CHEBYSHEV FITTING OF COMPLEX SURFACES FOR PRECISION METROLOGY

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

Abstract

The form qualities of precision components are essential for their functionalities. The Peak-to-Valley parameters are widely adopted to assess the form accuracy 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 optimization problem is converted into an unconstrained differentiable minimization problem by 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.

Keywords

form error, minimum zone, minimax problem, exponential penalty function, Chebyshev fitting

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IMEKO-WC-2012-JS-O3.pdf

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