Geometrical optical design in phase space

The phase space concept in optics is a powerful method to treat many optical phenomena, including diffraction and interference. Phase space can be used to evaluate an optical design having regard on the effect on ray angles and ray positions simultaneously. Thus the analysis of the phase space transformation provides an entire picture of the optical functionality of the design. Especially for illumination problems, where the transport of radiance is relevant, the phase space concept provides an interesting access. We show that also in geometrical optics limit phase space provides an alternative perspective and tool for evaluating optical designs, as compared to ray-tracing. As an example we consider integrator rods and optical arrays, the most commonly used components to homogenize radiation fields. Since both components affect the spatial light distribution as well as the angular distribution of the radiation field, phase space methods allow to evaluate their operation principle, performance and also differences.