Chebyshev Fitting of Complex Surfaces for Precision Metrology

Xiangqian Jiang, Xiangchao Zhang, Hao Zhang, Xiaoying He, Min Xu

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The form qualities of precision components are essential for their functionalities. The Peakto- Valley parameters are widely adopted to assess the form accuracies of optical components. The commonly used least squares method is prone to over-estimation, thus the Chebyshev fitting should in turn be implemented. In this paper the original minimax optimisation problem is converted into an unconstrained differentiable minimisation problem by the exponential penalty functions. The fitting accuracy and numerical stability are balanced by employing an active-set strategy and adjusting the configuration parameters adaptively. Finally some benchmark data sets are applied to demonstrate the validity and efficiency of this method.

Original languageEnglish
Pages (from-to)3720-3724
Number of pages5
JournalMeasurement: Journal of the International Measurement Confederation
Volume46
Issue number9
DOIs
Publication statusPublished - Nov 2013

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metrology
penalty function
numerical stability
optimization
Exponential functions
Convergence of numerical methods
exponential functions
least squares method
valleys
adjusting
configurations

Cite this

Jiang, Xiangqian ; Zhang, Xiangchao ; Zhang, Hao ; He, Xiaoying ; Xu, Min. / Chebyshev Fitting of Complex Surfaces for Precision Metrology. In: Measurement: Journal of the International Measurement Confederation. 2013 ; Vol. 46, No. 9. pp. 3720-3724.
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Chebyshev Fitting of Complex Surfaces for Precision Metrology. / Jiang, Xiangqian; Zhang, Xiangchao; Zhang, Hao; He, Xiaoying; Xu, Min.

In: Measurement: Journal of the International Measurement Confederation, Vol. 46, No. 9, 11.2013, p. 3720-3724.

Research output: Contribution to journalArticle

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