General dielectric-lens shaping using complex co-ordinates

The formulation of design equations for shaped dielectric lenses is considered under the assumptions of geometrical optics. The use of complex co-ordinates to track the refracted-ray directions introduces a very flexible approach in which no symmetry assumptions are necessary. The problem of designing a lens to serve as an optical transformer for aperture distribution control is shown, in general, to require the solution of a Monge- Ampere equation.