Consequences of skewness conservation for rotationally symmetric nonimaging devices

An upper limit on concentration for any optical device has previously been derived from the conservation of etendue. In this contribution we derive more stringent upper limits for the efficiency and the concentration of rotationally symmetric optical devices which are a consequence of skewness conservation. If the desired source and target have different skewness distributions, then losses or dilution or both will limit the performance of the optical system. For all skewness values, for which the source contains more radiation than the target, the difference is lost. Conversely, for all skewness values, for which the target contains a larger etendue than the source: the difference remains empty and results in dilution. We calculate the limiting curve of optical transfer efficiency versus concentration relative to the maximum concentration possible and provide a design example that is practically at this limit. We also provide another design example that addresses the challenge posed at the last SPIE meeting, namely to transfer the maximum radiation from a Lambertian spherical source to a disk target of equal etendue under a reflector-to-source minimum distance constraint. We conjecture that even rotationally symmetric problems may benefit from asymmetric optical systems.