Ray optics of generalized lenses

摘要

We study the ray optics of generalized lenses (glenses), which are ideal thin lenses generalized to have different object- and image-sided focal lengths, and the most general light-ray-direction-changing surfaces that stigmatically image any point in object space to a corresponding point in image space. Gabor superlenses [UK patent 541,753 ( 1940); J. Opt. A 1, 94 ( 1999)] can be seen as pixelated realizations of glenses. Our analysis is centered on the nodal point. Whereas the nodal point of a thin lens always resides in the lens plane, that of a glens can reside anywhere on the optical axis. Utilizing the nodal point, we derive simple equations that describe the mapping between object and image space and the light-ray-direction change. We demonstrate our findings with the help of ray-tracing simulations. Glenses allow novel optical instruments to be realized, at least theoretically, and our results facilitate the design and analysis of such devices. Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License.