Rayleigh two-point resolution by a semi-transparent and φ-phase annular optical system operating in partially coherent light

A theoretical study has been made to investigate the dependence of the two-point resolution by an aberration free, semi-transparent and φ-phase annular aperture, on the real part of the complex degree of coherence. Rayleigh's criterion in its modified version has been used for the partially coherent optical systems and a comparison between Rayleigh and Sparrow resolution has been made. In order to reveal important information concerning the characteristics of the image, the intensity distribution from two mutually partially coherent point sources has also been evaluated.