Geometric limits to geometric optical imaging with infinite, planar, non-absorbing sheets

TL;DR

This paper investigates the fundamental geometric constraints of infinite, planar, non-absorbing sheets in optical imaging, revealing limitations and equivalences to various lens systems and negative refraction scenarios.

Contribution

It provides a comprehensive geometric analysis of how such sheets can image space, establishing their equivalence to thin lenses and other optical elements.

Findings

Limitations on space mapping imposed by geometry.

Equivalence of these sheets to thin lenses with different focal lengths.

Connections to negative refraction and lenslet arrays.

Abstract

New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar, non-absorbing sheet that images the entire three-dimensional space. The most general case of such a sheet is equivalent to a thin lens with different object- and image-sided focal lengths. Special cases include ordinary thin lenses, confocal lenslet arrays, and negative refraction with n_2 = -n_1.