Discreteness of the real point emitters as a physical condition for diffraction

The discreteness of the zeroth-order class of the spectrum of classes of point emitters is shown as a necessary and sufficient physical condition for describing diffraction from the aperture plane to the far field. Although it does not contradict the continuity requirement of the cross-spectral density, it points out that this mathematical requirement is physically redundant. This feature gives new insight on the understanding of diffraction as well as novel tools for design and development of efficient non-paraxial propagation algorithms. It also leads to new criteria for characterizing physical point sources of light.