Abstract

The gradient-index Maxwell fish-eye lens is an example of an absolute instrument, meaning that it stigmatically images a 3-D domain. An additional characteristic of such a system is that the image is an accurate geometrical projection of the object, i.e., there is no distortion. The ray paths inside this gradient-index lens are always sections of circles. A much more common situation is that of an aplanatic surface, which only perfectly images one spherical surface onto another one. This case is much more limited than a Maxwell’s lens, as it cannot perfectly image an extended volume of space; it is therefore not a perfect system. The number of known perfect systems can be counter on two thumbs: variations of the Maxwell lens and a plane mirror. This paper describes a new perfect instrument, which forms a perfect real image, at unit magnification, of a 3-D object volume. It is a single-element catadioptric design, involving one reflection. All orders of all aberrations are zero. In its most useful embodiment, it images one plane surface onto another, perfectly. The Dyson design and the Wynne-Dyson design can be regarded as crude approximations to this new system.

© 1991 Optical Society of America