Measuring the profile of a convex aspherical surface by solving a bi-objective optimization problem

Juan Jaime Sanchez Escobar

doi:10.1117/1.OE.51.7.073607

17 July 2012 Measuring the profile of a convex aspherical surface by solving a bi-objective optimization problem

Juan Jaime Sanchez Escobar

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Optical Engineering, Vol. 51, Issue 7, 073607 (July 2012). https://doi.org/10.1117/1.OE.51.7.073607

Abstract

This paper describes a method based on bi-objective evolutionary algorithms to obtain the profile of a convex aspherical surface, which is defined by a set of synthetic points placed on an xyz coordinate system. The set of points to be analyzed is constructed considering the sources of measurement error in a coordinate measuring machine (CMM), such as machine, probe, and positioning errors. The proposed method is applied to solve a bi-objective optimization problem by minimizing two objective functions. By minimizing the first objective function the positioning error is removed from the coordinates of each affected point. Once the first goal is achieved, the second objective function is minimized to determine from the resulting data all parameters related to the test surface, such as paraxial radius of curvature, the conic constant and the deformation constants. Hence, this method can obtain the correct surface profile even when the positioning error tends to increase the CMM measurement error in the set of analyzed points. The bi-objective evolutionary algorithm (BEA) was tested against a single-objective evolutionary algorithm, and illustrative numerical examples demonstrate that the BEA performs better.

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Juan Jaime Sanchez Escobar "Measuring the profile of a convex aspherical surface by solving a bi-objective optimization problem," Optical Engineering 51(7), 073607 (17 July 2012). https://doi.org/10.1117/1.OE.51.7.073607

Published: 17 July 2012

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KEYWORDS

Evolutionary algorithms

Error analysis

Optimization (mathematics)

Optical engineering

Numerical analysis

Inspection

Computer programming

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