"Suppose we start with a disk radiator and we place a mirror in the form of a hyperboloid of revolution coincident with a set of flow lines... We truncate the mirror at some distance so the open end is a circle... Considering the inside as a mirror, this forms a nonimaging concentrator with unusual properties. The foci of the hyperbolas in this section are at... the ends of the diameter of the original disk. Then all rays entering the aperture... and pointing somewhere inside the disk will be reflected by the mirror so as to strike, eventually, the inner disk... Thus, the concentrator takes all rays from the virtual source... which can pass the entry aperture... and concentrate them into an exit aperture. This result is easily proved for rays in the meridional section... the extreme angle rays emerge from the exit aperture but only after an infinite number of reflections. ...rays at angles inside the extreme angles all emerge. Thus, in the meridional plane this is a concentrator of maximal theoretical concentration. This property holds for skew rays, although this is not quite so obvious. ...When used in reverse, the same design produces a virtual ring that fills the space between a Lambertian source and the larger diameter... [disk]. The visual effect produced is striking."