ratio and enlarged field-of-view performance when compared to conventional AO techniques. We have demonstrated improved MCAO performance with the implementation of a routine that minimizes the generalized isoplanatism when turbulent layers do not correspond to deformable mirror conjugate altitudes. Finally, we have demonstrated suitability of the system for closed loop operation when configured to feed back conditional mean estimates of wavefront residuals rather than the directly measured residuals. This technique has recently been referred to as the "pseudo-open-loop" control law in the literature.     

Reflectivity and optical surface height requirements in a broadband coronagraph. 1. Contrast floor due to controllable spatial frequencies

We derive the broadband contrast floor in a coronagraphic telescope having nonideal optical surfaces. We consider only fundamental spatial frequencies within the control bandwidth of the coronagraph's deformable mirror. Cross terms arising from the beating of spatial frequencies beyond the deformable mirror control bandwidth will be considered in a second paper. Two wavefront control systems are analyzed:a zero-path difference Michelson interferometer with two deformable mirrors at a pupil image, and a sequential pair of deformable mirrors with one placed at a pupil image. We derive requirements on optical surface figure and reflectivity uniformity for both cases.     

Compact adaptive optical system based on blind optimization and a micromachined membrane deformable mirror

We describe and demonstrate an adaptive optical system based on the combination of a micromachined membrane deformable mirror and the stochastic parallel gradient descent control algorithm. This compact and relatively inexpensive adaptive optical system is used to maximize the coupling of a distorted laser beam into a single-mode optical fiber. The coupling efficiency is improved by 12 dB, and the coupling efficiency after correction is 64% of the diffraction-limited coupling efficiency.     

Thermomechanical characterization of a membrane deformable mirror

A membrane deformable mirror has been investigated for its potential use in high-energy laser systems. Experiments were performed in which the deformable mirror was heated with a 1 kW incandescent lamp and the thermal profile, the wavefront aberrations, and the mechanical displacement of the membrane were measured. A finite element model was also developed. The wavefront characterization experiments showed that the wavefront degraded with heating. Above a temperature of 35 degrees C, the wavefront characterization experiments indicated a dramatic increase in the high-order wavefront modes before the optical beam became immeasurable in the sensors. The mechanical displacement data of the membrane mirror showed that during heating, the membrane initially deflected towards the heat source and then deflected away from the heat source. Finite element analysis (FEA) predicted a similar displacement behavior as shown by the mechanical displacement data but over a shorter time scale and a larger magnitude. The mechanical displacement data also showed that the magnitude of membrane displacement increased with the experiments that involved higher temperatures. Above a temperature of 35 degrees C, the displacement data showed that random deflections as a function of time developed and that the magnitude of these deflections increased with increased temperature. We concluded that convection, not captured in the FEA, likely played a dominant role in mirror deformation at temperatures above 35 degrees C.     

High-resolution retinal imaging with micro adaptive optics system

Based on the dynamic characteristics of human eye aberration, a microadaptive optics retina imaging system set is established for real-time wavefront measurement and correction. This paper analyzes the working principles of a 127-unit Hartmann-Shack wavefront sensor and a 37-channel micromachine membrane deformable mirror adopted in the system. The proposed system achieves wavefront reconstruction through the adaptive centroid detection method and the mode reconstruction algorithm of Zernike polynomials, so that human eye aberration can be measured accurately. Meanwhile, according to the adaptive optics aberration correction control model, a closed-loop iterative aberration correction algorithm based on Smith control is presented to realize efficient and real-time correction of human eye aberration with different characteristics, and characteristics of the time domain of the system are also optimized. According to the experiment results tested on a USAF 1951 standard resolution target and a living human retina (subject ZHY), the resolution of the system can reach 3.6?LP/mm, and the human eye wavefront aberration of 0.728λ (λ=785?nm) can be corrected to 0.081λ in root mean square (RMS) so as to achieve the diffraction limit (Strehl ratio is 0.866), then high-resolution retina images are obtained.     

Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters

A scalable adaptive optics (AO) control system architecture composed of asynchronous control clusters based on the stochastic parallel gradient descent (SPGD) optimization technique is discussed. It is shown that subdivision of the control channels into asynchronous SPGD clusters improves the AO system performance by better utilizing individual and/or group characteristics of adaptive system components. Results of numerical simulations are presented for two different adaptive receiver systems based on asynchronous SPGD clusters-one with a single deformable mirror with Zernike response functions and a second with tip-tilt and segmented wavefront correctors. We also discuss adaptive wavefront control based on asynchronous parallel optimization of several local performance metrics-a control architecture referred to as distributed adaptive optics (DAO). Analysis of the DAO system architecture demonstrated the potential for significant increase of the adaptation process convergence rate that occurs due to partial decoupling of the system control clusters optimizing individual performance metrics.     

Stroke amplifier for deformable mirrors

We demonstrate a simple optical configuration that amplifies the usable stroke of a deformable mirror. By arranging for the wavefront to traverse the deformable mirror more than once, we correct it more than once. The experimental implementation of the idea demonstrates a doubling of 2.0 and 2.04 by two different means.     

星体目标自适应光学成象补偿

大气湍流等动态波前扰动限制大型望远镜的分辨能力，是从有望远镜以来几百年的老问题，自适应学技术提供了解这一问题的途径。但对星体目标来说由于所能利用的光能极为有限，动态扰动的时间－空间特性又对系统提出很高要求，因而难度很大。本文报导我们用２１单元自适应光学系统在云南天文台１．２ｍ望远镜上对星体目标进行的首次试验。介绍了针对弱光动态目标的特点对系统的改进。实验结果表明了这一自适应光学系统可以在光子计数率     

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.     

Calibration and performance of a pyramid wavefront sensor for the eye

We describe the calibration and performance of a pyramid wavefront sensor designed for use in a retinal imaging camera. The effect of the image modulation and the sensor binning on the measurements are explained in detail and various tests to validate the performance are described. The wavefront sensor was incorporated into an adaptive optics system that used a magnetically actuated deformable mirror, and results on static test optics are shown.     

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.     

Tomography approach for multi-object adaptive optics

Multi-object adaptive optics (MOAO) is a solution developed to perform a correction by adaptive optics (AO) in a science large field of view. As in many wide-field AO schemes, a tomographic reconstruction of the turbulence volume is required in order to compute the MOAO corrections to be applied in the dedicated directions of the observed very faint targets. The specificity of MOAO is the open-loop control of the deformable mirrors by a number of wavefront sensors (WFSs) that are coupled to bright guide stars in different directions. MOAO calls for new procedures both for the cross registration of all the channels and for the computation of the tomographic reconstructor. We propose a new approach, called "Learn and Apply (L&A)", that allows us to retrieve the tomographic reconstructor using the on-sky wavefront measurements from an MOAO instrument. This method is also used to calibrate the registrations between the off-axis wavefront sensors and the deformable mirrors placed in the science optical paths. We propose a procedure linking the WFSs in the different directions and measuring directly on-sky the required covariance matrices needed for the reconstructor. We present the theoretical expressions of the turbulence spatial covariance of wavefront slopes allowing one to derive any turbulent covariance matrix between two wavefront sensors. Finally, we discuss the convergence issue on the measured covariance matrices, we propose the fitting of the data based on the theoretical slope covariance using a reduced number of turbulence parameters, and we present the computation of a fully modeled reconstructor.     

Methods for the characterization of deformable membrane mirrors

We demonstrate two methods for the characterization of deformable membrane mirrors and the training of adaptive optics systems that employ these mirrors. Neither method employs a wave-front sensor. In one case, aberrations produced by a wave-front generator are corrected by the deformable mirror by use of a rapidly converging iterative algorithm based on orthogonal deformation modes of the mirror. In the other case, a simple interferometer is used with fringe analysis and phase-unwrapping algorithms. We discuss how the choice of singular values can be used to control the pseudoinversion of the control matrix.     

环形阵列微变形镜两种设计准则的分析比较

在波前校正中,环形阵列的分立式微变形镜充分利用了各个单元。环形阵列的分立式微变形镜有等单元面积和等单元宽度两种设计准则,以37单元环形阵列微变形镜为例,从校正波前适配误差和校正后剩余波前的Strehl比两方面对两种设计准则进行比较。结果表明,采用等单元面积设计的环形微变形镜校正畸变波前的性能更好。特别是波前畸变严重时,这种效果更加明显。