  New ray-optical elements allow generalized refraction of light rays, but
geometry imposes limitations on possible mappings between the positions of an
object and its geometric image. Here I study the case of an infinite, planar,
non-absorbing sheet that images the entire three-dimensional space. The most
general case of such a sheet is equivalent to a thin lens with different
object- and image-sided focal lengths. Special cases include ordinary thin
lenses, confocal lenslet arrays, and negative refraction with n_2 = -n_1.
