Wavefront correction with high-order curvature adaptive optics systems

We demonstrate the existence of higher-order curvature adaptive optics (AO) systems and compare their performance with the current 85-element system being built at the Institute for Astronomy at the University of Hawaii. Simulation results show that systems with in excess of 500 actuators are possible with actuator patterns that are simple extensions of the 85-element design. The attenuation of residual phase error within the Nyquist frequency of the deformable mirror (DM) satisfies the (-5/6) power law. A high-order system is also analyzed in which the pattern of wavefront sensor is synthesized from square pixels and the curvature actuators of the DM are also rectangular. The Strehl performance is approximately 2% worse than its annular analog.     

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.     

Concept, modeling, and performance prediction of a low-cost, large deformable mirror

While it is attractive to integrate a deformable mirror (DM) for adaptive optics (AO) into the telescope itself rather than using relay optics within an instrument, the resulting large DM can be expensive, particularly for extremely large telescopes. A low-cost approach for building a large DM is to use voice-coil actuators connected to the back of the DM through suction cups. Use of such inexpensive voice-coil actuators leads to a poorly damped system with many structural modes within the desired bandwidth. Control of the mirror dynamics using electro-mechanical sensors is thus required for integration within an AO system. We introduce a distributed control approach, and we show that the "inner" back sensor control loop does not need to function at low frequencies, leading to significant cost reduction for the sensors. Incorporating realistic models of low-cost actuators and sensors together with an atmospheric seeing model, we demonstrate that the low-cost mirror strategy is feasible within a closed-loop AO system.     

Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics

A Lagrange multiplier-based damped least-squares control algorithm for woofer-tweeter (W-T) dual deformable-mirror (DM) adaptive optics (AO) is tested with a breadboard system. We show that the algorithm can complementarily command the two DMs to correct wavefront aberrations within a single optimization process: the woofer DM correcting the high-stroke, low-order aberrations, and the tweeter DM correcting the low-stroke, high-order aberrations. The optimal damping factor for a DM is found to be the median of the eigenvalue spectrum of the influence matrix of that DM. Wavefront control accuracy is maximized with the optimized control parameters. For the breadboard system, the residual wavefront error can be controlled to the precision of 0.03 μm in root mean square. The W-T dual-DM AO has applications in both ophthalmology and astronomy.     

Distributed modal command for a two-deformable-mirror adaptive optics system

The design of future single-altitude conjugated adaptive optics (AO) systems may include at least two deformable mirrors (DMs) instead of one as in the current AO system. Each DM will have to correct for a specific spatial frequency range. A method is presented to derive a DM modal basis based on the influence functions of the DM. The modal bases are derived such that they are orthogonal to a given set of modes that restrict the DM correction to a spatial frequency domain. The modal bases have been tested on the woofer-tweeter test bench at the University of Victoria. It has been shown that the rms amplitude of the woofer DM and tweeter DM stroke can be reduced by factors of 3 and 9, respectively, when making the transition from a zonal-driven closed loop to a modal-driven closed loop with the same performance in both cases.     

Double-deformable-mirror adaptive optics system for phase compensation

Two kinds of algorithm for an adaptive optics (AO) system that uses two deformable mirrors (DMs), one with large stroke and the other with high spatial frequency, to correct different aberrations are described. The algorithms are based on modal method and direction-gradient method, respectively. Numerical simulations for the algorithms have been made. The simulation results indicate that the two DMs in the AO system can correct different aberrations with different characteristics, and the closed-loop performance of a double-DM AO system will be almost the same as that of an AO system that uses a single DM with an ideal stroke.     

140单元MEMS变形镜研制及测试分析

为了满足自适应光学技术更广泛的应用需求,针对传统变形镜体积大、成本高的问题,本文研制了基于微机电系统技术的MEMS变形镜并进行了实验测试。本文研制的变形镜共有140个六边形平行板电容静电驱动器,驱动器为12×12正方形排列,间距400 μm。采用表面MEMS工艺加工了变形镜样品,并利用陶瓷PGA管壳和石英玻璃盖板对样品进行了封装,同时还研制了与之配套的小型化多通道高压驱动电源。测试结果表明,该变形镜表面PV值411 nm,RMS值78 nm,在600 nm到900 nm波段的反射率接近80%,行程1.8 μm,交连值约15%,工作带宽13 kHz,阶跃响应时间23 μs,具有体积小、成本低、响应快等优势。除了进行了单元性能的测试之外,还开环控制变形镜进行了Zernike像差的拟合测试,验证了变形镜的校正能力。结果表明,该变形镜能初步满足自适应光学系统的应用需求。

     

力法非线性梁柱单元的合理单元长度划分

针对目前结构非线性分析中最常用的力法非线性梁柱单元模型,从理论上分析出了能消除其计算失真问题的合理单元长度及对应积分点数量。然后基于OpenSees有限元程序,使用该理论分析结果建立了一组单墩循环推倒试验的数值分析模型,通过加载点力-位移滞回曲线的对比分析和墩底截面曲率滞回曲线的对比分析验证了理论结果的正确性。结果表明：使用力法非线性梁柱单元模型进行结构的非线性数值分析时,其单元长度划分应根据积分点数量确定,确定原则应基于使单元屈服后变形增长的分布长度与塑性铰长度相等进行计算;在实际使用中,可利用等效塑性铰长度计算积分点数量与单元长度的关系,初步确定单元划分的合理长度;在保证单元长度与积分点数量的对应关系前提下,力法非线性单元的积分点数量越多,计算结果越稳定。     

Factors affecting the performance of piezoelectric bending actuators for advanced applications: an overview

The behaviors of piezoelectric bending actuators both in static and dynamic conditions driven by a high electric field were investigated and are summarized in this paper. In the static condition, the polarization and the displacement were measured and analyzed. It was found that the displacement hysteresis loop is the superposition of displacement loop induced by each layer of the actuator. The shape variation of the hysteresis loop is affected by the actuator configuration, i.e., the arrangement of electric field and poling direction. When the poling direction is parallel to an even electric field, such as parallel bimorph, the domain turns to switch at the exact coercive field of the piezoelectric material. However, when the poling direction is antiparallel to the electric field, such as series bimorph, the effect of electric field redistribution will take place during the domain reorientation, which reduces the actual electric field in the electric field–poling direction antiparallel layer, therefore prohibiting further domain reorientation. As a result, the series bimorph is noted to be more resistant to domain reorientation than the parallel bimorph. In the dynamic condition, the functions and relations of vibration velocity, heat generation, stress, and frequency were examined both theoretically and experimentally. It was found that the stress effect dominates at low frequency. At low frequency the failure mode of the actuator is often the physical fracture of the material. However, at high frequency, the failure modes mainly resulted from heat generation, unstable operation, depoling, and domain reorientation of the actuators. The vibration velocity will also decrease accordingly at the high frequency range due to more losses and heat generation.     

A nonlinear electromechanical model for ferroelectric materials: application to soft-PZT thick films screen-printed on alumina substrate

Motivated by experimental observations made on soft-PZT/alumina cantilever bimorphs, a nonlinear electromechanical model is presented describing the characteristic phenomena of ferroelectricity: the dielectric hysteresis, the butterfly loop, and the ferroelastic hysteresis. This model uses a phenomenological formulation, written within the general framework of thermodynamics of irreversible processes. The one-dimensional formulation of the model is successfully validated using experimental data from the literature. The model is used to predict the electromechanical behavior of a PZT/alumina cantilever bimorph. The results of the simulations are very promising.     

Comparison of curvature-based and Shack-Hartmann-based adaptive optics for the Gemini telescope

We present the results of independent numerical simulations of adaptive optics systems for 8-m astronomical telescopes that use both Shack-Hartmann and wave-front curvature sensors. Four differents codes provided consistency checks and redundancy. All four simulate a complete system and model noise and servo-lag effects. A common atmospheric turbulence generator was used for consistency. We present the main characteristics of the codes, and we report the system performance in term of Strehl ratio and full width at half-maximum versus the magnitude of the (on-axis) guide star. We show that a Shack-Hartmann plus stacked actuator mirror system with 10 x 10 subapertures or a curvature plus bimorph mirror system with 56 subapertures yields a 50% Strehl ratio at 1.6 mum for a m(R) = 14.7 magnitude star, with almost equivalent performance at both brighter and dimmer light levels.     

疲劳裂纹扩展速率试验中裂纹曲率修正方法研究

针对目前疲劳裂纹扩展速率试验标准中仅提出裂纹长度需进行曲率修正但未给出具体修正方法及步骤的问题,作者推荐了线性插值法和等比例法两种裂纹曲率修正方法,并通过分析两种方法的修正原理,结合试验结果,将两种曲率修正方法进行对比。结果表明,在双对数坐标系上,修正后的da/dN-ΔK曲线向低ΔK方向偏移,最大偏移量约15%,在利用da/dN-ΔK曲线进行选材对比或疲劳寿命评估时,修正后的曲线与未修正的曲线相比是偏安全的。基于两种方法修正后的da/dN-ΔK曲线之间差异较小,最大相差约2%,两种方法均可作为疲劳裂纹扩展速率试验中裂纹长度的曲率修正方法。     

Bimorph变形镜10.6μm薄膜研究

基于压电驱动器的Bimorph变形镜是10.6 μm系统的一个重要元件.为了镀制薄膜,本文首先利用有限元软件对两种镀膜夹持方式与沉积温度进行了计算,对热应力产生的热变形进行了分析,选择了合适的镀膜夹持方式.为了预测bimorph变形镜受激光辐照后的温升,对单晶硅与石英玻璃制作的bimorph变形镜有限元模型进行了计算与分析.最后,利用光度计对镀制的薄膜进行了反射率测量.试验结果显示反射率测量值大于99.5％,满足实际系统的需要.     

Study on the effects of monochromatic aberrations in the accommodation response by using adaptive optics

The effect of asymmetric monochromatic aberrations in the accommodation response was studied by using an adaptive optics (AO) system. This approach permits the precise modification of ocular aberrations during accommodation. The AO system is composed of a real-time Hartmann-Shack wavefront sensor and a membrane deformable mirror with 37 independent actuators. The accommodation response was measured in two subjects with their normal aberrations and with the asymmetric aberrations terms corrected. We found a significant and systematic increase in the response accommodation time, and a reduction in the peak velocity, in both subjects when the aberrations were corrected in real time. However, neither the latency time nor the precision of the accommodation were affected. These results may indicate that the monochromatic aberrations play a role in driving the accommodation response.     

Calibration and precompensation of noncommon path aberrations for extreme adaptive optics

Noncommon path aberrations (NCPAs) are one of the main limitations of an extreme adaptive optics (AO) system. NCPAs prevent extreme AO systems from achieving their ultimate performance. These static aberrations are unseen by the wavefront sensor and therefore are not corrected in closed loop. We present experimental results validating what we believe to be new procedures of measurement and precompensation of the NCPAs on the AO bench at ONERA (Office National d'Etudes et de Recherches Aérospatiales). The measurement procedure is based on refined algorithms of phase diversity. The precompensation procedure makes use of a pseudo-closed-loop scheme to overcome the AO wavefront-sensor-model uncertainties. Strehl ratio obtained in the images reaches 98.7% at 632.8 nm. This result allows us to be confident of achieving the challenging performance required for direct observation of extrasolar planets.     

Correcting the aero-optical aberration of the supersonic mixing layer with adaptive optics: concept validation

We describe an adaptive optics (AO) system for correcting the aero-optical aberration of the supersonic mixing layer and test its performance with numerical simulations. The AO system is based on the measurement of distributed Strehl ratios and the stochastic parallel gradient descent (SPGD) algorithm. The aero-optical aberration is computed by the direct numerical simulation of a two-dimensional supersonic mixing layer. When the SPGD algorithm is applied directly, the AO cannot give effective corrections. This paper suggests two strategies to improve the performance of the SPGD algorithm for use in aero-optics. The first one is using an iteration process keeping finite memory, and the second is based on the frozen hypothesis. With these modifications, the performance of AO is improved and the aero-optical aberration can be corrected to some noticeable extent. The possibility of experimental implementation is also discussed.     

Hardness variation with indenter sharpness in an Au thin-film

The effects of the indenter shape on hardness were studied from thin-film nanoindentations. Two Berkovich indenters with different operating histories were prepared and their morphologies were measured with an atomic force microscope. The curvature radii of both indenters that were measured through an image analysis were 58.8 nm and 732.2 nm, respectively. The nanoindentations were carried out on a 1.2 microm-thick Au thin-film with a Nanoindenter XP system with both indenters. Various nanoindentation data with indenter exchanges were surveyed, and they showed that the peak indentation loads under the blunter indenter were higher than those of the sharper indenter at the same indentation depths. The indenter sharpness parameter was used to correct the raw nanoindentation curves. The corrected curves overlapped well and the resulting hardness values were consistent regardless of the indenter sharpness. The intrinsic hardness values of the Au thin-film from both indenters agreed with each other, with only a 0.6% difference. This means the indenter sharpness was properly corrected and that the sharpness must be considered when the contact properties are measured at shallow indentations.     

Optimization of doubly Q-switched lasers with both an acousto-optic modulator and a GaAs saturable absorber

A doubly Q-switched laser with both an acousto-optic (AO) modulator and a GaAs saturable absorber can obtain a more symmetric and shorter pulse with high pulse peak power, which has been experimentally proved. The key parameters of an optimally coupled doubly Q-switched laser with both an AO modulator and a GaAs saturable absorber are determined, and a group of general curves are generated for what we believe is the first time, when the single-photon absorption (SPA) and two-photon absorption (TPA) processes of GaAs are combined, and the Gaussian spatial distributions of the intracavity photon density and the initial population-inversion density as well as the influence of the AO Q-switch are considered. These key parameters include the optimal normalized coupling parameter, the optimal normalized GaAs saturable absorber parameters, and the normalized parameters of the AO Q-switch, which can maximize the output energy. Meanwhile, the corresponding normalized energy, the normalized peak power, and the normalized pulse width are given. The curves clearly show the dependence of the optimal key parameters on the parameters of the gain medium, the GaAs saturable absorber, the AO Q-switch, and the resonator. Sample calculations for a diode-pumped Nd3+:YVO4 laser with both an AO modulator and a GaAs saturable absorber are presented to demonstrate the use of the curves and the relevant formulas.     

Electromechanical modeling and analytical investigation of nonlinearities in energy harvesting piezoelectric beams

Piezoelectric materials are extensively applied for vibrational energy harvesting especially in micro-scale devices where other energy conversion mechanisms such as electromagnetic and electrostatic methods encounter fabrication limitations. A cantilevered piezoelectric bimorph beam with an attached proof (tip) mass for the sake of resonance frequency reduction is the most common structure in vibrational harvesters. According to the amplitude and frequency of applied excitations and physical parameters of the harvester, the system may be pushed into a nonlinear regime which arises from material or geometric nonlinearities. In this study nonlinear dynamics of a piezoelectric bimorph harvester implementing constitutive relations of nonlinear piezoelectricity together with nonlinear curvature and shortening effect relations, is investigated. To achieve this goal first of all a comprehensive fully-coupled electromechanical nonlinear model is presented through a variational approach. The governing nonlinear partial differential equations of the proposed model are order reduced and solved by means of the perturbation method of multiple scales. Results are presented for a PZT/Silicon/PZT laminated beam as a case study. Findings indicate that material nonlinearities of the PZT layer has the dominant effect leading to softening behavior of the frequency response. At the primary resonance, different frequency responses of the extracted power can be distinguished according to the excitation amplitude, which is due to harmonic generation as a result of piezoelectric nonlinearity. The extracted power is analytically computed and validated with a good agreement by a numerical solution.