Ray optics of generalised lenses (glenses)

We study the ray optics of glenses, ideal thin lenses generalised to have different objectand 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 [Gabor, UK Patent 541,753 (1940); Hembd-Sölner et al., J. Opt. A: Pure Appl. Opt. 1, 94 (1999)] can be seen as pixellated realisations of glenses. Our analysis is centred on the nodal point. Whereas the nodal point of a thin lens always lies in the lens plane, that of a glens can lie anywhere on the optical axis. Utilising the nodal point, we derive simple equations that describe the mapping between object and image space and the light-raydirection change. We demonstrate our findings with the help of ray-tracing simulations. Glenses allow novel optical instruments to be realised, at least theoretically, and our results facilitate the construction and analysis of such devices. © 2016 Optical Society of America