Response analysis of holography-based modal wavefront sensor

The crosstalk problem of holography-based modal wavefront sensing (HMWS) becomes more severe with increasing aberration. In this paper, crosstalk effects on the sensor response are analyzed statistically for typical aberrations due to atmospheric turbulence. For specific turbulence strength, we optimized the sensor by adjusting the detector radius and the encoded phase bias for each Zernike mode. Calibrated response curves of low-order Zernike modes were further utilized to improve the sensor accuracy. The simulation results validated our strategy. The number of iterations for obtaining a residual RMS wavefront error of 0.1λ is reduced from 18 to 3.     

Performance analysis of multiplexed phase computer-generated hologram for modal wavefront sensing

We investigate the performance and capability of a holographic modal wavefront sensor (HMWS) that is based on a multiplexed phase computer-generated hologram (MPCGH). The theoretical treatments of the HMWS are presented with scalar diffraction approximations and Fourier analysis. Several MPCGHs have been designed with different linear carrier frequencies, by using of the multiplexed coding scheme we have proposed, and by coding some common Zernike modes. The numerical simulation is carried out to investigate the performance of the HMWS to detect particular aberration mode(s), by considering the effect of different carrier frequency selections and the capability of coding a large number of modes. The results exhibit the expected characteristics of a corresponding symmetric spot pair, and indicate that the wavefront distorted by a particular Zernike mode(s) can be retrieved immediately through solving the amplitude of each mode coded in MPCGHs through the response curves of the HMWS.     

Optimal modal reduction of vibrating substructures

A structure which consists of a main part and a number of attached substructures is considered. A ‘model reduction’ scheme is developed and applied to each of the discrete substructures. Linear undamped transient vibrational motion of the structure is assumed, with general external forcing and initial conditions. The goal is to replace each discrete substructure by another substructure with a much smaller number of degrees of freedom, while minimizing the effect this reduction has on the dynamic behaviour of the main structure. The approach taken here involves Ritz reduction and the Dirichlet‐to‐Neumann map as analysis tools. The resulting scheme is based on a special form of modal reduction, and is shown to be optimal in a certain sense, for long simulation times. The performance of the scheme is demonstrated via numerical examples, and is compared to that of standard modal reduction. Copyright © 2003 John Wiley & Sons, Ltd.     

Improving the performance of a pyramid wavefront sensor with modal sensitivity compensation

We describe a solution to increase the performance of a pyramid wavefront sensor (P-WFS) under bad seeing conditions. We show that most of the issues involve a reduced sensitivity that depends on the magnitude of the high frequency atmospheric distortions. We demonstrate in end-to-end closed loop adaptive optics simulations that with a modal sensitivity compensation method a high-order system with a nonmodulated P-WFS is robust in conditions with the Fried parameter r 0 at 0.5 microm in the range of 0.05-0.10 m. We also show that the method makes it possible to use a modal predictive control system to reach a total performance improvement of 0.06-0.45 in Strehl ratio at 1.6 microm. Especially at r 0=0.05 m the gain is dramatic.     

Designing a holographic modal wavefront sensor for the detection of static ocular aberrations

The extent to which holographic modal wavefront sensing can be applied to the detection of ocular aberrations was investigated. First, the idea of extending the dynamic range of the sensor by increasing the mask bias and the collection area of the pinhole detectors used in the sensor is reviewed. Errors in the detection of single-mode aberrations owing to reduced coherence from retinal scattering, photon, readout, and quantization noise are evaluated. A sensitivity-to-noise metric is introduced to evaluate sensor designs and is found to be maximized by using a pinhole detector radius of 8.6(flambda/NDelta) for every wave of mask bias (where f=transform lens focal length, lambda=wavelength, and N and Delta are the number and size of the hologram pixels, respectively). The problem of detecting ocular aberrations composed of multiple modes required a generalization of the sensitivity measure to include all incident aberration modes. A "detect and correct" ocular aberration detection scheme was implemented that reduced the effects of cross talk and showed a maximum sensitivity-to-noise ratio of 40, which varied inversely with the size of the ocular aberration being detected.     

车辆整备状态车体垂弯频率优化方法研究

为提高轨道车辆整备状态车体垂向一阶弯曲频率,提出基于灵敏度分析和车下设备弹性吊挂参数设计方法优化车体垂向一阶弯曲频率。以车身型材骨架厚度为设计变量,用模态灵敏度理论对车体垂弯进行优化设计;结合改进车下设备与车体连接方式,研究了不同吊挂形式及刚度对车体垂向弯曲频率的影响。研究结果表明:采用灵敏度分析调整车体敏感部件厚度后,车体垂向一阶弯曲频率由9.70Hz提升至10.60Hz,但车体质量相应增加0.93 t;而采用基于车下设备弹性吊挂参数设计的方法,设置下吊设备固有频率为7Hz时,整备状态车体的垂向一阶弯曲模态频率提升至10.51Hz,相对而言基于弹性吊挂参数设计的方法更易于实际工程应用且不增加车体结构质量。     

Predictive wavefront control for adaptive optics with arbitrary control loop delays

We present a modification of the closed-loop state space model for adaptive optics control that allows delays that are a noninteger multiple of the system frame rate. We derive the new forms of the predictive Fourier control Kalman filters for arbitrary delays and show that they are linear combinations of the whole-frame delay terms. This structure of the controller is independent of the delay. System stability margins and residual error variance both transition gracefully between integer-frame delays.     

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.     

Real-time modal control implementation for adaptive optics

The electronics, computing hardware, and computing used to provide real-time modal control for a laser guide-star adaptive optics system are presented. This approach offers advantages in the control of unobserved modes, the elimination of unwanted modes (e.g., tip and tilt), and automatic handling of the case of low-resolution lens arrays. In our two-step modal implementation, the input vector of gradients is first decomposed into a Zernike polynomial mode by a least-squares estimate. The number of modes is assumed to be less than or equal to the number of actuators. The mode coefficients are then available for collection and analysis or for the application of modal weights. Thus the modal weights may be changed quickly without recalculating the full matrix. The control-loop integrators are at this point in the algorithm. To calculate the deformable-mirror drive signals, the mode coefficients are converted to the zonal signals by a matrix multiply. When the number of gradients measured is less than the number of actuators, the integration in the control loop will be done on the lower-resolution grid to avoid growth of unobserved modes. These low-resolution data will then be effectively interpolated to yield the deformable-mirror drive signals.     

Optimal modal reduction of dynamic subsystems: Extensions and improvements

The problem of optimal reduction of a linear dynamic subsystem is revisited. The subsystem may represent, for example, a complex but minor part of a large elastic structure. The goal is to drastically reduce the number of degrees of freedom of a subsystem attached through an interface to a main system in such a way as to affect the dynamic behavior of the main system in the least possible way. In a recent publication, the Optimal Modal Reduction (OMR) algorithm was developed to this end. This algorithm seeks a reduction of the subsystem that will have minimal effect, in the L₂ norm, on the Dirichlet‐to‐Neumann (DtN) map on the interface. Here this algorithm is extended and improved in a number of ways. First, a family of alternative formulations are derived for the DtN map, which lead to alternative OMR algorithms; one of them, called OMR _j=2, is shown to yield better results than the original formulation. Second, the OMR algorithm, which was originally developed for undamped subsystems, is extended to subsystems undergoing Rayleigh damping. In addition, an enhanced derivation of the original OMR algorithm is presented, and the good pointwise performance of OMR is explained by relating to minimization with respect to the H¹ norm. The extensions mentioned above are discussed theoretically as well as demonstrated via numerical examples. Experiments and discussion include comparison of the OMR algorithm to simple coarsening of the subsystem discretization. In all cases, central finite difference discretization in space and explicit time‐stepping are employed to solve the scalar wave equation. Copyright © 2010 John Wiley & Sons, Ltd.     

砂轮划片机模态测试中的传感器测点优化研究

针对砂轮划片机这类复杂设备振动模态测试中测试时间长、传感器数目难以确定和测点难以定位的问题,提出了结合有效独立法、QR分解法及模态验证准则、香农扩展定理对砂轮划片机主系统进行测点优化的方法。采用锤击模态测试方法对某一型号的砂轮划片机测点优化前后的模态进行了测试,识别出划片机主系统的振型和模态参数,比较测点优化前后的测试结果,表明测点优化的模态测试实现了将有限个传感器布置在关键的测点位置上并获取最接近真实信息的目的,缩短了测试时间,提高了测试精度,为复杂设备的振动模态测试提供了参考。     

Wavelength-dependent characteristics of modulo Nlambda0 optical wavefront control

A Fourier analysis treatment of the wavelength dependences associated with modulo lambdar optical path control, treating the general case of a modulo lambdar optical path difference function OPD (x, y) mod lambdar in which the reset wavelength lambdar, is allowed to be an integer multiple of a nominal wavelength lambda0, lambdar=Nlambda0, is presented. Equations are derived describing the wavelength-dependent characteristics of the diffraction efficiency and the wavefront errors associated with all diffracted orders. The results are applied to the cases of diffraction of a planar wavefront and compensation of large aberrations and show that over an extended spectral bandwidth the output field consists of multiple diffracted orders with a range of fractional wavefront errors that diminishes with increasing reset multiple N, but does not reach the diffraction limit associated with conventional optics.     

主动隔振平台模态区间参数模型的独立模态控制方法

针对六自由度隔振平台模态区间参数模型的控制器设计问题,提出了一种模态参数存在摄动时的独立模态控制设计方法,其中将振型矩阵存在不确定性时的模态位移变换转换为模态坐标下增广的等效模态位移测量噪声,在模态控制器设计时通过对噪声的适当加权进行处理;将振型矩阵存在不确定性时的实际控制力变换等效为模态控制器设计时的控制输入矩阵的摄动.通过所提出的方法,将振型矩阵存在不确定性的模态控制器设计问题转换为输入矩阵存在摄动的新辅助系统的控制器设计,为模态参数区同模型的性能鲁棒控制器设计奠定了理论基础.对六自由度隔振平台进行了直接干扰和地基干扰下的主被动隔振实验,实验结果证实了所提方法的有效性.     

Adaptive wavefront control with asynchronous stochastic parallel gradient descent clusters

A scalable adaptive optics (AO) control system architecture composed of asynchronous control clusters based on the stochastic parallel gradient descent (SPGD) optimization technique is discussed. It is shown that subdivision of the control channels into asynchronous SPGD clusters improves the AO system performance by better utilizing individual and/or group characteristics of adaptive system components. Results of numerical simulations are presented for two different adaptive receiver systems based on asynchronous SPGD clusters-one with a single deformable mirror with Zernike response functions and a second with tip-tilt and segmented wavefront correctors. We also discuss adaptive wavefront control based on asynchronous parallel optimization of several local performance metrics-a control architecture referred to as distributed adaptive optics (DAO). Analysis of the DAO system architecture demonstrated the potential for significant increase of the adaptation process convergence rate that occurs due to partial decoupling of the system control clusters optimizing individual performance metrics.     

Fourier transform wavefront control with adaptive prediction of the atmosphere

Predictive Fourier control is a temporal power spectral density-based adaptive method for adaptive optics that predicts the atmosphere under the assumption of frozen flow. The predictive controller is based on Kalman filtering and a Fourier decomposition of atmospheric turbulence using the Fourier transform reconstructor. It provides a stable way to compensate for arbitrary numbers of atmospheric layers. For each Fourier mode, efficient and accurate algorithms estimate the necessary atmospheric parameters from closed-loop telemetry and determine the predictive filter, adjusting as conditions change. This prediction improves atmospheric rejection, leading to significant improvements in system performance. For a 48x48 actuator system operating at 2 kHz, five-layer prediction for all modes is achievable in under 2x10(9) floating-point operations/s.     

Two-wavelength interferometry that uses a fourier-transform method

Two-wavelength interferometry that is based on a Fourier-transform method has been investigated. A phase profile at a synthetic wavelength has been measured from a two-wavelength interferogram with two spatial carrier frequencies. A phase error caused by the difference between modulation intensities at two wavelengths has been theoretically and numerically analyzed. A phase map without the error can be obtained from a power-spectrum adjustment in the two-wavelength interferogram.     

悬臂Kagome夹心板独立模态空间振动控制研究

针对悬臂板挠度大、低频振动突出问题,对悬臂Kagome夹心板的振动主动控制进行研究。建立结构及压电作动器有限元模型;将独立模态空间控制与模态观测器相结合,提出悬臂Kagome夹心板的主动控制策略;针对突风载荷作用下夹心板基于独立模态空间的振动控制进行仿真,重点研究观测器极点对控制效果影响。结果表明,所提控制方法能显著提高悬臂Kagome夹心板结构的阻尼特性,观测器衰减系数越大控制效果越好;该夹心板在振动控制方面较传统板结构优势明显。     

Apodizing holographic gratings for the modal control of semiconductor lasers

We first present the fabrication technique of apodizing holographic gratings. Gratings with a spatially variable reflectivity profile were obtained by the interference of two Gaussian beams on a glass plate covered with a photoresist. When the exposure time was short enough to avoid saturation of the photoresist, gratings with a quasi-Gaussian reflectivity profile for the beam reflected in the -1 order were produced; the reflectivity at the center could be as high as 71%, and the half-width of the reflectivity profile at the e(-1) position could be as small as 180 mum. Apodizing gratings were used as the end mirror of the external cavity of a broad-area semiconductor laser. Single longitudinal- and lateral-mode operation was observed over the full range of allowed injection currents.     

Beam splitter layer emission in fourier-transform infrared interferometers

The self-emission from the splitting layer of a Fourier-transform infrared interferometer is modeled with basic properties of optical thin films. The resulting equation gives explicitly the self-emission contribution in terms of the temperature, the complex refractive index, the reflection coefficient, and the thickness of the beam splitter layer.     

Performance comparison of wavefront reconstruction and control algorithms for Extremely Large Telescopes

Extremely Large Telescopes (ELTs) are very challenging with respect to their adaptive optics (AO) requirements. Their diameters and the specifications required by the astronomical science for which they are being designed imply a huge increment in the number of degrees of freedom in the deformable mirrors. Faster algorithms are needed to implement the real-time reconstruction and control in AO at the required speed. We present the results of a study of the AO correction performance of three different algorithms applied to the case of a 42-m ELT: one considered as a reference, the matrix-vector multiply (MVM) algorithm; and two considered fast, the fractal iterative method (FrIM) and the Fourier transform reconstructor (FTR). The MVM and the FrIM both provide a maximum a posteriori estimation, while the FTR provides a least-squares one. The algorithms are tested on the European Southern Observatory (ESO) end-to-end simulator, OCTOPUS. The performance is compared using a natural guide star single-conjugate adaptive optics configuration. The results demonstrate that the methods have similar performance in a large variety of simulated conditions. However, with respect to system misregistrations, the fast algorithms demonstrate an interesting robustness.