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A Minimax Fitting Algorithm for Ultra-Precision Aspheric Surfaces

Zhang, Xiangchao, Jiang, Xiang and Scott, Paul J. (2011) A Minimax Fitting Algorithm for Ultra-Precision Aspheric Surfaces. In: The 13th International Conference on Metrology and Properties of Engineering Surfaces, 12-15 April 2011, National Physical Laboratory, Teddington, UK. (Unpublished)

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Abstract

Aspheric lenses show significant superiority over traditional spherical ones. The peak-to-valley form deviation is an
important criterion for surface qualities of optical lenses. The peak-to-valley errors obtained using traditional methods
are usually greater than the actual values, as a consequence causing unnecessary rejections.
In this paper the form errors of aspheric surfaces are evaluated in the sense of minimum zone, i.e. to directly minimize
the peak-to-valley deviation from the data points to the nominal surface. A powerful heuristic optimization algorithm,
called differential evolution (DE) is adopted. The control parameters are obtained by meta-optimization. Normally the number of data points is very large, which makes the optimization program unacceptably slow. To improve the efficiency, alpha shapes are employed to decrease the number of data points involved in the DE optimization. Finally numerical examples are presented to validate this minimum zone evaluation method and compare its results
with other algorithms.

Item Type: Conference or Workshop Item (Paper)
Subjects: T Technology > TJ Mechanical engineering and machinery
Schools: School of Computing and Engineering
School of Computing and Engineering > Centre for Precision Technologies
School of Computing and Engineering > Centre for Precision Technologies > Surface Metrology Group
School of Computing and Engineering > Systems Engineering Research Group
Related URLs:
Depositing User: Xianchao Zhang
Date Deposited: 27 Jan 2011 10:39
Last Modified: 24 Aug 2015 01:33
URI: http://eprints.hud.ac.uk/id/eprint/9417

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