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.

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.

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.

Laser beam shaping with magnetic fluid-based liquid deformable mirrors

A new controllable laser beam shaping technique is demonstrated, where a magnetic fluid-based liquid deformable mirror is proposed to redistribute the laser phase profile and thus change the propagation property of the beam. The mirror is driven by an inner miniature actuator array along with a large outer actuator. The inner actuator array is used for deforming the magnetic fluid surface, while the outer actuator is used to linearize the fluid surface response and amplify the magnitude of the deflection. In comparison to other laser beam shaping techniques, this technique offers the advantages such as simplicity, low cost, large shape deformation, and high adaptability. Based on a fabricated prototype of the liquid deformable mirror, an experimental AO system was set up to produce a desired conical surface shape that shaped the incident beam into a Bessel beam. The experimental results show the effectiveness of the proposed technique for laser beam shaping.

Performance of an Adaptive Optics System with Dual Deformable Mirrors

One deformable mirror （DM） in conventional adaptive optics system can not meet the needs of large scale and high order aberration compensation. In this paper, a dual DMs way is presented, which needs the decoupling of dual DMs. In dual DMs adaptive optics （AO） system, the decoupling algorithm of dual DMs is deduced. Stroke of one of DMs is large, spatial frequency of the other is high. According to the algorithm, the large stroke DM （LSDM） corrects low order aberration only, and the high spatial frequency DM （HSFDM） corrects other aberration. The experimental result for two 61-DM AO system is presented. The result indicates that the experimental performance of dual DMs AO system is almost the same with that of the conventional AO system using single DM with ideal stroke and equivalent spatial frequency.

高带宽压电片变形镜的动力学仿真与优化方法研究

为进一步提高压电波前校正器的响应速度和轻量化程度,对面向高动态形状控制的压电片变形镜的动力学仿真与优化方法进行了研究。首先,基于压电片变形镜的参数化有限元模型,提出了高效、高精度的电-力耦合动力学仿真分析方法。然后,通过正交遍历多维设计参数(光学反射镜与压电陶瓷的材料类型、几何尺寸和固定方式等),探究了不同参数对压电片变形镜动态形状控制性能的影响规律。最后,优化得到具有预期响应带宽和驱动位移性能的压电片变形镜设计方案,并通过制备压电片变形镜的原理样件来验证其性能。实验结果表明,所研制的压电片变形镜的固有频率和镜面驱动位移幅值符合预期,验证了所提出的动力学仿真与优化方法的有效性,这可为高带宽压电片变形镜的高效研制提供科学的理论方法。

双曲形复合材料构件成型精度修正技术研究

双曲形复合材料构件固化变形是影响零件质量和几何精度的关键问题之一,为了提高双曲形复合材料构件成型几何精度,本文提出了一种基于试验数据的变形修正方法,详细阐述了试验数据获取、去噪和数据对齐以及基于多截面的试验数据搜索法和镜像法等关键问题;并基于CATIA/CAA二次开发技术开发了修正模块,该模块能够对双曲形复合材料构件的固化变形进行有效补偿。以某机上双曲形零件为例进行试验验证,经过该模块修正后,零件的制造误差显著减小,证明了该方法的有效性和可行性。本研究结果对于提高双曲形复合材料构件的制造精度和性能具有重要意义。

基于MEMS可变形反射镜的激光整形研究

应用MEMS可变形反射镜进行激光光束整形技术研究。首先建立平顶光束整形的理论模型,通过近轴透镜聚焦后的光场,利用柯林斯广义衍射积分公式对高斯光束整形模拟仿真,分析不同束腰半径和发散角的高斯光束对整形成平顶光束的影响。设计基于可变形反射镜的平顶光束整形的光路实验,通过平顶光束整形的理论模型和泽尼克多项公式,得到MEMS可变形反射镜各单元的驱动电压参数,实现平顶光束整形光场分布。在基于MEMS可变形反射镜的激光整形研究分析中,利用波前传感器对整形平顶光束进行光斑分析,得到基于可变形反射镜的平顶光束整形实验结果。对实验结果和理论仿真进行对比分析,得到其规律基本一致,结果较为理想。

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.

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。

倒立式三视场施密特望远镜关键技术研究

研制了基于三分区镜的倒立式三视场施密特型望远镜,对其关键技术进行了分析。利用正三棱锥的几何对称性,推导了3个视场的视轴夹角与分区镜面夹角之间的关系式,设计了用于实现多视场观测功能的三分区镜;通过有限元法分析了倒立式施密特望远镜主镜重力形变对像质的影响,阐述了检测光路关键参数对施密特修正镜加工误差的影响程度,采用蒙特卡罗法对该光学系统的杂散光进行了分析。最后对整个光学系统进行了实验检测,检测结果表明:实际研制的三分区镜镜面之间的夹角为133.08°,可同时对相互垂直的3个视场进行观测;该望远镜光学系统的PV=0.614λ,RMS=0.105λ(λ=632.8 nm)。该系统可用于地球空间姿态测量,拓展了施密特望远镜的应用范围。

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。

自重作用下中心支撑主反射镜面形变化研究

利用ＦＥＭ研究了弯月形主反射镜中心支撑条件下自重所引起的面形变化，通过计算所得镜面变形的ＰＶ值和ＲＭＳ值来评价是否超差，利用Ｚｅｒｎｉｋｅ多项式进行数据处理，分解出中心支撑方式下自重引起的像差成份，并相应地提出了提高成像质量的改进措施。最后进行了主反射镜背部形状优化。

200单元硅基单压电变形镜的设计与测试

针对天文望远镜对变形镜的需求,设计了200单元级硅基单压电变形镜并对其进行了性能测试。首先,通过有限元方法对单压电变形镜进行结构建模,分析比较了电极排列形式和边界支撑方式对变形镜性能的影响。然后,制备了3款200单元变形镜样机(环形简支,环形固支,六边形简支)。最后,利用干涉仪测量了变形镜的影响函数,并通过激光多普勒测振仪测量其频响特性。仿真与实验结果表明:致动器在50V电压下变形量可达1μm,固支条件下谐振频率在1kHz左右,对前100项Zernike像差具有良好的校正能力。该变形镜在低成本天文自适应光学系统中具有应用潜力。