Optimal design of an optical lens
type: Item
instance of: scholarly article
title: Optimal design of an optical lens
zbMATH Open document ID: 0634.35063
DOI: 10.1007/BF00275875
author: A. Friedman
author: J. B. McLeod
published in: Archive for Rational Mechanics and Analysis
publication date: 1987-01-01T00:00:00Z
review text: One considers a lens which focuses all rays from a given source onto a given focal point. The nonlinear differential equations which define the lens are first derived by using the Fermat principle of least time and then the existence and the uniqueness of the solution is considered. To this end, by using a fixed point theorem, one first constructs a local solution in a vicinity of zero, and then this solution is analytically extended. This is a global study of a system of two nonlinear functional differential equations.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 78A05
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 4032236
zbMATH Keywords: optical lens
zbMATH Keywords: Fermat principle of least time
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: fixed point theorem
zbMATH Keywords: local solution
zbMATH Keywords: analytically extended
zbMATH Keywords: nonlinear functional differential equations
MaRDI profile type: Publication
cites work: Successive Approximation and Expansion Methods in the Numerical Design of Microwave Dielectric Lenses
cites work: On a Multiple Boundary Value Problem in Generalized Aplanatic Lens Design and its Solution in Series
cites work: On a numerical minimization problem for a new class of nonlinear partial differential equations arising in nonspherical geometrical optics and beamforming lenticular antennas
full work available at URL: https://doi.org/10.1007/bf00275875
OpenAlex ID: W1966389204
description: scientific article; zbMATH DE number 4032236