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| The Mathematical Theory of Multifocal Lenses |
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Citation： |
Jacob RUBINSTEIN.The Mathematical Theory of Multifocal Lenses[J].Chinese Annals of Mathematics B,2017,38(2):647~660 |
| Page view： 797
Net amount： 425 |
Authors： |
Jacob RUBINSTEIN; |
Foundation： |
This work was supported by a grant from the ISF. |
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| Abstract： |
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. |
Keywords： |
Optical design, Differential geometry, Eikonal functions, Multifocallenses |
Classification： |
35J30, 35J50, 78A05 |
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