A Minimax Fitting Algorithm for Ultra-Precision Aspheric Surfaces

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