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.

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.

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.

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.

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.

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.

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.

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。

一种高密度压电变形镜驱动电源的设计

压电变形镜是自适应光学系统的执行机构。针对压电变形镜高精度、高动态应用的问题,设计了一款新型的压电陶瓷驱动电源,同时采取线性校正网络确保了放大电路的稳定性,并对影响输出精确度及非线性失真的原因进行了分析。实验结果表明,当驱动容性负载为0.33μF时,该驱动电源的大信号带宽可达3 kHz,阶跃响应的上升时间优于80μs,下降时间优于130μs,输出线性度为99.6%。

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。

两种方式构建的正中矢状面在面部畸形患者中的准确性研究

目的探讨本体/镜像关联法和点构法所构建的三维头颅的正中矢状面(median sagittal plane,MSP)在面部畸形患者中的准确性,为颌面部对称性分析提供依据。方法本研究通过医院伦理委员会批准。选取30例面部畸形患者的锥形束CT数据,以DICOM格式保存输出,在Mimics21.0下完成数据分割获取数字化三维头颅,将所生成数字化头颅数据导入逆向工程软件geomagic studio 2014中。分别使用本体/镜像关联法、点构法构建头颅的MSP。本体/镜像关联法对数字化头颅数据进行左右镜像后合并,获取对称特征平面即为所构建的MSP平面(S1)。点构法通过Mimics21.0在数字化头颅数据中选取鼻根点(nasion,N)、鸡冠点(crista galli,CG)、蝶鞍点(sella,S)、颅底点(basion,Ba)、梨骨点(vomer,V)、后鼻棘点(posterior nasal spine,PNS)、切牙孔点(incisive foramen,IF)、前鼻棘点(anterior nasal spine,ANS);一并导入geomagic studio 2014中,获取的最佳拟合平面即为所构建的MSP平面(S2)。由5位颌面外科高年资医生,采用单盲法对两种方法构建的S1、S2结果进行主观评分,对两组评分进行配对t检验。再次重复实验评分,对5位颌面外科高年资医生的前后两次评分进行一致性分析,验证专家评价法的可重复性。结果本体/镜像关联法构建S1平均得分为65.73,点构法构建S2平均得分为75.90。S1、S2组配对t检验得出点构法得分高于本体/镜像关联法,差异具有统计学意义(P<0.01)。一致性分析检验结果表明本研究的专家评分具有可重复性及一致性。结论在面部畸形患者中,点构法所构建的MSP优于本体/镜像关联法所构建的MSP,可为颌面部对称性分析提供依据,具有临床可行性。

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。

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.

Closed-loop correction and ocular wavefronts compensation of a 62-element silicon unimorph deformable mirror

Adaptive optics （AO） systems greatly improve the resolution of retinal imaging instruments by actively cor- recting ocular aberrations. In this Letter, closed-loop correction as well as ocular aberration compensation of a 62-element silicon unimorph deformable mirror （DM） driven by only positive voltage is performed. The ex- perimental results show that the root-mean square （RMS） wavefront of the initial nlirrof surface is reduced to 0.011 μm in a closed-loop AO system. The DM reproduces Zernike shapes from the third to 35th mode accurately. The simulated compensation of 200 ocular wavefronts shows that the average RMS value after col rection is reduced to 0.017 μm.