A two incoherent sources resolution criterion in the phase space

Abstract

The aim of this work is to propose a positiveness constraint on the Wigner Distribution Function (WDF) of the detected image of two incoherent point sources: if WDF lacks of zeroes along the frequency coordinate the object can not be resolved by imaging and detected systems; otherwise, it can. This criterion can be applied without preference for a circular clear diffraction limited aperture and for complex apertures with small aberration values; furthermore, it holds if the intensity of each source is different or even when the sources are not points.