KEYWORDS: Statistical modeling, Monte Carlo methods, Statistical analysis, Measurement uncertainty, Data modeling, Matrices, Linear regression, Engineering, Data acquisition
In response to the problem of solving multiple linear regression measurement model in the case of small sample calibration test data, a method of parameter estimation for regression coefficient of measurement model based on Monte Carlo sampling idea and uncertainty evaluation theory is presented. In detail, the general form of multidimensional linear regression measurement model is introduced, and the principle and evaluation process based on Monte Carlo method (MCM) of solving the estimates and their standard deviations of the regression coefficient in measurement model are put forward. The optimization scheme for Monte Carlo sampling is further given, which can be adopted to ensure the reliability of parameter estimation under small sample condition. Finally, the feasibility and practicability of the proposed method are verified by a simulation example. In the case of small sample test data, this method can not only estimate the estimated values of each parameter in the multidimensional measurement model, but also evaluate the corresponding standard deviation. It can obtain a more scientific, reasonable and accurate measurement model, which provides a reliable model guarantee for practical measurement and evaluation applications.
KEYWORDS: Distortion, Fiber Bragg gratings, 3D metrology, Image processing, Signal processing, Edge detection, Detection and tracking algorithms, 3D image processing, Reflection, Data acquisition
In order to achieve the measurement of three-dimensional (3D) surface topography of microdevices, this study uses high-sensitivity fiber Bragg grating (FBG) as the sensitive element of the contact measurement probe system and studies the device surface microtopography scanning measurement system based on FBG probe, which is used for the measurement and characterization of micrometer-sized microdevices, with high measurement resolution and low cost. In this study, a low-priced micro-displacement output strategy combining macro- and micro-motion was adopted, and an improved image horizontal distortion correction algorithm was proposed to correct the horizontal distortion of the image. Through the performance experiments of the measurement system, a micro-displacement measurement sensitivity of 12.21 mV/nm and a measurement resolution of 0.46 nm are obtained. The measurement results of bar structure step standard specimens show that the system can distinguish the step height of 200 nm by contact scanning measurement, solve the problem of horizontal distortion in the global distribution of the image, and realize the 3D measurement and characterization of micron-scale surface topography.
This paper mainly focuses on the sphericity evaluation based on the minimum zone sphere (MZS) method in the Cartesian coordinate system. An asymptotic search method is proposed to search for the homocentric centre of MZS model and calculate the sphericity error. The search process of the proposed method consists two parts: geometric area search is implemented to obtain a quasi-MZS centre (close to the MZS centre) and 3+2 and 2+3 mathematical models dominating the minimum zone sphere are solved to obtain the MZS centre. The geometric area search is employed to fast convergence to the quasi-MZS centre by constructing a search sphere model. Some characteristic points distributed on the search sphere are selected to determine the search direction. A threshold is set to terminate the search process and the quasi-MZS centre is determined as a result. The quasi-MZS centre is employed as a reference centre to solve the 3+2 and 2+3 models to determine the MZS centre. According to the minimum conditions, the mathematical models are established to solve the two models. Then the judgment is implemented to ensure all the measured points are enveloped between the two homocentric spheres. As a result, the centre of two homocentric spheres is the MZS centre. The MZS sphericity error can be obtained as well. To verify the performance of the proposed method, simulation experiments and comparison experiments are implemented. The results demonstrated that the proposed method is effective, reliable and meet the requirement of sphericity evaluation.
Probe tip of the Micro-coordinate Measuring Machine (Micro-CMM) is a microsphere with diameter of several hundred microns, and its sphericity is generally controlled at tens to hundreds of nanometers. Due to the small size and high precision requirement, the measurement of the microsphere morphology is difficult. In this paper, a measurement method for probe microsphere of Micro-CMM is proposed based on two SPM (Scanning Probe Microscope) probes, and a ruby microsphere of a Renishaw commercial CMM stylus is measured by the proposed method. In the experiment, the repeatability error of a maximum section profile is test, and the repeatability error is 41 nm (peak-to-peak value). Two perpendicular maximum section profiles are measured, and the corresponding diameter and roundness are estimated by the least squares method.
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