The phase-space representation of non-paraxial light propagation reveals that the classical second-order wave fronts have a fundamental discontinuity, imposed by the spatial coherence without appealing to quantum features, i.e. the set of radiant point sources associated with each wave front must be discrete. So, discrete sets of radiant point sources account not only for interference but also for diffraction. Consequently, a novel criterion is proposed for specifying the source distributions that respectively give interference and diffraction patterns, as illustrated by the analysis of basic experiments. These ideas are important for the development of efficient and accurate algorithms for non-paraxial light propagation.