Nonimaging Optics

Appendix F THE LUNEBURG LENS

The Luneburg lens, discussed in Chapter 3, is not, of course, of any use as a practical concentrator. It is, however, the simplest example of an ideal concentrator with maximum theoretical concentration for collecting angles up to π/2, and therefore we develop its theory and general properties in this appendix. The main reference is to Luneburg’s own work (Luneburg, 1964). Some of the general geometrical optics background can also be found in Born and Wolf (1975), and extensions are given by Morgan (1958) and Cornbleet (1976).

Our starting point is the differential equation of the light rays. Let s be distance along a ray measured from some fixed origin, let r be the position vector of a point on a ray, and let ...