Discontinuous free-form lens design for prescribed irradiance.

For the problem of point source forming prescribed irradiance, a new, to the best of our knowledge, method-variable separation mapping method is presented, which establishes separately the correspondence between variables on the light source and the target plane. The role played by the optical surfaces is then to redirect the light rays to their corresponding target points. The surface of the lens is determined by first calculating the surface points and then their normal vectors. Considering that normal deviations are produced in the surface construction process, a normal deviation control method is also presented to restrict the deviation. With this normal deviation control method, discontinuities are introduced onto the lens surface. From these mapping and normal control methods, a fast and efficient algorithm has been developed for several prescribed irradiance problems with simple nonrotational shape of the illuminated region.