The Near Field Refractor
Analysis of PDEs
2015-06-16 v1 Optics
Abstract
We present an abstract method in the setting of compact metric spaces which is applied to solve a number of problems in geometric optics. In particular, we solve the one source near field refraction problem. That is, we construct surfaces separating two homogenous media with different refractive indices that refract radiation emanating from the origin into a target domain contained in an n-1 dimensional hypersurface. The input and output energy are prescribed. This implies the existence of lenses focusing radiation in a prescribed manner.
Cite
@article{arxiv.1307.5709,
title = {The Near Field Refractor},
author = {Cristian E. Gutierrez and Qingbo Huang},
journal= {arXiv preprint arXiv:1307.5709},
year = {2015}
}
Comments
39 pages, 4 figures, Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire (to appear). Geometric optics, lens design, measure equations, Descartes ovals, Monge-Ampere type equations