Abstract: A method for manufacturing an apparatus and the apparatus being configured to convert a first distribution of an input radiation to a second distribution of output radiation. The method consists of the steps of generating a two-dimensional representation of at least three active optical surfaces of an optical device including calculating a segment of a first surface based on edge ray sets as a first generalized Cartesian oval, calculating a segment of an entry surface based on the edge ray set as a second generalized Cartesian oval, calculating a segment of a second surface based on the edge ray set as a third generalized Cartesian oval, and successively repeating the steps of calculating the segment of the first surface and calculating the segment of the second surface in a direction towards a source, and rotationally sweeping the two-dimensional representation about a central axis providing a three-dimensional representation of the optical device.