On the existence of a radiance function for finite planar sources of arbitrary states of coherence

In this paper we show that one cannot associate a radiance function with a finite, partially coherent planar source of arbitrary state of coherence that would have all the usual properties attributed to it in elementary radiometry. More specifically, we show that in general there is no radiance function which depends linearly on the correlations existing between any pair of points in the source plane, gives the correct angular distribution of radiant intensity and which, moreover, is nonnegative and vanishes outside the source area. However, regardless of this result, the concept of generalized radiance appears to be a useful mathematical tool in radiometry with partially coherent sources.