基于圆锥曲线参数方程的渐进多焦点镜片设计  

Design of Progressive Addition Lenses Based on Conic Parametric Equations

作　　者：詹小蝶 项华中[1] 王亚琼 张云进 张欣[1] 丁琦慧 郑泽希 王成[1,3] 张大伟[4,5] 陈家璧[5] 庄松林[4,5] Zhan Xiaodie;Xiang Huazhong;Wang Yaqiong;Zhang Yunjin;Zhang Xin;Ding Qihui;Zheng Zexi;Wang Cheng;Zhang Dawei;Chen Jiabi;Zhuang Songlint(Institute of Biomedical Optics and Optometry,School of Health Science and Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China;Shanghai Engineering Research Center of Interventional Medical Device,University of Shanghai for Science and Technology,Shanghai 200093,China;Engineering Research Center of Optical Instruments and Systems,Ministry of Education,University of Shanghai for Science and Technology,Shanghai 200093,China;School of Optical-Electrical and Computer Engineering,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学健康科学与工程学院生物医学光学与视光学研究所,上海200093 [2]上海理工大学机械工程学院,上海200093 [3]上海理工大学上海市介入医疗器械工程研究中心,上海200093 [4]上海理工大学教育部光学仪器与系统工程研究中心,上海200093 [5]上海理工大学光电信息与计算机工程学院,上海200093

出　　处：《光学学报》2023年第7期182-190,共9页Acta Optica Sinica

基　　金：国家自然科学基金(61605114,52206102)。

摘　　要：在渐进多焦点镜片(PAL)的直接设计法中,光焦度轮廓分布对镜片的光学性能至关重要。在子午线上同一曲率变化的基础上,引入不同圆锥曲线方程来描述镜片光焦度轮廓分布。利用椭圆、双曲线、抛物线和圆的定义设定镜片内表面子午线上每个点曲线的离心率以及开口大小。根据圆锥曲线分布情况加入偏移量,实现远近视区视配点可视区宽度调整。设计、仿真和加工了4块镜片。结果表明,基于双曲线方程计算得到的渐进多焦点镜片的周边最大像散大于1倍加光度(ADD),而基于椭圆方程、圆方程和抛物线方程计算得到的渐进多焦点镜片周边最大像散小于1倍ADD,光学性能更好。当定焦区较大时,基于椭圆方程设计得到的镜片定焦点可视区宽度最接近理论值;当定焦区较小时,基于圆方程设计得到的镜片定焦点可视区宽度最接近理论值。所提方法可为渐进多焦点镜片的优化设计提供新的方案。Objective Progressive addition lenses(PALs)not only solve the problem that the elderly need different focal powers for distance and near visions but also overcome the image jump of bifocal lenses owing to their continuously varying focal power along the meridian.Therefore,PAL design methods have a broad development prospect.PALs are mainly designed by a direct method and an indirect method.Although the indirect method offers convenient design,its prism is large when the focal power changes.The design of PALs by the direct method has the disadvantage that the maximum peripheral astigmatism exceeds two times the addition power(ADD)according to the Minkwitz theorem.Nevertheless,the direct method has relatively favorable advantages for the distance and near areas.The optimization of the direct method in China and abroad mainly focused on the changes in the focal power along the meridian,the optimization of the local average focal power,and the calculation equations for different surface heights.In contrast,how to obtain reasonable focal power profile distributions on the lenses has rarely been reported.In addition,a conic parametric equation can be changed into an equation satisfying the conditions of the focal power profile distribution along the meridian.Therefore,this paper proposes a method based on a conic parametric equation to reasonably distribute the focal power profile on the entire lens,achieve the design of PALs by the direct method,and ultimately reduce peripheral astigmatism.Methods On the basis of the principles of geometry and the direct method,the law of curvature change along the meridian of the lens is determined to satisfy the trigonometric function in this study,and the surface height equation is calculated as a spherical equation.Specifically,the function of the focal power profile distribution is solved by the circular parametric equation and also by the hyperbolic,parabolic,and elliptic equations.Then,the four sets of surface height data are used to simulate the focal power and astigmatism of

关 键 词：光学设计 直接设计法 渐进多焦点镜片 光焦度分布 离心率 像散 

分 类 号：TH74[机械工程—光学工程]