Modeling the interferometric radius measurement using Gaussian beam propagation

We model the interferometric radius measurement using Gaussian beam propagation to identify biases in the measurement due to using a simple geometric ray-trace model instead of the more complex Gaussian model. The radius measurement is based on using an interferometer to identify the test part's position when it is at two null locations, and the distance between the positions is an estimate of the part's radius. The null condition is observed when there is no difference in curvature between the reflected reference and the test wavefronts, and a Gaussian model will provide a first-order estimate of curvature changes due to wave propagation and therefore changes to the radius measurement. We show that the geometric ray assumption leads to radius biases (errors) that are a strong function of the test part radius and increase as the radius of the part decreases. We tested for a bias for both microscaled (<1 mm) and macroscaled parts. The bias is of the order of parts in 10(5) for micro-optics with radii a small fraction of a millimeter and much smaller for macroscaled optics. The amount of bias depends on the interferometer configuration (numerical aperture, etc.), the nominal radius of the test part, and the distances in the interferometer.     

Laser differential confocal radius measurement system

A laser differential confocal radius measurement system with high measurement accuracy is developed for optical manufacturing and metrology. The system uses the zero-crossing point of the differential confocal intensity curve to precisely identify the cat's-eye and confocal positions and uses an interferometer to measure the distance between these two positions, thereby achieving a high-precision measurement for the radius of curvature. The coaxial measuring optical path reduces the Abbe error, and the air-bearing slider reduces the motion error. The error analysis indicates the theoretical accuracy of the system is up to 2?ppm, and the experiment shows that the system has high focusing sensitivity and is little affected by environmental fluctuations; the measuring repeatability is between 4 and 12?ppm.     

Visually Servoed 3-D Alignment of Multiple Objects with Subnanometer Precision

This paper presents a visual measurement technique and the associated visual servo control method that enable 3-D alignment of multiple objects with subnanometer precision. Such high precision is achieved through eliminating the bias error caused by spatial sampling in the in-plane motion estimation, using a highly sensitive measurement technique based on interference for the out-of-plane motion, and continuously compensating for time varying uncertainties induced by mechanical forces and thermal drifts. The developed measurement technique is integrated with a motion stage to experimentally demonstrate visually servoed 3-D alignment, in which two microcantilevers are aligned in the 3-D space with alignment errors below 1 nm (rms) in all axes. Nanostepping of 0.5 nm magnitude along the out-of-plane z-axis is also performed between the two microcantilevers to illustrate the super precision of the visually served 3-D alignment.     

基于部分补偿干涉的非球面顶点曲率半径加工误差测量

测量非球面顶点曲率半径加工误差对预估成像系统质量和计算机辅助装校有重要意义。传统的部分补偿干涉系统只能测量非球面面形误差,即被测非球面与标称非球面之间的不规则偏差。通过分析系统剩余波前特定像差项随被测面位置的变化关系,基于部分补偿干涉原理,提出了一种非球面顶点曲率半径加工误差测量方法,测得非球面顶点曲率半径加工误差。仿真实验结果表明,所提出的误差测量方法具有可行性,其原理相对测量精度不低于0.003%。     

Assessment of Digital Image Correlation Measurement Accuracy in the Ultimate Error Regime: Main Results of a Collaborative Benchmark

We report on the main results of a collaborative work devoted to the study of the uncertainties associated with Digital image correlation techniques (DIC). More specifically, the dependence of displacement measurement uncertainties with both image characteristics and DIC parameters is emphasised. A previous work [Bornert et al. (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp. Mech. 49, 353–370] dedicated to situations with spatially fluctuating displacement fields demonstrated the existence of an ‘ultimate error’ regime, insensitive to the mismatch between the shape function and the real displacement field. The present work is focused on this ultimate error. To ensure that there is no mismatch error, synthetic images of in‐plane rigid body translation have been analysed. Several DIC softwares developed by or in use in the French community have been used to explore the effects of a large number of settings. The discrepancies between DIC evaluated displacements and prescribed ones have been statistically analysed in terms of random errors and systematic bias, in correlation with the fractional part τ of the displacement component expressed in pixels. Main results are as follows: (i) bias amplitude is almost always insensitive to subset size, (ii) standard deviation of random error increases with noise level and decreases with subset size and (iii) DIC formulations can be split up into two main families regarding bias sensitivity to noise. For the first one, bias amplitude increases with noise while it remains nearly constant for the second one. In addition, for the first family, a strong dependence of random error with τ is observed for noisy images.     

Cutter path preview for contour machining based on efficient identification of motion error sources

This paper presents an efficient approach to the identification of the motion error sources in CNC contour machining. The motion error sources include the mismatch of feed drives, the friction disturbances and the cutter path curvature. Their effects on the contour error in linear and circular motions are analyzed, respectively. On the basis of the analysis, the procedure for the identification of these error-source effects is developed. With the identification results, the cutter path trajectory can be previewed before the real run.     

抽样引起的测量不确定度评定

若测量值定义为抽样目标中的分析物浓度,那么与抽样相关的不确定性必然导致最终测量结果的不确定度。抽样不确定度主要来源于抽样目标的不均匀性、抽样方案不明确、抽样和样品制备过程中引入的交叉污染、分析物损失等。以欧洲分析化学会的指南为基础,介绍了抽样不确定度评定的经验方法,该方法将测量不确定度来源区分为抽样过程和分析过程中的随机效应与系统效应。通过实例说明了如何通过重复实验和方差分析来量化抽样和分析过程中的随机效应,从而评估抽样和样品制备所引入的不确定度。     

Uniformity test of bias when the reference value contains experimental error

The uniformity test of biases for analytical methods must address uncertainties in the reference method. If the uncertainty associated with the estimates of true values is significant but ignored in the test of bias equality, the type I error can exceed the prespecified error rate. In general, when biases at each concentration level are confounded with a random component (confounding bias), the usual test of bias equality tests the uniformity of the combined bias, rather than the uniformity of fixed bias-the bias without the random component. Based on a confounding model that takes both the fixed and the confounding biases into account, the actual type I error rate of the uniformity test can be calculated. To eliminate the impact of confounding bias on the uniformity test of fixed biases, a new F'-test is proposed. The new F'-test is simply adding a correction factor to the conventional F-test. The correction factor is directly related to the uncertainty associated with the estimates of true values. A simulation study is conducted to show that the proposed test can bring the type I error rate down to the prespecified level. Data from two aldehyde methods are used to demonstrate how the proposed F'-test works. Recommendations on optimal sample allocation are also provided.     

成形磨砂轮圆弧廓形关键参数在位检测方法及试验研究

针对成形磨砂轮精密磨削加工中准确高效地检测砂轮形状精度的需求,提出砂轮廓形参数在位检测新方法。首先采用线状激光位移传感器采集砂轮表面微观形貌数据,构建测量矩阵模型,再通过滤波去噪、宏观轮廓线提取、非线性曲线拟合等算法分析处理出砂轮廓形曲率半径和圆度误差检测指标。通过磨削验证试验分析和检测不确定度评定,证明该方法稳定可靠,检测结果可以准确反映工件加工精度,满足复杂圆弧廓形砂轮检测需求,具有较好的工程应用价值。     

脉冲地震动缩放水平对结构非线性位移反应影响的分析

研究缩放速度脉冲型地震动强度水平引起的单自由度(SDOF)体系非线性位移反应的偏差。采用30条速度脉冲地震记录,通过SDOF的体系动力时程分析,分析了速度脉冲型地震动分别缩放到不同目标谱加速度(Sa)、峰值加速度(PGA)、峰值速度(PGV)、峰值位移(PGD)水平时,SDOF体系非线性位移反应偏差随系统自振周期和强度折减系数变化的规律;通过对散点数据的对数线性回归确定了位移反应偏差的变化趋势,并比较了不同地面运动强度表征参数下位移偏差的稳定性。分析结果表明：位移偏差对地震动缩放系数、系统的基阶自振周期和系统的强度有一定的依赖性,合理选用缩放系数和地面运动强度表征参数能有效减小估算结构地震位移响应的偏差。     

Quantitative Error Assessment in Pattern Matching: Effects of Intensity Pattern Noise, Interpolation, Strain and Image Contrast on Motion Measurements

Abstract: Basic concepts in probability are employed to develop analytic formulae for both the expectation (bias) and variance for image motions obtained during subset‐based pattern matching. Specifically, the expectation and variance in image motions in the presence of uncorrelated Gaussian intensity noise for each pixel location are obtained by optimising a least squares intensity matching metric. Results for both 1D and 2D image analyses clearly quantify both the bias and the covariance matrix for image motion estimates as a function of: (a) interpolation method, (b) sub‐pixel motion, (c) intensity noise, (d) contrast, (e) level of uniaxial normal strain and (f) subset size. For 1D translations, excellent agreement is demonstrated between simulations, theoretical predictions and experimental measurements. The level of agreement confirms that the analytical formulae can be used to provide a priori estimates for the ‘quality’ of local, subset‐based measurements achievable with a given pattern. For 1D strain with linear interpolation, theoretical predictions are provided for the expectation and co‐variance matrix for the local displacement and strain parameters. For 2D translations with bi‐linear interpolation, theoretical predictions are provided for both the expectation and the co‐variance matrix for both displacement components. Theoretical results in both cases show that the expectations for the local parameters are biased and a function of: (a) the interpolation difference between the translated and reference images, (b) magnitude of white noise, (c) decimal part of the motion and (d) intensity pattern gradients. For 1D strain, the biases and the covariance matrix for both parameters are directly affected by the strain parameter p₁ as the deformed image is stretched by (1 + p₁). For 2D rigid body motion case, the covariance matrix for measured motions is shown to have coupling between the motions, demonstrating that the directions of maximum and minimum variability do not generally coincide with the x and y directions.     

Form-Profiling of Optics Using the Geometry Measuring Machine and the M-48 CMM at NIST

We are developing an instrument, the Geometry Measuring Machine (GEMM), to measure the profile errors of aspheric and free form optical surfaces, with measurement uncertainties near 1 nm. Using GEMM, an optical profile is reconstructed from local curvatures of a surface, which are measured at points on the optic’s surface. We will describe a prototype version of GEMM, its repeatability with time, a measurements registry practice, and the calibration practice needed to make nanometer resolution comparisons with other instruments. Over three months, the repeatability of GEMM is 3 nm rms, and is based on the constancy of the measured profile of an elliptical mirror with a radius of curvature of about 83 m. As a demonstration of GEMM’s capabilities for curvature measurement, profiles of that same mirror were measured with GEMM and the NIST Moore M-48 coordinate measuring machine. Although the methods are far different, two reconstructed profiles differ by 22 nm peak-to-valley, or 6 nm rms. This comparability clearly demonstrates that with appropriate calibration, our prototype of the GEMM can measure complex-shaped optics.     

基于在线测量的滚动直线导轨副精度保持性测试方法及试验研究

针对滚动直线导轨副精度保持性检测要求,提出了一种基于激光位移传感器测距的滚动直线导轨副运动精度在线检测方法。根据相对运动定理,该方法将4个激光位移传感器在线测量的滑块相对导轨基准的距离变化量转化成导轨平行度和滑块偏转角的变化量。通过滚动直线导轨副精度保持性测试方法,在线测量滚动直线导轨副在实际运行过程中的精度损失量,并与滚动直线导轨副的离线数据对比,有效验证了测试原理的可行性。最后,从多方面进行了误差分析。     

基于计算全息的无衍射光莫尔条纹三自由度测量方法研究

针对工作台运动误差,提出了一种基于计算全息的无衍射光莫尔条纹三自由度测量方法。通过液晶空间光调制器(SLM)生成无衍射光,利用两束无衍射光干涉生成莫尔条纹。设计了无衍射光莫尔条纹三自由度测量光路,建立了三自由度运动误差数学模型,并用几何分析法将三种运动误差(偏摆角、滚转角和俯仰角)进行分离。利用旋转台模拟不同大小的三自由度运动误差,带有误差信息的无衍射光和莫尔条纹图案分别由CCD1和CCD2接收。实验结果表明,通过光斑中心偏移量计算出的实际运动误差值接近理论值,测量误差不超过0.0104°,验证了无衍射光莫尔条纹三自由度测量系统的可行性与正确性。     

Analyzing Rotor Rotating Error by Using Fractal Theory

Based on the judgement of fractional Brownian motion, this paper analyzes the radial rotating error of a precision rotor. The results indicate that the rotating error motion of the precision rotor is characterized by basic fractional Brownian motions, i. e. randomicity, non-sequencity, and self-simulation insinuation to some extent. Also, this paper calculates the fractal box counting dimension of radial rotating error and judges that the rotor error motion is of stability, indicating that the motion range of the future track of the axes is relatively stable.     

共路激光干涉测量系统的研究

激光干涉测量系统在精密测量领域占有重要地位,它对温度变化、大气变化、激光波长变化、机械安装误差和外界振动等比较敏感,影响系统的测量精度和稳定性。针对此情况,该文提出一种新型的激光干涉光路,两光臂呈完全共路结构,使干涉条纹信号具有极强的抗干扰能力;对光路进行抗干扰分析和理论推导;构建位移测量系统,进行系统测试实验和误差分析。实验表明,本系统测量分辨力0.72nm,合成标准不确定度5．2nm（k=2）,运行速度0．56mm／s,量程0．01mm。     

光学三维测量中结构光栅投影系统的开发

为解决结构光三维测量系统中的光栅投影质量问题,提出并实现了以物理光栅为核心的结构光栅投影系统。该系统以现代光栅制造技术制造的精密光栅元件为核心,基于幻灯投影原理实现高质量的光栅条纹投影,利用步进电机带动高精密滚轴丝杆进行平移实现投影光栅的切换。实验结果表明,基于该系统实现的光学三维测量系统的可以达到1：100以上的对比度,具有较大的光强和良好的景深,同时能获得连续的强度分布及较好的正弦性,测量误差小于0．04mm,测量精度约为0．03mm,满足工业应用的要求。     

Simple Monte Carlo methods to estimate the spectra evaluation error in differential-optical-absorption spectroscopy

Differential-optical-absorption spectroscopy (DOAS) permits the sensitive measurement of concentrations of trace gases in the atmosphere. DOAS is a technique of well-defined accuracy; however, the calculation of a statistically sound measurement precision is still an unsolved problem. Usually one evaluates DOAS spectra by performing least-squares fits of reference absorption spectra to the measured atmospheric absorption spectra. Inasmuch as the absorbance from atmospheric trace gases is usually very weak, with optical densities in the range from 10(-5) to 10(-3), interference caused by the occurrence of nonreproducible spectral artifacts often determines the detection limit and the measurement precision. These spectral artifacts bias the least-squares fitting result in two respects. First, spectral artifacts to some extent are falsely interpreted as real absorption, and second, spectral artifacts add nonstatistical noise to spectral residuals, which results in a significant misestimation of the least-squares fitting error. We introduce two new approaches to investigate the evaluation errors of DOAS spectra accurately. The first method, residual inspection by cyclic displacement, estimates the effect of false interpretation of the artifact structures. The second method applies a statistical bootstrap algorithm to estimate properly the error of fitting, even in cases when the condition of random and independent scatter of the residual signal is not fulfilled. Evaluation of simulated atmospheric measurement spectra shows that a combination of the results of both methods yields a good estimate of the spectra evaluation error to within an uncertainty of ~10%.     

光弹调制式反射差分光谱仪的理论分析

反射差分光谱仪是一种测量灵敏度和精度较高的研究表面／界面的新型分析仪器，但微弱的反射差分信号易受到各种噪声的干扰．作者利用Jones表示法，对光弹调制式反射差分光谱仪构建了包含器件自身缺陷和安装误差的数学模型，通过确立误差源与测量结果的联系，分析出各误差源对测量结果的影响，特别是起偏器、光弹调制器和样品的安装误差以及位相调制误差，这些系统误差经过标定可得到补偿．     

On-sky performances of an optical phasing sensor based on a cylindrical lenslet array for segmented telescopes

New optical phasing sensor technologies have been studied with a test bench experiment, called Active Phasing Experiment, on-sky at the European Southern Observatory Very Large Telescope. One of the sensors was of the Shack-Hartmann type using cylindrical lenslets across the segment borders for the measurement of the phasing errors. With bright stars, the precision of the measurement of piston steps at a single border was better than 9 nm wavefront RMS, and the precision of the closed-loop correction of the piston errors of the segments across the whole mirror was better than 10 nm wavefront RMS. With dimmer stars of magnitude up to 14.5, precisions of the order of 22 nm wavefront RMS were obtained.