基于拉普拉斯方程的渐进多焦点眼用镜片轮廓线优化设计  

Contour Line Optimization Design of Progressive Addition Lenses Based on Laplace Equation

作　　者：张皓[1,2] 唐运海 吴泉英 陈晓翌[2] 

机构地区：[1]苏州科技大学数理学院江苏省微纳热流技术与能源应用重点实验室,江苏苏州215009 [2]苏州苏大明世光学股份有限公司江苏省企业研究生工作站,江苏苏州215028

出　　处：《激光与光电子学进展》2017年第11期352-357,共6页Laser & Optoelectronics Progress

基　　金：国家自然科学基金(61378056);江苏省"十三五"光学工程重点学科(20168765);江苏省高校优势学科建设工程(2015PAPD);江苏省研究生科研创新计划项目(KYLX15_1313);苏州科技大学研究生科研创新计划项目(SKCX16_059);苏州科技大学协同创新项目;苏州科技大学科研基金青年项目(XKQ201614);江苏省"六大人才高峰"第十二批资助项目(DZXX-026);苏州市重点产业技术创新项目(SYG201646)

摘　　要：设计渐进多焦点眼用镜片(PAL)的轮廓线u以得到近用区可视范围广且渐变通道长度变短的渐进多焦点眼用镜片。对渐进多焦点眼用镜片采取对称设计,设置子午线上u的变化曲线作为拉普拉斯方程的边界条件,并给出边界条件的具体形式。结合自然边界条件,运用分离变量法和傅里叶变换法求解拉普拉斯方程的解析解。设计实例表明:该设计方法不仅能使渐进多焦点眼用镜片拥有宽阔的近用区可视范围,还能使渐进多焦点眼用镜片的渐变通道变短。将设计数据进行实际加工,并对加工获得的渐进多焦点眼用镜片进行测试分析,结果表明设计与实际测试结果基本相符。The contour u of the progressive addition lens （PAL） surface is designed to obtain a PAL whose near visuaI area is obviously expanded and the progressive channel length is decreased. The PAL is designed symmetrically. The curve of u at meridian line is set as the boundary conditions of the Laplace equation, and the specific form of the boundary conditions is given. Combined with the natural boundary condition, the analytic solution of the Laplace equation is solved using the separation of variables method and the Fourier transform method. The design example shows that this design method not only expands the wide range of near zone visible area of PAL, but also shortens the progressive channel length. The design data are processed actually, and the PAL obtained is tested and analyzed. The results show that the design and the actual test results are basically consistent.

关 键 词：光学设计 渐进多焦点眼用镜片 拉普拉斯方程 光焦度 散光度 

分 类 号：TH74[机械工程—光学工程]