Abstract
In lens systems, the constituent lenses usually share a common optical axis, or at least a common optical-axis direction, and such combinations of lenses are well understood. However, in recent proposals for lens-based transformation-optics devices [Opt. Express26, 17872 (2018)OPEXFF1094-408710.1364/OE.26.017872], the lenses do not share an optical-axis direction. To facilitate the understanding of such lens systems, we describe here combinations of two ideal lenses in any arbitrary arrangement as a single ideal lens. This description has the potential to become an important tool in understanding novel optical instruments enabled by skew-lens combinations.
Highlights
Geometrical optics is a mature field, but new ideas keep emerging [1,2]
The optical axis is the straight line through the principal points of the two lenses, whereas in the Buchroeder description, the optical axis is defined by the trajectory of the one light ray that is perpendicular to the transverse planes both in object and in image space
We present a simple and elegant description of imaging by a pair of lenses that do not share an optical-axis direction. We describe such a combination as a single lens in which the object and image spaces are sheared
Summary
Geometrical optics is a mature field, but new ideas keep emerging [1,2]. This applies to the field of lenses: on the one hand, lenses are amongst the oldest optical elements For a standard combination of lenses, in which the lenses share an optical axis, it has proved useful and elegant to describe such a system as a single lens with an effective focal length and object- and image-sided principal planes that, in general, do not coincide with each other nor with the principal plane(s) of the individual lenses. This is done by describing object- and imagespace positions in special coordinates constructed such that the equations describing the mapping between these spaces have the same form as the standard equations describing the mapping due to a single thin lens. We compare the lens-imaging coordinates in Section 5, consider the relevance of our results to physical lenses in Section 6, and discuss several aspects not mentioned elsewhere in Section 7, before concluding (Section 8)
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