三次样条插值优化渐进多焦点镜片非对称设计

打开文本图片集

中图分类号：TH74 文献标识码：Adoi：10. 37188/OPE. 20253306. 0839 CSTR：32169. 14. OPE. 20253306. 0839

Optimization of asymmetric progressive addition lens design with cubic spline interpolation

XIANG Huazhong1*，WU Keting1，MA Lefei1，MEI Zhixian1，XIE Min1，FAN Jun1， ZHENG Zexi2，ZHANG Dawei2，ZHUANG Songlin2

（1. School of Health Science and Engineering，University of Shanghai for Science and Technology， Shanghai ，China；

2. School of Optical-Eletrical and Computer Engineering，University of Shanghai for Science and Technology，Shanghai ，China） * Corresponding author，E-mail：xiang3845242@usst. edu. cn

Abstract：In order to improve and optimize the traditional symmetrical design of progressive addition lens⁃ es，there were problems such as blind angle and distortion of the field of view. Two offset methods based on a rotation translation algorithm and an interpolation algorithm were proposed. Firstly，the binocular convergence phenomenon of the human eye was analyzed，and two asymmetric design methods were intro⁃ duced：rotational translation offset and interpolation shift. Secondly，an offset function was set，and the in⁃ terpolation function through the initial offset point was constructed by using Lagrange interpolation，New ⁃ ton interpolation，and cubic spline interpolation. Thirdly，by setting two boundary conditions of two sets of offset point values and cubic spline interpolation values on two sets of meridians，three interpolation al⁃ gorithms were analyzed and compared. Finally，the optical power and astigmatism distribution were given through simulation and actual processing. The experimental results show that the cubic spline interpolation in the interpolation algorithm is smoother and has no inflection point，the astigmatism gradient of the two asymmetric design methods in the near and far areas has achieved a smooth transition，the maximum astig⁃ matism is reduced from 1. 125 times the added luminosity to 0. 875 times the added luminosity，and the off⁃ set angle is between 20∘ and 23∘ ，which basically meets the characteristics of automatic convergence of the human eye and improves the problems of distortion and distortion of human vision.

Key words：optical design；progressive addition lenses；asymmetrical design；cubic spline interpolation

1 引 言

随着社会老龄化加剧，老花眼问题日益突出［1］。（剩余12275字）