Characterization of the thermodynamic quality of light sources

The edge ray theorem has become a tenet for illumination design. For idealized configurations this theorem has proved extremely powerful and has led to new methods of design. However, many real life sources have no clean delimitation and thus the boundary of the phase space is not easy to specify. Optical efficiency expressed by the fraction of the light captured by the optical system and transferred to the target on one hand and average radiance at the target on the other hand become two conflicting objectives in illumination design. Optimal design generally requires a single scalar merit function. Two different objectives require a metric which specifies the relative valuation before optimality may even be defined. In practice the relative valuation depends on the application and seldom may be specified in advance. It is, however, possible to refer to a slightly weaker criterion, called pareto-optimality which allows to postpone the decision on the relative valuation. In this contribution we show how to derive the upper limits of efficiency and average radiance for all paretooptimal illumination designs using a given source. If an optical system observes the edge ray principle such that the boundary of the source follows a iso-radiance hyper-surface in phase space, then this system is pareto-optimal. To calculate the characteristic curve one needs to sort phase space according to radiance. We show an example of an illumination lens which was inspired by phase space sorting. We have found this tool extremely useful because it allows to outline the range of options before actually embarking on the optical design.