Wave-front generation of Zernike polynomial modes with a micromachined membrane deformable mirror

We investigate the characteristics of a 37-channel micromachined membrane deformable mirror for wave-front generation. We demonstrate wave-front generation of the first 20 Zernike polynomial modes, using an iterative algorithm to adjust driving voltages. The results show that lower-order-mode wave fronts can be generated with good accuracy and large dynamic range, whereas the generation of higher-order modes is limited by the number of the actuator channels and the working range of the deformable mirror. The speed of wave-front generation can be as fast as several hundred hertz. Our results indicate that, in addition to generation of wave fronts with known aberrations, the characteristics of the micromachined membrane deformable mirror device can be useful in adaptive optics systems for compensating the first five orders of aberration.     

Double drive modes unimorph deformable mirror for low-cost adaptive optics

This paper reports the development and characterization of a low-cost thin unimorph deformable mirror (DM) driven by positive voltage. The developed DM consists of both an inner actuator array and an outer ring actuator, which works two drive modes: the inner actuator array is used for aberration correction, while the outer ring actuator is used to generate an overall defocus bias. An analytical model based on the theory of plates and shells is studied for predicting the behavior of the developed DM. Measurement results indicate that dual direction maximum defocus deformations of the developed DM are -14.3 and 14.9 μm, respectively, and the resonant frequency is 1.8 kHz. The root-mean-square deformation of the mirror surface after correction is better than λ/20 for λ=633 nm. The replication of Zernike mode shapes up to the fifth order demonstrates that this developed DM is satisfactory for low-order aberration correction.     

单压电片悬臂梁式压电俘能器效能分析

以线性压电理论为基础,建立了单压电片悬臂梁式压电俘能器的输出功率与压电结构的构型、驱动频率以及外载荷阻抗等物理参数之间的解析关系。数值计算结果表明,优化负载阻抗、金属层厚度以及金属层材料可有效提高俘能器的俘能效率。文中还将单压电片悬臂梁式压电俘能器与双压电片悬臂梁式压电俘能器进行了对比,理论分析结果表明当外界机械振动的频率较稳定时,前者具有更高的俘能效率。     

基于MEMS技术的新型变形反射镜

基于MEMS技术体硅工艺,提出一种新型大有效面积的连续变形反射镜的设计制造方法。依工艺流程中的实际情况与结果,分析了在制造过程中遇到的大面积腔体深腐蚀中凸角腐蚀和键合中小空隙粘合等关键问题,设计实施了T形补偿角、延长驱动线等解决方案。用此方法制造出有效反射面积30mm×30mm,最大变形量1.2μm,49驱动电极的新型变形反射镜。10-200V电压范围内得到的该变形反射镜镜面变形数据与模拟结果具有很好的一致性。     

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.     

Analytical solutions for the transverse deflection of a piezoelectric circular axisymmetric unimorph actuator

This paper presents analytical solutions to the transverse deformation shape of a circular axisymmetric piezoelectric-metal composite unimorph actuator. The solutions account for both the influence of an applied electric field and a concentrated or uniformly distributed mechanical load. Using piezoelectric constitutive equations, combined with thin plate and small bending elastic theory, the generalized equation of motion for bending of thin piezoelectric-metal composite plates has been derived. Our approach predicts that there is an optimum thickness ratio between the piezoelectric and metal plates, which leads to a maximum combination of deflection and load carrying capabilities. Derived formulas are very simple that offer a quick method for engineering design and optimization of a circular unimorph piezoelectric actuator.     

On the use of polynomial series with the Rayleigh-Ritz method

Extensive literature emphasising the use of special sets of polynomials for Rayleigh-Ritz solutions to plate problems exists. It is commonly suggested that convergence can be improved by the use of special sets of polynomials, which are often orthogonal over the plate domain. This paper shows analytically that the polynomial series chosen does not affect convergence directly. It is shown that the only effect of the choice of set (for given polynomial degree) is on the numerical stability of the solution. These assertions are supported by numerical results for bending and vibration of laminated composite plates.     

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.     

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.     

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。

     

Generation of Bessel beams using a magnetic liquid deformable mirror

A deformable mirror made of a magnetic liquid has been used to produce conical surfaces with subwavelength (λ/4) accuracy. The surface profile of the liquid mirror is controlled by 91 small magnetic coils. The mirror exhibits a linear response with respect to the currents driving the coils, and it allows for real-time changes of its surface profile. The magnetic liquid deformable mirror has been used to produce reflected beams having a conical wavefront; the propagation of the reflected beams was verified to be consistent with that of Bessel beams in the near and far field. The large dynamic range of such a deformable mirror has made it possible to generate Bessel beams with a broad range of beam parameters.     

Aberration-free dynamic focusing with a multichannel micromachined membrane deformable mirror

We demonstrate aberration-free dynamic focusing with a low-cost 19-channel continuous-surface micromachined membrane deformable mirror (MMDM). A lookup table of the optimum control voltages for various focal lengths is obtained with an adaptive optics algorithm. Diffraction-limited imaging resolution is achieved owing to the capablility of the MMDM for aberration compensation. The measured speed of the MMDM supports dynamic focusing operations at several hundred hertz. Our dynamic focusing approach is shown to function with either monochromatic or broadband optical sources.     

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.     

Open-loop control of a MEMS deformable mirror for large-amplitude wavefront control

A method is introduced for predicting control voltages that will generate a prescribed surface shape on a MEMS deformable mirror. The algorithm is based upon an analytical elastic model of the mirror membrane and an empirical electromechanical model of its actuators. It is computationally simple and inherently fast. Shapes at the limit of achievable mirror spatial frequencies with up to 1.5 microm amplitudes have been achieved with less than 15 nm rms error.     

High-aspect-ratio line focus for an x-ray laser by a deformable mirror

A high-aspect-ratio line focus is required on a plane target in x-ray laser experiments for obtaining a high gain-length product. Inherent wave-front aberrations in line-focusing optics, which consist of a cylindrical lens and a spherical lens, are discussed with respect to beam diameter. The nonuniformity of the linewidth that is due to the aberrations is also calculated by the ABCD matrix method. A deformable mirror of a continuous plate type with a diameter of 185 mm provides an adequate wave-front distribution for compensating for the wave-front aberration. The wave-front control by the deformable mirror realizes a fine linewidth of 25 mum and 18.2 mm long, corresponding to the aspect ratio of 728. The linewidth is three times the diffraction limit. The intensity distribution along the line focus is also improved.     

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.     

Cavity with a deformable mirror for tailoring the shape of the eigenmode

We demonstrate an optical cavity that supports an eigenmode with a flattop spatial profile--a profile that has been proposed for the cavities in the Advanced Laser Interferometer Gravitational Wave Observatory, the second-generation laser interferometric gravitational wave observatory--because it provides better averaging of the spatially dependent displacement noise on the surface of the mirror than a Gaussian beam. We describe the deformable mirror that we fabricated to tailor the shape of the eigenmode of the cavity and show that this cavity is a factor of 2 more sensitive to misalignments than a comparable cavity with spherical mirrors supporting an eigenmode with a Gaussian profile.     

Theory of spherical holographic gratings recorded by use of a multimode deformable mirror

We present the theory of spherical holographic gratings recorded by use of a deformable plane mirror and consider its application to the optimized Rowland Mounting. We illustrate the efficiency of such a mounting by computing two high-resolution gratings (3800 grooves/mm) with f/24 and f/10 apertures.     

Comparative analysis of Zernike aberrations generation with deformable mirrors for ocular adaptive optics

The micromachined membrane deformable mirror (MMDM) and piezoelectric deformable mirror (PDM) are two types of cost-effective deformable mirrors (DMs) that are widely used in ocular adaptive optics. In the current study, a 59ch MMDM and a 37ch PDM are tested and compared in generation of Zernike aberrations which are the most dominant of the human eye. The results reveal that although PDM performs better in larger scope, both DMs have almost similar performance if the individual generation coefficient is within the range of ±1 µm.     

Development of a new technology of deformable mirror for ultra intense laser applications

Adaptive optics is now a standard feature for the current ultra high intensity lasers facilities. Aberration induced by both the optical components and the thermal effects in the amplification stages can be corrected with an adaptive optics system to reach both maximum peak energy and fluence. In this article, we present the development of a new technology of deformable mirror. These mirrors are designed taking into account the needs and specificities of ultra intense laser applications. They provide exceptional stability, optical quality and innovative features like scalability and maintenance of the reflective surface.