The Near Field Refractor

TL;DR

This paper introduces an abstract mathematical method for designing optical lenses that precisely control radiation refraction from a point source into a target domain, with applications in geometric optics.

Contribution

It develops a novel abstract framework in metric spaces to solve the near field refraction problem, enabling the construction of lenses with prescribed focusing properties.

Findings

Constructed surfaces that refract radiation into a target domain.

Proved the existence of lenses with prescribed energy distribution.

Applied the method to solve near field refraction problems in geometric 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.