Just because I found it, and someone needs to code up this sick new lens for
POV-Ray  :)

https://www.osapublishing.org/oe/abstract.cfm?uri=oe-23-5-5716


"We propose a three dimensional optical instrument with an isotropic gradient
index in which all ray trajectories form Lissajous curves. The lens represents
the first absolute optical instrument discovered to exist without spherical
symmetry (other than trivial cases such as the plane mirror or conformal maps of
spherically-symmetric lenses). An important property of this lens is that a
three-dimensional region of space can be imaged stigmatically with no
aberrations, with a point and its image not necessarily lying on a straight line
with the lens center as in all other absolute optical instruments. In addition,
rays in the Lissajous lens are not confined to planes. The lens can optionally
be designed such that no rays except those along coordinate axes form closed
trajectories, and conformal maps of the Lissajous lens form a rich new class of
optical instruments."

I'm probably gonna have to read the whole PDF 3 or more times just to understand
what it does  :O

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