Irradiance and phase control with two freeform surfaces using partial differential equations

A design method of two coupled freeform surfaces for the control of the irradiance and phase of the input and output wavefronts without the restriction to paraxiality or spherical/planar wavefronts is presented. It can be applied to the design of coupled lens surfaces, coupled mirrors or the combination of lens and mirror surfaces. The method is based on the description of the freeform surfaces through a system of coupled partial differential equations (PDE) for the first freeform surface and a ray-mapping projection. By calculating the required output wavefront between two predefined complex illumination patterns, we demonstrate that the presented algorithm can be applied directly to the calculation of a single optical element for the generation of two different irradiance distributions on separated target planes. Additionally, a manufacturing analysis of the corresponding freeform surfaces of a double lens system is provided. Furthermore, an extension of the design approach for a single freeform lenses with a predefined entrance surface from [J. Opt. Soc. Am. A 34, 1490-1499 (2017)] to single freeform lenses with a predefined exit surface is presentend. Limitations of the design method and possible improvements are discussed.