The Mathematical Theory of Multifocal Lenses(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)  

作　　者：Jacob RUBINSTEIN 

机构地区：[1]department of mathematics,Technion,Haifa 32000,Israel

出　　处：《Chinese Annals of Mathematics,Series B》2017年第2期647-660,共14页数学年刊（B辑英文版）

基　　金：supported by a grant from the ISF

摘　　要：This paper presents the fundamental optical concepts of designing multifocal ophthalmic lenses and the mathematical methods associated with them. In particular, it is shown that the design methodology is heavily based on differential geometric ideas such as Willmore surfaces. A key role is played by Hamilton's eikonal functions. It is shown that these functions capture all the information on the local blur and distortion created by the lenses. Along the way, formulas for computing the eikonal functions are derived. Finally,the author lists a few intriguing mathematical problems and novel concepts in optics as future projects.This paper presents the fundamental optical concepts of designing multifocal ophthalmic lenses and the mathematical methods associated with them. In particular, it is shown that the design methodology is heavily based on differential geometric ideas such as Willmore surfaces. A key role is played by Hamilton's eikonal functions. It is shown that these functions capture all the information on the local blur and distortion created by the lenses. Along the way, formulas for computing the eikonal functions are derived. Finally,the author lists a few intriguing mathematical problems and novel concepts in optics as future projects.

关 键 词：Optical design  Differential geometry  EIKONAL functions Multifocal lenses 

分 类 号：O186.11[理学—数学] O43[理学—基础数学]