Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors

Scanning topography measurements using systems of coupled distance sensors suffer from the presence of scanning stage and systematic sensor errors. While scanning stage errors can be estimated for suitably-designed sensor systems, it is usually not possible to simultaneously estimate both scanning stage and systematic sensor errors. Additional angular scanning stage measurements can solve this problem, and potentials and limitations of such a proceeding will be assessed.It is shown that perfect topography reconstruction can be achieved in the presence of systematic sensor and certain scanning stage errors provided that the measurements are noise-free and no further systematic errors emerge. In general, the topography is reconstructed by the application of least-squares, and the uncertainty associated with the reconstructed topography is derived. Resulting topography accuracies are evaluated for different noise levels of the distance sensor and angular scanning stage measurements, and practical considerations are discussed. The gain in accuracy due to accounting for scanning stage and systematic sensor errors can be large, and high accuracies can be reached.     

星点质心亚像元定位的高精度误差补偿法

在CCD星敏感器设计过程中,星点坐标的提取精度不仅影响星图识别的正确性,也直接影响星敏感器的最终姿态输出精度。本文通过分析传统质心法亚像元提取算法误差模型,证明该模型存在系统误差和随机误差。针对系统误差,提出了用最小二乘拟合法来估计质心位置和系统误差大小的对应关系,利用这个关系对系统误差进行补偿;针对随机误差,提出用边缘阈值法和星图整体相消法来消除。本文还分析了CCD成像数学模型,星光成像的能量分布近似服从二维高斯分布,星点高斯分布弥散半径不同,用于误差补偿的曲线方程也不一样,根据不同的高斯弥散半径,设计了误差补偿模板,用于补偿质心法的系统误差。实验表明,采用误差补偿模板,可以将质心法精度从1/20pixel提高到1/200pix-el,满足了星敏感器高精度星点质心提取的要求。     

Model error correction from truncated modal flexibility sensitivity and generic parameters. II: experimental verification

This paper reports on the experimental verification of the truncated modal flexibility sensitivity based model updating method proposed in the companion paper (Wu and Law, Mechanical System and Signal Processing, doi: 10.1016/S0888-3270 (03) 00094-3) with real measurements on a three-dimensional cantilever frame structure in the laboratory. Two schemes of model error correction are presented to improve the initial inaccurate finite-element model of the structure. The first procedure updates the initial model in two stages. The systematic model errors are firstly updated using macrogeneric parameters. The local errors are then improved using elemental eigenparameters. The second procedure improves both the systematic and local errors without a measured baseline reference simultaneously. The first procedure can differentiate the types of errors in the structure while the latter procedure removes the usual requirement in most existing model based updating methods that an accurate finite -element model should be used as reference.     

Method of compensation for systematic errors in goniometric systems

A method based on invariants of in-plane motion of an object is developed for compensation of systematic errors of measurements in goniometric systems. Exact equations are derived for systematic errors of measurement of the object latitude with ignored fluctuating errors of measurement. Analytical expressions are also derived to calculate the standard deviation of the error in estimating systematic errors being taken into account, which allow us to impose grounded requirements to tactical and technical characteristics of goniometric systems designed for observation of various objects.     

Detection and registration of ion clots in laser time-of-flight mass spectrometers

A number of factors influencing the measurement errors of analytic signals detected with secondary electron multipliers (SEMs) and registered with fast ADCs are analyzed. Such signals are generated in laser time-of-flight mass spectrometry at the stage of ion detection and recording of mass spectra. In particular, the effect of statistical factors and sources of systematic errors during both measurements of isotope ratios and elemental analysis is considered. Such errors as the statistics of formation of ion clots, the limited range of ADC records, discrimination during detection of ions of different masses, and others are considered. It is shown that, without taking into account the features of operation of SEMs and ADCs, both the statistical and systematic errors of measuring isotope ratios may reach several percent. The proposed operating modes of the detector, with allowance for its features, the design of the recording system, and use of formulas for calculating and correcting errors, allow their reduction to ～0.10–0.01%     

Calibration method to characterize the accuracy of phase-shifting point diffraction interferometer

Characterization of measurement accuracy of the phase-shifting point diffraction interferometer (PS∕PDI) is usually performed by two-pinhole null test. In this procedure, the geometrical coma and detector tilt astigmatism systematic errors are almost one or two magnitude higher than the desired accuracy of PS∕PDI. These errors must be accurately removed from the null test result to achieve high accuracy. Published calibration methods, which can remove the geometrical coma error successfully, have some limitations in calibrating the astigmatism error. In this paper, we propose a method to simultaneously calibrate the geometrical coma and detector tilt astigmatism errors in PS∕PDI null test. Based on the measurement results obtained from two pinhole pairs in orthogonal directions, the method utilizes the orthogonal and rotational symmetry properties of Zernike polynomials over unit circle to calculate the systematic errors introduced in null test of PS∕PDI. The experiment using PS∕PDI operated at visible light is performed to verify the method. The results show that the method is effective in isolating the systematic errors of PS∕PDI and the measurement accuracy of the calibrated PS∕PDI is 0.0088λ rms (λ = 632.8 nm).     

Modified single point calibration with improved accuracy in direct sensor-to-microcontroller interface

A simple sensor-to-microcontroller interface with improved accuracy is described. The sensor interface is based on single point calibration and uses one additional resistor to reduce the overall systematic errors. The errors are reduced by a systematical approach to control the nonlinearity of the transfer characteristic in such way that the system acts as it uses a two point calibration. In the paper, a theoretical model for implementation of the modified single point calibration technique is presented. When analyzing the measurement range typical for PT1000 temperature sensor, the systematic errors reduce by than a factor of two depending on the width of the measurement range. Different theoretical and experimental aspects for implementation of the proposed calibration technique are considered, as well as: process, voltage, temperature variation and power consumption.     

Error Analysis of Indirect Broadband Monitoring of Multilayer Optical Coatings using Computer Simulations

Results of studying the errors of indirect monitoring by means of computer simulations are reported. The monitoring method is based on measuring spectra of reflection from additional monitoring substrates in a wide spectral range. Special software (Deposition Control Simulator) is developed, which allows one to estimate the influence of the monitoring system parameters (noise of the photodetector array, operating spectral range of the spectrometer and errors of its calibration in terms of wavelengths, drift of the radiation source intensity, and errors in the refractive index of deposited materials) on the random and systematic errors of deposited layer thickness measurements. The direct and inverse problems of multilayer coatings are solved using the OptiReOpt library. Curves of the random and systematic errors of measurements of the deposited layer thickness as functions of the layer thickness are presented for various values of the system parameters. Recommendations are given on using the indirect monitoring method for the purpose of reducing the layer thickness measurement error.     

复杂曲面零件在线检测与误差补偿方法

复杂曲面零件的高精度加工与精密检测一直是数字化制造领域的研究热点。为提高复杂曲面零件的加工精度、检测精度,提出一种集数控机床在线检测、加工误差分解与补偿加工为一体的集成化方法。介绍集成化在线检测方法及补偿系统的基本原理,分析数控加工后曲面零件测点数据的误差组成,提出一种基于空间统计分析的加工误差分解方法,在建立基于B样条曲面的确定性曲面回归模型的基础上,对回归模型残差进行空间独立性分析,分解出系统误差和随机误差,进而通过数控代码的修改,实现零件加工过程的系统误差补偿。列举一个曲面零件的加工与检测实例,进行方法有效性验证。通过加工工件的在线检测、误差分解、代码修改及补偿加工等环节,实例零件的加工精度有了大幅提高,而该系统的检测精度也通过与三坐标测量机(Coordinate measuring machine, CMM)检验结果的对比,得到了有效验证。     

重构曲面精度评价方法研究

随着计算机技术、测量技术、曲面重构技术的飞速发展,基于功能表面的高精度逆向工程已成为可能,这对重构曲面的精度控制技术提出了更为苛刻的要求。现有方法一般是对误差产生原因进行定性分析,很不完善。本文首先通过精度设计,对逆向工程产生的各种误差进行合理分配;并首次引入曲面轮廓度的概念,在此基础上定量地对曲面重构误差进行了快速计算和有效分析;本文最后给出了增压器叶轮各个功能曲面的重构精度评价效果图,效果图很好地揭示了测量点云对于重构曲面的偏差值以及数据点云在各个误差带中的分布情况。     

一种测试多因素引起的系统误差的新方法

本文提出了一种测试多种因素引起的系统误差的新方法。建立了模拟和数字混合电路的系统误差的数学模型,给出了相应的数据处理方法。数据处理考虑了试验点选择和模糊群消除等问题。本文还给出了两个实用和具有复杂模型的应用实例。     

Geometrical error compensation of machines with significant random errors

In this paper, we present a new statistical approach towards soft geometrical error compensation of machines with significant errors. The approach, based on an analysis of the probability of the random error recurring, can reduce the adverse influence of random errors on the compensation of systematic errors. The proposed methodology is made up of three steps. First, error classes are defined from the error bands obtained from calibration. Second, the probability of the magnitude of random error belonging to each of these classes is computed based on the density of the data set within the class. Based on these probabilities, the most probable systematic part of the error measurement can be statistically deduced. Finally, the geometrical error compensation is carried out based on this value. Experimental results are provided for the linear error compensation of a single-axis piezo-ceramic motion system.     

Proposition for a Volumetric Error Model Considering Backlash in Machine Tools

This paper proposes a new scheme for evaluating the machine tool volumetric error model including the backlash error. The effects of backlash errors are assessed by experiments, conducted on a three-axis vertical-type machining centre. The assessment was taken for 18 error components out of the 21 geometric errors of a machine tool. It was shown that the backlash error of a machine tool is one of the systematic errors. Some important characteristics of the backlash error were identified; that is, the backlash error is a function of position, it decreases as the feedrate increases, and its size and shape vary according to the machine structure.     

Modelling of errors in measurement

The purpose of this paper is to show different standpoints concerning the modelling and calculation of measurement errors, to discover reasons for topical metrological problems in error analysis, to mention selected confidence limits of measurement errors which have been proved and to recommeend future activities to the unified application of proved error models as well as the concentration of investigations on systematic and residual errors which are insufficiently mastered today.     

基于ICA的动态测量误差分解重构方法

提出了利用独立成分分析（ICA）方法对动态测量误差进行分解重构的方法。详细介绍了利用ICA方法进行误差分解重构的基本算法,利用三坐标测量机和双频激光干涉仪设计了动态测量误差测量装置,并进行了实验。分别利用自适应滤波、小波分析和ICA方法对动态误差数据进行处理,分离重构线性变化、周期变化的系统误差和动态随机误差。研究结果表明,要精确分析动态测量误差和辨别误差组成成分,必须充分应用测量得到的误差总体样本进行分析。与自适应滤波、小波分析两种方法相比,利用ICA方法可以更有效地精确分离重构线性变化、周期变化的系统误差和动态随机误差。     

Volumetric error modelling of a stereo vision system for error correction in photogrammetric three-dimensional coordinate metrology

Optical three-dimensional coordinate measurement using stereo vision has systematic errors that affect measurement quality. This paper presents a scheme for measuring, modelling and correcting these errors. The position and orientation of a linear stage are measured with a laser interferometer while a stereo vision system tracks target points on the moving stage. With reference to the higher accuracy laser interferometer measurement, the displacement errors of the tracked points are evaluated. Regression using a neural network is used to generate a volumetric error model from the evaluated displacement errors. The regression model is shown to outperform other interpolation methods. The volumetric error model is validated by correcting the three-dimensional coordinates of the point cloud from a photogrammetry instrument that uses the stereo vision system. The corrected points from the measurement of a calibrated spherical artefact are shown to have size and form errors of less than 50 μm and 110 μm respectively. A reduction of up to 30% in the magnitude of the probing size error is observed after error correction is applied.     

System of four distance sensors for high-accuracy measurement of topography

A novel sensor system consisting of four distance sensors is proposed for the scanning measurement of topography. The system achieves high accuracy and allows high lateral resolution. The configuration of the system can be chosen such that it guarantees perfect reconstruction of the topography in the presence of offset and pitch errors of the scan system provided the sensor measurements are error-free. Moreover, a favorable propagation of the random and systematic errors of the sensor measurements is achieved. The error influences are investigated and the sensor system is compared to a previously proposed three-sensor system by analyzing simulated data.     

Synthesis of gradient algorithms with the minimum systematic error for estimating directional fields

A method is proposed for constructing noise-resistant mask differentiating filters minimizing systematic errors in estimating directional fields by a gradient algorithm. A comparative analysis of the accuracy of gradient algorithms was performed by computer modeling It is shown that a decrease in the systematic error leads to a considerable increase in the accuracy of directional field estimation     

Achievement of accuracy by error compensation of large CMMs

In this paper we will discuss the limit of the possible compensation for the systematic geometrical errors in large coordinate measurement machines (CMMs). One of the main problems is that the methods of measuring the errors produce errors themselves, which statistically add up to a total uncertainty of the compensation. The standard methods of error compensation cannot improve the measuring uncertainty of the machine beyond this limit, and this limit can only be reached if the reproducibility of the machine (ie the statistical error) is improved.     

Measurement accuracy in X-ray computed tomography metrology: Toward a systematic analysis of interference effects in tomographic imaging

In this paper an investigation of interference effects leading to limitations of metrological performance of X-ray computed tomography (CT) used as a coordinate measuring technique is presented. Using reconstruction data, image quality metrics, and calculations of artifact formation, a deeper understanding and explanation of the physical and technical limitations of CT used in dimensional metrology is given. This is demonstrated in a case study using a simple hollow cylinder made of steel as a test object and calibration measurements from a tactile coordinate measuring machine (CMM). Two different threshold determination strategies for surface computation are applied. Within the study it is also shown that CT image properties, threshold determination strategies, and systematic and random measurement errors must have a definite correlation. As a conclusion it is recommended to focus more strongly on the correlation of local CT image quality and data evaluation operations in order to reduce systematic errors in surface computation and to increase repeatability of dimensional CT measurements.