Improved compensation of turbulence-induced amplitude and phase distortions by means of multiple near-field phase adjustments

An approach for compensation of turbulence-induced amplitude and phase distortions is described. Two deformable mirrors are placed optically conjugate to the collecting aperture and to a finite range from this aperture. Two control algorithms are presented. The first is a sequential generalized projection algorithm (SGPA) that is similar to the Gerchberg-Saxton phase retrieval algorithm. The second is a parallel generalized projection algorithm (PGPA) that introduces constraints that minimize the number of branch points in the control commands for the deformable mirrors. These approaches are compared with the approach of placing the second deformable mirror conjugate to the far field of the collecting aperture and using the Gerchberg-Saxton algorithm to determine the optimal mirror commands. Simulation results show that placing the second deformable mirror at a finite range can achieve near-unity Strehl ratio regardless of the strength of the scintillation induced by propagation through extended paths, while the maximum Strehl ratio of the far-field approach drops off with increasing scintillation. The feasibility of the solutions is evaluated by counting the branch points contained in the deformable mirror commands. There are large numbers of branch points contained in the control commands that are generated by the Gerchberg-Saxton SGPA-based algorithms, irrespective of where the second deformable mirror is located. However, the control commands generated by the PGPA with branch point constraints achieves excellent Strehl ratio and minimizes the number of branch points.     

Application of the parallel generalized projection algorithm to the control of two finite-resolution deformable mirrors for scintillation compensation.

A modification of the parallel generalized projection algorithm is presented that allows for the use of projections in a weighted norm. Convergence properties of the modified algorithm, denoted the weighted parallel generalized projection algorithm, are developed. The weighted parallel generalized projection algorithm is applied to the control of two finite-resolution deformable mirrors to compensate for both the amplitude and the phase fluctuations that result from propagation through a turbulent medium. Numerical results are shown that indicate that a two-deformable-mirror system can provide improved performance over that of a single-deformable-mirror system.     

Convergence rates for iterative vector space projection methods for control of two deformable mirrors for compensation of both amplitude and phase fluctuations

The control of two deformable mirrors for compensation of time-varying fluctuations in the complex field that results from wave propagation through a turbulent medium is considered. Iterative vector space projection methods are utilized to determine the control commands to be applied to the two deformable mirrors. Convergence of the iterative algorithm is accelerated when the algorithm is initialized, at each measurement period, with the values for the phase commands obtained from the previous measurement period. Furthermore, it is found that, if the sample frequency is sufficiently greater than the Greenwood frequency, then only a single iterative step at each measurement period is required to obtain good compensation of both amplitude and phase fluctuations.     

Multiconjugate adaptive optics for large telescopes: analytical control of the mirror shapes

We present an analytical algorithm for deriving the shapes of the deformable mirrors to be used for multiconjugate adaptive correction on a large telescope. The algorithm is optimal in the limit where the overlap of the wave-front contributions from relevant atmospheric layers probed by the guide stars is close to the size of the pupil. The fundamental principle for correction is based on a minimization of the sum of the residual power spectra of the phase fluctuations seen by the guide stars after correction. On the basis of the expressions for the mirror shapes, so-called layer transfer functions describing the distribution of the correction of a single atmospheric layer among the deformable mirrors and the resulting correction of that layer have been derived. It is shown that for five guide stars distributed in a regular cross, two- and three-mirror correction will be possible only up to a maximum frequency defined by the largest separation of the conjugate altitudes of the mirrors and by the angular separation of the guide stars. The performance of the algorithm is investigated in the K band by using a standard seven-layer atmosphere. We present results obtained for two guide-star configurations: a continuous distribution within a given angular radius and a five-star cross pattern with a given angular arm length. The wave-front fluctuations are subjected to correction using one, two, and three deformable mirrors. The needed mirror dynamic range is derived as required root-mean-square stroke and actuator pitch. Finally the performance is estimated in terms of the Strehl ratio obtained by the correction as a function of field angle. No noise has been included in the present analysis, and the guide stars are assumed to be at infinity.     

Methods for the characterization of deformable membrane mirrors

We demonstrate two methods for the characterization of deformable membrane mirrors and the training of adaptive optics systems that employ these mirrors. Neither method employs a wave-front sensor. In one case, aberrations produced by a wave-front generator are corrected by the deformable mirror by use of a rapidly converging iterative algorithm based on orthogonal deformation modes of the mirror. In the other case, a simple interferometer is used with fringe analysis and phase-unwrapping algorithms. We discuss how the choice of singular values can be used to control the pseudoinversion of the control matrix.     

Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere

A two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier-transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained with a technique based on the Fienup phase-retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable-mirror system, this field-conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared with a conventional phase-only correction system.     

Finite element modeling and testing of a deformable carbon fiber reinforced polymer mirror

Thin-shelled composite mirrors have been recently proposed for use as deformable mirrors in optical systems. Large-diameter deformable composite mirrors can be used in the development of active optical zoom systems. We present the fabrication, testing, and modeling of a prototype 0.2 m diameter carbon fiber reinforced polymer mirror for use as a deformable mirror. In addition, three actuation techniques have been modeled and will be presented.     

Reflectivity and optical surface height requirements in a broadband coronagraph. 1. Contrast floor due to controllable spatial frequencies

We derive the broadband contrast floor in a coronagraphic telescope having nonideal optical surfaces. We consider only fundamental spatial frequencies within the control bandwidth of the coronagraph's deformable mirror. Cross terms arising from the beating of spatial frequencies beyond the deformable mirror control bandwidth will be considered in a second paper. Two wavefront control systems are analyzed:a zero-path difference Michelson interferometer with two deformable mirrors at a pupil image, and a sequential pair of deformable mirrors with one placed at a pupil image. We derive requirements on optical surface figure and reflectivity uniformity for both cases.     

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.     

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.     

High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors

Adaptive optics scanning laser ophthalmoscopes have been used to produce noninvasive views of the human retina. However, the range of aberration compensation has been limited by the choice of deformable mirror technology. We demonstrate that the use of dual deformable mirrors can effectively compensate large aberrations in the human eye while maintaining the quality of the retinal imagery. We verified experimentally that the use of dual deformable mirrors improved the dynamic range for correction of the wavefront aberrations compared with the use of the micro-electro-mechanical-system mirror alone and improved the quality of the wavefront correction compared with the use of the bimorph mirror alone. We also demonstrated that the large-stroke bimorph deformable mirror improved the capability for axial sectioning with the confocal imaging system by providing an easier way to move the focus axially through different layers of the retina.     

环形子孔径检测技术中测量数据的准确提取方法

环形子孔径拼接测试技术是一种无需辅助元件就能检测旋转对称大口径非球面镜的有效手段。根据该技术的检测原理及基于Zemike多项式的“拼接”算法,提出了一种相应的环形子孔径数据提取方法。该方法基于商用相移干涉仪的CCD成像系统和其数据处理软件提供的Mask编辑功能,利用被测镜面上方的三个可移动的基准标记进行绝对定位,给出了具体的实施方案。对一口径700mm、F2的抛物面主镜进行实验,研究结果表明,该数据提取方法操作简单可行,适合于加工车间的实施,取得了符合“拼接”算法需求的子孔径测试数据和对应环带的内外半径值。     

Closed-loop stable control of two deformable mirrors for compensation of amplitude and phase fluctuations

A method for closed-loop stable control of two deformable mirrors for compensation of both amplitude and phase fluctuations is described. A generic implementation is described as well as an implementation that integrates the concept behind a point diffraction interferometer with a two-deformable-mirror system. The relationship of the closed-loop control algorithm to previously developed open-loop iterative algorithms is described. Simulation results are presented that indicate that the system is stable and provides superior performance over that of a single-deformable-mirror system. The impact of finite servo bandwidth on control of two deformable mirrors is evaluated by means of wave optical simulation, and it is found that to achieve a performance improvement attributable to compensation of amplitude fluctuations, the bandwidth of the two-deformable-mirror system must be at least twice the Greenwood frequency.     

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.     

Nanoengineered liquid mirrors shaped by thermal fields

We discuss a new type of deformable mirror made from nanoengineered reflective layers deposited onto liquids. The surfaces are shaped by heating with a laser. The response times of the deformed surfaces are slow (> 1 s). Simplicity and low cost appear to be the main advantages of thermally deformable liquid mirrors.     

Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror

Piezoelectric bimorph- or unimorph-type deformable mirrors are commonly used in adaptive optics to correct for time-dependent phase aberrations. In the optics community, the surface deformations that deformable mirrors are required to achieve, are routinely and conveniently described using Zernike polynomials. A Rayleigh-Ritz structural model, which uses Zernike polynomials directly to describe the displacements, is proposed in this paper. The proposed formulation produces a numerically inexpensive model that predicts deformations with remarkable accuracy. Since design variables, such as electrode layout, material properties, and mirror dimensions, are represented analytically, the model is well suited to optimization or sensitivity analysis applications. Furthermore, since the numerical implementation is very efficient, it could be employed in closed-loop control applications. Results achieved with the proposed model compare well with results from a traditional finite element analysis as well as experimental results of a representative design.     

Adaptive optics based on analog parallel stochastic optimization: analysis and experimental demonstration

Wave-front distortion compensation using direct system performance metric optimization is studied both theoretically and experimentally. It is shown how different requirements for wave-front control can be incorporated, and how information from different wave-front sensor types can be fused, within a generalized gradient descent optimization paradigm. In our experiments a very-large-scale integration (VLSI) system implementing a simultaneous perturbation stochastic approximation optimization algorithm was applied for real-time adaptive control of multielement wave-front correctors. The custom-chip controller is used in two adaptive laser beam focusing systems, one with a 127-element liquid-crystal phase modulator and the other with beam steering and 37-control channel micromachined deformable mirrors. The submillisecond response time of the micromachined deformable mirror and the parallel nature of the analog VLSI control architecture provide for high-speed adaptive compensation of dynamical phase aberrations of a laser beam under conditions of strong intensity scintillations. Experimental results demonstrate improvement of laser beam quality at the receiver plane in the spectral band up to 60 Hz.     

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.     

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.     

Optically addressed microelectromechanical systems driven with high-frequency modulated light

We propose and analyze a new mode of operation for an optically addressed deformable mirror device. The device consists of an array of metallized membrane mirrors supported above an optically addressed photoconductive substrate. A conductive transparent electrode is deposited on the backside of the substrate. A variable polarity voltage is applied between the membrane and the back electrode of the device accompanied with high-frequency modulated light. The membrane is deformed when a modulated light illuminates the backside of the device. This occurs due to impedance and bias redistribution between the two cascaded impedances. This operating mechanism of a microelectromechanical systems device is suitable for detecting moving targets.