A slope-based decoupling algorithm to simultaneously control dual deformable mirrors in a woofer–tweeter adaptive optics system

We propose a slope-based decoupling algorithm to simultaneously control the dual deformable mirrors （DMs） in a woofer-tweeter adaptive optics system. This algorithm can directly use the woofer＇s response matrix measured from a Shack-Hartmann wave-front sensor to construct a slope-based orthogonal basis, and then selectively distribute the large- amplitude low-order aberration to woofer DM and the remaining aberration to tweeter DM through the slope-based orthogonal basis. At the same moment, in order to avoid the two DMs generating opposite compensation, a constraint matrix used to reset tweeter control vector is convenient to be calculated with the slope-based orthogonal basis. Numeral simulation demonstrates that this algorithm has a good performance to control the adaptive optics system with dual DMs simultaneously. Compared with the typical decoupling algorithm, this algorithm can take full use of the compensation ability of woofer DM and release the stroke of tweeter DM to compensate high-order aberration. More importantly, it does not need to measure the accurate shape of tweeter＇s influence function and keeps better performance of restraining the coupling error with the continuous-dynamic aberration.

Fuzzy Proportional Integral Derivative control of a voice coil actuator system for adaptive deformable mirrors

Research on adaptive deformable mirror technology for voice coil actuators(VCAs)is an important trend in the development of large ground-based telescopes.A voice coil adaptive deformable mirror contains a large number of actuators,and there are problems with structural coupling and large temperature increases in their internal coils.Additionally,parameters of the traditional proportional integral derivative(PID)control cannot be adjusted in real-time to adapt to system changes.These problems can be addressed by introducing fuzzy control methods.A table lookup method is adopted to replace real-time calculations of the regular fuzzy controller during the control process,and a prototype platform has been established to verify the effectiveness and robustness of this process.Experimental tests compare the control performance of traditional and fuzzy proportional integral derivative(Fuzzy-PID)controllers,showing that,in system step response tests,the fuzzy control system reduces rise time by 20.25%,decreases overshoot by 78.24%,and shortens settling time by 67.59%.In disturbance rejection experiments,fuzzy control achieves a 46.09%reduction in the maximum deviation,indicating stronger robustness.The Fuzzy-PID controller,based on table lookup,outperforms the standard controller significantly,showing excellent potential for enhancing the dynamic performance and disturbance rejection capability of the voice coil motor actuator system.

Bimorph deformable mirror based adaptive optics scanning laser ophthalmoscope for retina imaging in vivo

A bimorph deformable mirror （DM） with a large stroke of more than 30 μm using 35 actuators is presented and characterized for an adaptive optics （AO） confocal scanning laser ophthalmoscope application. Facilitated with a Shack-Hartmann wavefront sensor, the bimorph DM-based AO operates closed-loop AO corrections for hu- man eyes and reduces wavefront aberrations in most eyes to below 0.1 μm rms. Results from living eyes, including one exhibiting ~5D of myopia and ~2D of astigmatism along with notable high-order aberrations, reveal a prac- tical efficient aberration correction and demonstrate a great benefit for retina imaging, including improving resolution, increasing brightness, and enhancing the contrast of images.

Zonal decoupling algorithm for dual deformable mirror adaptive optics system

A zonal decoupling algorithm used to control a dual deformable mirror （DM） is proposed. One of the two DMs is characterized with a large stroke （woofer）, while the other one is characterized by a high spatial frequency （tweeter）. A numerical model is used to compare the zonal decoupling algorithm with some traditional zonal decoupling algorithms. The simulation results indicate that the algorithm presented in this Letter improves the performance in suppressing the coupling error. An experimental system is built to prove the effectiveness of this algorithm. The experiments demonstrate that the phase aberrations could be effectively compensated and that the coupling error could also be suppressed.

Thermal stability test and analysis of a 20-actuator bimorph deformable mirror

One of the important characteristic of adaptive mirrors is the thermal stability of surface flatness. In this paper, the thermal stability from 13℃ to 25℃ of a 20-actuator bimorph deformable mirror is tested by a Shack-Hartmann wavefront sensor. Experimental results show that, the surface P-V of bimorph increases nearly linearly with ambient temperature. The ratio is 0.11 μm/℃ and the major component of surface displacement is defocused, compared with which, astigmatism, coma and spherical aberration contribute very small. Besides, a finite element model is built up to analyse the influence of thickness, thermal expansion coefficient and Young＇s modulus of materials on thermal stability. Calculated results show that bimorph has the best thermal stability when the materials have the same thermal expansion coefficient. And when the thickness ratio of glass to PZT is 3 and Young＇s modulus ratio is approximately 0.4, the surface instability behaviour of the bimorph manifests itself most severely.

Wavefront correction of Ti:sapphire terawatt laser with varying precision of phase conjugation between deformable mirror and wavefront sensor

The phase conjugation between the deformable mirror and the wavefront sensor in the aberration correction of a terawatt Ti：sapphire laser is studied experimentally and theoretically in this paper. At varying values of phase- conjugation precision, we focus the corresponding beams into spots of the same size of 5.1 μm × 5.3 μm with a f/4 parabola in the 32 TW/36 fs Ti：sapphire laser system. The results show that the precision of conjugation can induce an intensity modulation but does not significantly affect the wavefront correction.

Numerical model of the influence function of deformable mirrors based on Bessel Fourier orthogonal functions

A numerical model is presented to simulate the influence function of de- formable mirror actuators. The numerical model is formed by Bessel Fourier orthog- onal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems.

High-resolution visible imaging with piezoelectric deformable secondary mirror: experimental results at the 1.8-m adaptive telescope

Integrating deformable mirrors within the optical train of an adaptive telescope was one of the major innovations in astronomical observation technology,distinguished by its high optical throughput,reduced optical surfaces,and the incorporation of the deformable mirror.Typically,voice-coil actuators are used,which require additional position sensors,internal control electronics,and cooling systems,leading to a very complex structure.Piezoelectric deformable secondary mirror technologies were proposed to overcome these problems.Recently,a high-order piezoelectric deformable secondary mirror has been developed and installed on the 1.8-m telescope at Lijiang Observatory in China to make it an adaptive telescope.The system consists of a 241-actuator piezoelectric deformable secondary mirror,a 192-sub-aperture Shack-Hartmann wavefront sensor,and a multi-core-based real-time controller.The actuator spacing of the PDSM measures 19.3 mm,equivalent to approximately 12.6 cm when mapped onto the primary mirror,significantly less than the voicecoil-based adaptive telescopes such as LBT,Magellan and VLT.As a result,stellar images with Strehl ratios above 0.49 in the R band have been obtained.To our knowledge,these are the highest R band images captured by an adaptive telescope with deformable secondary mirrors.Here,we report the system description and on-sky performance of this adaptive telescope.

Combinational-deformable-mirror adaptive optics system for compensation of high-order modes of wavefront

A new kind of adaptive optics （AO） system, in which several low spatial frequency deformable mirrors （DMs） with optical conjugation relationship are combined to correct high-order aberrations, is proposed. The phase compensation principle and the control method of the combinational AO system are introduced. The numerical simulations for the AO system with two 60-element DMs are presented. The results indicate that the combinational DM in the AO system can correct different aberrations effectively as one single DM with more actuators, and there is no change of control method. This technique can be applied to a large telescope AO system to improve the spatial compensation capability for wavefront by using current DM.

37-element solar adaptive optics for 26-cm solar fine structure telescope at Yunnan Astronomical Observatory

A 37-element solar adaptive optics （AO） system was built and installed at the 26-cm solar fine structure telescope of Yunnan Astronomical Observatory. The AO system is composed of a fine tracking loop with a tip/tilt mirror and a correlation tracker, a high-order correction loop with a 37-element deformable mirror, a correlating Shack-Hartmann wavefront sensor based on the absolute difference algorithm, and a real time controller. The system was completed on Sep. 28, 2009 and was used to obtain AO-corrected high-resolution solar images. The contrast and resolution of the images are clearly improved after wavefront correction by AO. To the best of out knowledge, this system is the first solar AO system in China.

Design of deformable mirrors for high power lasers

We present the workflow of the design, realization and testing of deformable mirrors suitable for high power diode pumped solid-state lasers. It starts with the study of the aberration to be corrected, and then it continues with the design of the actuators position and characteristic. In this paper, we present and compare three deformable mirrors realized for multi-J level laser facilities. We show that with the same design concept it is possible to realize deformable mirrors for other types of lasers. As an example, we report the realization of a deformable mirror for femtosecond lasers and for a CW CO_2 laser.

Programmable super-resolution pupil phase filter with a deformable mirror

Compared with binary diffractive super-resolving elements, programmable super-resolution pupil filters permit the analysis of various filter designs and allow the filters to be changed rapidly to modify the response of an optical system. In this Letter, a deformable mirror is employed as a programmable super-resolution pupil phase filter. Continuous phase-only filters based on the Zernike polynomial series are designed by the genetic algorithm and fitted through closed-loop adaptive optics with a piezoelectric deformable mirror. Experimental superresolution results are in agreement with the theoretical predictions. This method has no polarization light requirement and is convenient for application.

Adaptive Shape Control for Thermal Deformation of Membrane Mirror with In-plane PVDF Actuators

Optical membrane mirrors are promising key components for future space telescopes. Due to their ultra-thin and high flexible properties, the surfaces of these membrane mirrors are susceptible to temperature variations. Therefore adaptive shape control of the mirror is essential to maintain the surface precision and to ensure its working performance. However, researches on modeling and control of membrane mirrors under thermal loads are sparse in open literatures. A 0.2 m diameter scale model of a polyimide membrane mirror is developed in this study. Three Polyvinylidene fluoride(PVDF) patches are laminated on the non-reflective side of the membrane mirror to serve as in-plane actuators. A new mathematical model of the piezoelectric actuated membrane mirror in multiple fields,(i.e., thermal,mechanical, and electrical field) is established, with which dynamic and static behaviors of the mirror can be analyzed.A closed-loop membrane mirror shape control system is set up and a surface shape control method based on an influence function matrix of the mirror is then investigated. Several experiments including surface displacement tracking and thermal deformation alleviation are performed. The deviations range from 15 μm to 20 μm are eliminated within 0.1 s and the residual deformation is controlled to micron level, which demonstrates the effectiveness of the proposed membrane shape control strategy and shows a satisfactory real-time performance. The proposed research provides a technological support and instruction for shape control of optical membrane mirrors.

非正交多址光通信系统信道均衡的虚拟时反方法

室内非正交多址(non-orthogonal multiple access, NOMA)可见光通信系统(visible light communications, VLC)可实现高速率多用户通信,但多径效应会造成通信可靠性及用户公平性明显下降,为此,提出一种虚拟时间反转技术(virtual time reversal mirror, VTRM)对NOMA-VLC进行信道均衡,消除多径效应对通信过程的影响。分析了多用户场景下室内NOMA-VLC系统模型及其通信光链路的特性,依据光链路增益的稀疏特性采用稀疏度自适应匹配追踪(sparsity adaptive matching pursuit,SAMP)算法,估计NOMA-VLC系统的信道冲激响应(channel impulse response, CIR)。在此基础上,采用VTRM方法对NOMA-VLC进行信道均衡,通过VTRM的时空聚焦特性减少信道衰落影响,并重构接收信号,抑制多径效应。理论分析和实验结果表明:经论文算法均衡后的NOMAVLC系统,在满足前向纠错(forward error correction,FEC)误码率阈值的同时,用户1性能提高了4.4 dB,用户2性能提高了5.7 dB,两用户平均性能提高了5.05 dB,用户间性能差异由1.6 dB降为0.5 dB,为NOMA-VLC信道均衡提供了有效的解决方案。

抗拉可压型压电陶瓷性能测试及疲劳试验

压电陶瓷是自适应光学系统中的核心器件变形镜的主要作动元件,其性能的好坏直接影响变形镜甚至自适应光学系统校正能力。开展了加载电压为±350 V、外形尺寸为5 mm×5 mm×38 mm的抗拉可压型压电陶瓷的性能测试,包括位移、迟滞、电容、阻抗和热膨胀系数等,对压电陶瓷的抗拉能力进行了考核,获得三个样品抗拉能力均大于250 N。采用疲劳测试仪对同批次生产的压电陶瓷进行疲劳试验,在此过程中获得了压电陶瓷的压电效应并对试验数据进行了分析,最后对5#样品进行了1000万次疲劳试验(±150 N@5 Hz正弦载荷),试验后压电陶瓷的位移减小约5%,其他指标变化较小。通过抗拉能力测试和疲劳试验,初步考核了该型压电陶瓷的抗拉压特性和疲劳特性以及压电陶瓷的使用寿命,为变形镜的研制提供一定的数据支撑。

高波前拟合精度的紧凑型音圈变形镜

为了满足小型化自适应光学系统校正波前畸变的需求,基于系统理论分析设计了一种使用微型音圈驱动器的变形镜。使用电磁理论和有限元方法优化了微型音圈驱动器的结构参数。从热变形、共振频率、耦合系数等多个参数的角度对变形镜进行了优化。最后根据影响函数完成了波前拟合和残差计算。优化后的69单元紧凑型音圈变形镜具有大相位调制量、良好的热稳定性,第一共振频率为2220 Hz。对于PV值为1μm的前35项泽尼克模式,紧凑型音圈变形镜的拟合残差均小于30 nm。对于复杂随机像差,紧凑型VCDM能够将波前RMS降至原来的10%以下。结果表明,与传统的音圈变形镜相比,紧凑型音圈变形镜具有更高的波前拟合精度。高性能、低成本的紧凑型音圈变形镜在视网膜成像和机载成像系统中具有良好的应用前景。

提高眼底自适应光学成像系统的普适性设计

自适应光学技术被广泛应用于人眼像差的校正,从而实现眼底细胞和微血管进行高分辨率成像。传统自适应光学系统受夏克哈特曼波前探测器的动态范围限制,只对部分人群适用,无法对高屈光不正人群进行眼底高分辨率成像。为了提高眼底自适应光学成像系统普适性,本文设计了一种基于音圈变形镜高分辨率眼底自适应光学成像系统:引入Badal调焦系统,能够对人眼屈光度在-8~8 D的眼底进行高分辨率成像;用轴锥透镜组代替传统的环形光阑,控制正、负轴锥透镜间距可以调节环形光内径,以适应不同人眼的角膜,同时避免角膜反射的杂光;通过视标引导实现大视场成像。仿真结果表明,照明子系统在眼底视网膜照度分布均匀;在设定的公差范围内,至少有90%的MTF值在25 lp/mm达到0.21(对应视网膜上4μm)。在实验室搭建了相应的光路,对大畸变的模拟人眼进行了成像,获得了较好的成像效果。

矩形水冷压电变形镜的制备与表征

针对板条激光器射出激光束畸变问题,提出了一种边缘驱动的矩形水冷压电变形镜.首先建立有限元模型对变形镜校正性能和热性能进行仿真,结果显示在功率为10kW的激光照射下加载冷却条件,变形镜镜面温度降至45℃,冷却效果显著;然后通过实验成功制备了60单元20 mm×4mm口径的变形镜样机,搭建了基于Shack-Hartman传感器的自适应光学测试系统,并对变形镜典型致动器影响函数、校正性能、频率响应特性进行了表征.测试结果显示:变形镜典型致动器在100V电压驱动下的变形量为1.0~1.5μm,能够较准确重构低阶正弦函数面形,一阶固有频率约为650Hz.该矩形水冷压电变形镜具备一定的校正能力,在低成本板条激光器校正领域具有一定的应用前景.

基于RUN优化算法的波前校正系统

将龙格-库塔优化器用于无波前探测自适应光学系统,提出基于RUN的自适应光学控制方法。以61单元变形镜为波前校正器件,不同湍流强度下的畸变波前为校正对象,建立基于RUN优化算法的自适应光学系统模型。对比分析基于RUN、PSO、DEA和GA等算法的波前校正效果、校正速度和局部极值。结果表明,相比基于粒子群优化算法、差分进化算法和遗传算法的自适应光学系统,在取得相同校正效果时,基于RUN优化算法的波前校正系统在不同湍流条件下的校正速度均提高三倍以上,且RUN算法不易陷入局部极值。研究结果可为基于RUN优化算法的波前校正系统的实际应用提供理论基础。

波前校正的变论域模糊控制方法

自适应光学校正技术中常用的PID控制依赖于变形镜的响应模型,响应模型易受扰动影响因此标定过程较为复杂。针对此问题提出一种不依赖变形镜响应模型的变论域模糊控制方法,将哈特曼重构波前中提取的波面评价指标的残差参数与残差差分参数作为变论域模糊控制器的输入,对输出的比例积分微分参数进行自整定,实现自适应控制。利用Matlab进行变论域模糊控制方法与传统模糊控制方法进行对比的相关仿真。波前校正实验结果表明,变论域方法校正后波面数据优于传统模糊控制方法,波前残差的均方根值也更小。控制器系统性能实验中,传统模糊控制器的超调量偏大,而变论域模糊控制器的超调量几乎为零,调节时间也更短。变论域模糊控制方法在保证系统的鲁棒性,提升系统的快速性的同时,利用参数自整定的特性克服了扰动因素对变形镜响应模型造成的不利影响,提高了校正效率,对于波前校正更具有实用性。