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基于Zernike多项式光滑优化的均匀方斑透镜设计

Design of Uniform Square Spot Lens Based on Smooth Optimization of Zernike Polynomials

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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。

Abstract

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.

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中图分类号:O435

DOI:10.3788/lop55.102202

所属栏目:光学设计与制造

基金项目:国家自然科学基金(61474100)

收稿日期:2018-04-11

修改稿日期:2018-05-06

网络出版日期:2018-05-23

作者单位    点击查看

张航:浙江工业大学理学院光电子智能化技术研究所, 浙江 杭州 310000
陆建东:浙江工业大学理学院光电子智能化技术研究所, 浙江 杭州 310000
刘锐:浙江工业大学理学院光电子智能化技术研究所, 浙江 杭州 310000
马佩服:浙江工业大学理学院光电子智能化技术研究所, 浙江 杭州 310000

联系人作者:陆建东(lujdzjut@163.com); 张航(physzhang@zjut.edu.cn);

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引用该论文

Zhang Hang,Lu Jiandong,Liu Rui,Ma Peifu. Design of Uniform Square Spot Lens Based on Smooth Optimization of Zernike Polynomials[J]. Laser & Optoelectronics Progress, 2018, 55(10): 102202

张航,陆建东,刘锐,马佩服. 基于Zernike多项式光滑优化的均匀方斑透镜设计[J]. 激光与光电子学进展, 2018, 55(10): 102202

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