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The mathematical theory of multifocal lenses

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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.

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Acknowledgments

This paper is dedicated to Professor Haim Brezis for his 70th birthday. The author thanks his collaborators GershonWolansky, Dan Katzman and Sergio Barbero. He is pleased that Haim himself is using multifocal lenses that were designed using the principles explained above.

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Authors and Affiliations

  1. Department of Mathematics, Technion, Haifa, 32000, Israel

    Jacob Rubinstein

Authors
  1. Jacob Rubinstein
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Correspondence to Jacob Rubinstein.

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Dedicated to Professor Haim Brezis on the occasion of his 70th birthday

This work was supported by a grant from the ISF.

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Rubinstein, J. The mathematical theory of multifocal lenses. Chin. Ann. Math. Ser. B 38, 647–660 (2017). https://doi.org/10.1007/s11401-017-1088-3

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  • DOI: https://doi.org/10.1007/s11401-017-1088-3

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