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Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part I: Models, Algorithms Development and Validation

1
Department of Mechanical Engineering, Chemical and Industrial Design, ETS of Engineering and Industrial Design, Technical University of Madrid, 28012 Madrid, Spain
2
Department of Precision Mechanical Engineering, Shanghai University. No.333, Nanchen Rd., Shanghai 200444, China
*
Author to whom correspondence should be addressed.
Electronics 2019, 8(7), 733; https://doi.org/10.3390/electronics8070733
Received: 2 June 2019 / Revised: 25 June 2019 / Accepted: 26 June 2019 / Published: 27 June 2019
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Abstract

This work presents a method for characterizing and correcting the geometric errors of the movement of the lateral stage of Imaging Confocal Microscope (CM) in extended topography measurement. For an extended topography measurement, a defined number of 2D images are taken and stitched by correlation methods. Inaccuracies due to linear displacement, vertical and horizontal straightness errors, angular errors, and squareness errors based on the assumption of the rigid body kinematics are described. A mathematical model for the scale calibration of the X- and Y- coordinates is derived according to the system kinematics, the axis chain vector of CM, and the geometric error functions and their approximations by Legendre polynomials. The correction coefficients of the kinematic modelling are determined by the measured and certified data of a dot grid target standard artefact. To process the measurement data, algorithms for data partitions, fittings of cylinder centers, and determinations of coefficients are developed and validated. During which methods such as form removal, K-means clustering, linear and non-linear Least Squares are implemented. Results of the correction coefficients are presented in Part II based on the experimental studies. The mean residual reduces 29.6% after the correction of the lateral stage errors. View Full-Text
Keywords: geometric errors correction; kinematic modelling; lateral stage errors; Imaging Confocal Microscope; K-means clustering; data partition; Least Squares method geometric errors correction; kinematic modelling; lateral stage errors; Imaging Confocal Microscope; K-means clustering; data partition; Least Squares method
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Wang, C.; Gómez, E.; Yu, Y. Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part I: Models, Algorithms Development and Validation. Electronics 2019, 8, 733.

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