摘要
采用二次支撑面法(SQM)设计了一种均匀方斑透镜,建立了Zernike正交多项式曲面插值重构算法。在初始基面上对每一个子面选择映射守恒点,并按照相邻关系划分9点系统。针对9点系统,利用多项式的低阶项建立了线性方程组,并根据其唯一解构造了部分曲面。将所有部分曲面拼接,得到了完整的连续光滑的优化曲面。该算法可在一定程度上简化SQM初始基面的后期优化,得到良好的均匀方斑透镜设计效果。
A uniform square spot lens is designed by the supporting quadratic method （SQM） and an algorithm for the interpolation and reconstruction of the curved surfaces based on the Zernike polynomials is developed. The mapping conservation points are chosen on the initial base surface for each sub-surface and the 9-point system is partitioned according to the adjacency relationship. As for this 9-point system, the linear equation group is established by using the lower order terms included in the polynomials and the partial curved surface is constructed with its unique solution. All the partial curved surfaces are spliced together and thus a complete and continuously smooth curved surface is obtained. This algorithm can simplify the later optimization of the initial base surfaces in SQM to a certain extent, which can ensure a good design effect of the uniform square spot lens.
作者
张航
陆建东
刘锐
马佩服
Zhang Hang, Lu Jiandong, Liu Rui, Ma Peifu(Institute of Optoelectronics Intelligent and Technology, College of Science, Zhejiang University of Technology, Hangzhou, Zhejiang 310000, China)
出处
《激光与光电子学进展》
CSCD
北大核心
2018年第10期293-298,共6页
Laser & Optoelectronics Progress
基金
国家自然科学基金(61474100)
关键词
光学设计
非成像光学
曲面光滑优化
ZERNIKE多项式
二次支撑面法
optical design
non-imaging optics
smooth optimization of curved surface
Zernike polynomials
supporting quadratic method
