Mathematical treatment of condenser aberration

Given today's severe imaging requirements demanded in optical lithography all contrihuting factors to image quality need to be considered and assessed for a given optical design in order to maximize imaging performance. While aberrations of optical condenser system have previously been discussed and treated in the literature none of the treatments to date appear to be consistent with the fundamental low of radiance conservation. Here we derive rigorously the necessary equations and develop a self-consistent mathematical framework to treat condenser aberrations of arbitrary polynomial order in the context of Kohler illumination.