Free-form catadioptric illumination lens

An illumination lens for hemispherically emitting light emitting diodes is disclosed that produces a square illumination pattern too narrow for a refractive lens to produce by itself. The lens is freeform in that it departs from circular symmetry in order to produce a square pattern. It is catadioptric in that it comprises a central refractive lens with a square output of desired angular width and a surrounding TIR prism that produces the same square output, overlapping the first for better uniformity of the sum. The central lens and circumambient TIR prism are joined in a monolithic configuration suitable for injection molding. Vector equations are disclosed for generating the shapes of the five optically active surfaces of the invention, two internal surfaces forming a central cavity surrounding the LED and three external surfaces, all five departing from circular symmetry.