The present embodiments provide for apparatuses, and methods for manufacturing apparatuses to convert a first distribution of an input radiation to a second distribution of output radiation. The apparatus can be defined in some embodiments by generating a two-dimensional representation of three active optical surfaces including calculating a segment of first, entry and second surfaces based on first second, and third generalized Cartesian ovals, respectively, and successively repeating the calculating of the segments of the first and second surfaces, and rotationally sweeping the two-dimensional representation about a central axis providing a three-dimensional representation. In some embodiments, portion of the first and/or second surfaces can be totally internally reflective.