Two point resolution with non-uniform and non-symmetric illumination using partially coherent light

Expression for the dependence of critical resolution of a circular aperture, with non-uniform and non-symmetric illumination using partially coherent light, on the complex degree of coherence is obtained for the two cases viz: (I) when the two point objects are of equal intensity and (II) when they are of un-equal intensity. In the former case Sparrow criterion of resolution is used while in the later well known Rayleigh criterion is used. Applicability of these criteria in the two cases is discussed. In the case, when the two object points are of unequal intensity Sparrow criterion in its simple form cannot be applied.