Design of an axisymmetrical refractive optical element generating required illuminance distribution and wavefront.

The design of an axisymmetrical refractive optical element transforming a given incident beam into an output beam with prescribed illuminance distribution and wavefront is considered. The wavefront of the output beam is represented by the eikonal function defined in a certain plane behind the optical element. The design of the optical element is reduced to the solution of two explicit ordinary differential equations of the first order.