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.

Abstract: An optical device is for spatially displacing the output of a light-emitting diode (LED) and coupling the output to a predominantly spherical emission pattern produced at a useftul height above the LED. The device is made of a transparent dielectric material, such as an injection-molded plastic. It comprises a lower transfer section that receives the LED's light from below and an upper ejector section that receives the transferred light and spreads it spherically. One or more LEDs. are optically coupled to the bottom of the transfer section, which operates by total internal reflection upon their entire hemispherical emission. One embodiment operates as a flashlight-bulb substitute with the ejector section radiating onto a parabolic reflector, which forms the beam. Thus hemisphencally emitting LEDs can be used in parabolic-mirror flashlights wherein these LEDs by themselves may be unsuitable for that role.