利用五帧相移算法进行纳米台阶高度的表征

描述了一种用于纳米级台阶高度表征的相移显微干涉测量方法,它被广泛用于高精度的表面测量上。系统采用集成了高分辨力（0．7nm）电容传感器的纳米定位器实现移相、健壮的Hariharan五帧相移算法,利用ISO5436—1：2000国际标准对纳米台阶高度结构进行了评价。结果表明,该方法具有无损、快速和易于在晶片上进行的特点。系统测量的精度在纳米量级,重复性在亚纳米量级。     

时间相移显微干涉术用于微机电系统的尺寸表征

提出了将时间相移显微干涉测量方法用于微结构和器件的几何特性检测上．该方法速度快、无损、非接触、易在晶片级进行,具有亚微米级的水平分辨力,垂直分辨力在纳米量级．测量系统采用Mirau显微干涉物镜,利用高性能压电陶瓷物镜纳米定位器实现垂直方向的相移,并通过健壮的5帧Hariharan算法获取表面的相位信息．通过测量美国国家标准研究院（NIST）认证的标准台阶对系统进行了精度标定,并通过测量微谐振器和压力传感器微薄膜的几何尺寸说明了该方法作为测量和过程表征工具的功能．     

基于白光相移干涉术的微结构几何尺寸表征

将Carré等步长相移法与白光垂直扫描相结合形成了一种白光等步长相移算法,该方法快速、准确、非接触,垂直分辨力可达亚纳米级.测量系统集成了Mirau显微干涉物镜,并通过高精度压电陶瓷纳米定位器带动物镜进行垂直扫描.分析了Carré法应用于白光干涉信号的相位提取的精度,对不同扫描步距以及不同信噪比情况下的测量进行了计算机仿真,确定了测量参数.结合重心法将相位计算的数据范围直接定位于干涉信号的零级条纹,从而省去了相位解包裹过程.通过对微谐振器和标准台阶的测量说明了该方法的有效性,并使用白光相移干涉、白光垂直扫描和单色光相移干涉对44 nm标准台阶进行了测量,并对测量结果进行了比较.     

汽车车内噪声主动控制变步长NFB-LMS算法

为规避最小均方（Least Mean Square,LMS）算法不能同时提高收敛速度和降低稳态误差的固有缺陷,以及已有变步长LMS算法存在收敛速度慢和稳态误差估计精度差的问题,文中提出了一种基于变步长归一化频域块（Normalized Frequency-domain Block,NFB） LMS算法的汽车车内噪声主动控制方法。为了比较,应用传统的LMS算法、基于反正切函数的变步长LMS算法和变步长NFB-LMS算法分别进行实测汽车车内噪声的主动控制。结果表明,与其他两个算法相比,变步长NFB-LMS算法的收敛速度提高了70%以上,稳态误差减小了90%以上。变步长NFB-LMS算法在处理车内噪声信号时具有很高的效率,为进行汽车车内噪声主动控制提供了一种新方法。     

基于FxLMS的汽车车内噪声变步长主动均衡算法

提出了一种可用于汽车车内噪声主动均衡控制的变步长主动噪声均衡（Active Noise Equalization,ANE）算法,与传统车内噪声主动抵消控制方法所采用的滤波x最小均方（Filtered-x Least Mean Square,FxLMS）算法相比具有更好的实用性。应用固定步长主动噪声均衡（Active Noise Equalization,ANE）算法、所提出变步长ANE算法和已有变步长ANE算法分别进行汽车车内噪声主动均衡控制。结果表明,所提出变步长ANE算法具有更快的收敛速度和较低的稳态误差,并且能进一步降低汽车车内噪声响度,为汽车车内声品质主动控制提供了一种新方法。     

基于迭代学习控制的材料黏弹性纳米测量

原子力显微镜（AFM）是进行纳米材料力学特性（如材料黏弹性）测量的重要工具．压电陶瓷驱动器作为AFM的核心部件，由于其迟滞和蠕变特性的影响，致使在材料黏弹性纳米测量过程中，不仅测量速度慢，而且测量误差较大．为了解决以上问题，提出一种基于逆的迭代学习控制方法．通过在频域内学习系统的动态特性，补偿AFM的z轴动态误差，从而实现AFM系统的快速准确定位．该方法不仅避免了复杂的AFM系统建模过程，而且提高了系统输出时期望输入的跟踪精度．用美国DI公司的纳米原位测量仪对聚二甲基硅氧烷（PDMS）的纳米黏弹性进行了测量，验证了算法的适用性和有效性．     

随机相移误差的Lissajous标定与校正

将Lissajous标定技术应用到相移干涉测量的相移算法(PSA)中,提出一种基于Lissajous标定技术的随机相移误差校正算法。该算法不需要计算各帧干涉图之间的实际相移量,直接用Lissajous标定和椭圆拟合的方法计算相移算法的相位提取误差(包括离焦、偏倚、相移量偏差)然后进行校正。数值模拟结果表明:该算法不需要迭代运算就能从大于3帧的带有随机相移误差的干涉图中有效恢复出正确的相位信息,运算时间少,计算精度高并且适合于所有的相移算法。实验结果表明:基于Lissajous标定技术的随机相移误差校正算法与现有的迭代随机相移算法(AIA)精度相当,但计算速度得到明显提升。     

位相测量轮廓术中相移误差和最佳相移次数的研究

位相测量轮廓术是三维面形测量的一种重要方法,它采用的离散相移技术要求精确的相移,在实际系统中不可避免地存在着相移误差,它将导致计算位相和重建面形的误差,本文利用已建立的三维面形仿真系统,定量研究了不同线性相移误差下所引起的位相误差和面形误差大小,本文还讨论了应如何选取最佳的相移次数,本文的工作可为实际测量的校准提供理论数据,对实际测量工作具有指导意义。     

基于干涉显微原理的表面形貌测量系统

根据光学干涉显微法原理,设计开发了一套微纳结构表面形貌测量系统.该系统采用林尼克干涉显微镜,通过参考镜扫描的方法将扫描器与相移器集为一体,分别采用五步相移算法和基于采样定理的包络均方函数(SEST)算法实现相移干涉法(PSI)和垂直扫描干涉法(VSI)两种模式对微纳结构的表面形貌测量.为验证该系统性能,采用标准多刻线样板和标准台阶作为样件对VSI 和PSI 两种模式分别进行了测量实验.结果证明,该系统能够完成微纳结构表面形貌的快速精确测量,可以满足微电子、微机电系统中微纳结构的表面形貌测量要求.     

关节臂式测量机动态误差分析与补偿

关节臂式测量机误差来源多且易累积放大,其动态误差分析与补偿成为了国内外学者研究的重点。本文通过分析热变形误差、测量力误差与角度编码误差三种主要误差因素,得出了关节臂式测量机工作的最佳温度值以及表征其动态误差的三种误差因子——最大定位误差（MPE）、残余定位误差（RPE）和关节转角值（JA）。针对以上误差因子,本文提出了将T-S模糊神经网络（T-S Fuzzy Neural Network, T-S FNN）在自学能力和大规模运算方面的优势以及模拟退火算法（Simulated Annealing, SA）对全局寻优的能力相结合的新补偿方法,并建立了模型。经正交实验表明本文提出的补偿方法使动态过程中的误差分别减小了88.8%、80.2%、71.3%,证明该模型能够有效提高测量机的动态测量精度。     

Motion error correction of range migration algorithm for aircraft spotlight SAR imaging

Since a motion error is the main phase error source in the aircraft synthetic aperture radar, several reconstruction algorithms with motion error correction have been developed. An efficient motion compensation via the known motion error information is proposed. Specifically, the proposed method is based on the subarea technique with shifting and the subaperture technique via the mean values of the motion errors. Then, using the extended Taylor approximation and the principle of the stationary phase, the motion errors are corrected through compensation at the mixing stage and the Stolt interpolation stage.     

Interferometric phase reconstruction by nonuniform shifting of the reference beam

A method for phase measurement in common-path interferometers, believed to be novel, is presented. We use the property of phase reconstruction algorithms, such as the Carré and Hariharan algorithms, that do not require uniform phase across the reference beam. Only the ratio of the phase steps must be the same at each pixel. We show phase measurement and reconstruction in a common-path interferometer by shifting either the tilt or the focus of the reference wave front. We present a theoretical explanation of phase measurement using this property. We also present results from a proof-of-principle experiment using a scatterplate interferometer, in conjunction with the tilt phase-shifting technique, to measure the reflected phase of a test optical element. Furthermore, we present a computer simulation to demonstrate the mathematical validity of this measurement technique using defocus shifting, rather than tilt shifting, in the reference wave front.     

Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry

Phase-shifting interferometry suffers from two main sources of error: phase-shift miscalibration and detector nonlinearity. Algorithms that calculate the phase of a measured wave front require a high degree of tolerance for these error sources. An extended method for deriving such error-compensating algorithms patterned on the sequential application of the averaging technique is proposed here. Two classes of algorithms were derived. One class is based on the popular three-frame technique, and the other class is based on the 4-frame technique. The derivation of algorithms in these classes was calculated for algorithms with up to six frames. The new 5-frame algorithm and two new 6-frame algorithms have smaller phase errors caused by phase-shifter miscalibration than any of the common 3-, 4- or 5-frame algorithms. An analysis of the errors resulting from algorithms in both classes is provided by computer simulation and by an investigation of the spectra of sampling functions.     

Double three-step phase-shifting algorithm

We describe what we believe is a new phase-shifting algorithm called a double three-step algorithm developed to reduce the measurement error of a three-dimensional shape-measurement system, which is based on digital fringe-projection and phase-shifting techniques. After comparing the performance of different existing phase-shifting algorithms, we present the new double three-step algorithm based on the error analysis of the standard three-step algorithm. In this algorithm, three-step phase shifting is done twice with an initial phase offset of 60 degrees between them, and the two obtained phase maps are averaged to generate the final phase map. Both theoretical and experimental results showed that this new algorithm worked well in significantly reducing the measurement error.     

相移干涉三维形貌纳米检测及算法研究

基于相移干涉理论设计并实现了微平面三维形貌测试系统，针对三维形貌检测解包裹过程中出现的问题，改进了现有的残差点判断法，能够更加准确、快速地确定残差点的存在．对相位解包裹算法进行了系统研究．分析了干涉图中残差对相位解包裹的影响，提出了一种基于二阶导数的区域增长解包裹算法．在实际测量中，最终结果得到了明显的改善，证明了该方法的有效性，提高了系统精度、采用此算法，系统的纵向测量误差小于2nm．     

Method for designing error-compensating phase-calculation algorithms for phase-shifting interferometry

We propose a general approach to eliminating some error source effects in phase-calculation algorithms for phase-shifting interferometry. We express the actual phase shift in a convenient form that takes the errors into account and develop in series the detected phase from a generic algorithm. Setting to zero the terms of the series that involve unwanted errors leads to a set of linear equations for the algorithm coefficients, which can thus be found. By using this approach, one could develop an algorithm series for an individual interferometer based on relevant concerns about the main error sources in it and eliminate the error source effects to any desired order. Two examples of algorithm series, to eliminate distorted phase shifts caused by the geometric effect in an interferometer with a spherical Fizeau cavity and to eliminate vibration effects, are discussed.     

Algorithm immune to tilt phase-shifting error for phase-shifting interferometers

As a phase shifter usually suffers from both translational and tilt-shift errors during shifting, so every pixel in the same interferogram will have a different phase-shift value. Thus nonlinear phase-measurement errors cannot be avoided, but even translational-shift error has been corrected effectively. However, based on the fact that the shifted phases of all the pixels in the same interferogram remain on the phase-shift plane, by defining this plane one can eliminate a significant number of phase errors. A new algorithm that is immune to both translational- and tilt-shift errors in a phase shifter for phase-stepping interferometers is presented. A first-order Taylor series expansion replaces the nonlinear equations for defining the phase-shift plane, and iteration of the algorithm guarantees its accuracy. Results of a computer simulation show that phase-measurement errors caused by both translation- and tilt-shift error can be compensated for completely, even when the tilt-shift error is not more than ?1%.     

Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts

An advanced iterative algorithm is presented to extract phase distribution from randomly and spatially nonuniform phase-shifted interferograms. The proposed algorithm divides the interferograms into small blocks and retrieves local phase shifts accurately by iterations. Therefore, the phase distribution can be calculated with high precision by eliminating the effect of tilts occurring during phase shifting. Simulated results and experiments demonstrate that the proposed algorithm exhibits high precision and converges faster than previous algorithms even when the tilt errors are up to 27.6% of the normal phase step.