Intensity and resolution at the diffraction focus of optical systems with rotationally symmetric aberration functions

The intensities and resolutions at the diffraction focus of optical systems with rotationally symmetric minimum-variance aberration functions as well as functions with slight variations from this shape and a prescribed fixed maximum deviation value at the edge of the exit pupil are calculated for circular and annular exit pupils. The results for the intensity at the diffraction focus obtained either by numerical integration of the diffraction integral or by using the Maréchal formula show that the maxima of these intensities are achieved for optical systems with wave aberration functions of minimum variance, thus verifying the Maréchal criterion. The resolutions (first zeros of the intensities in the radial direction) at this diffraction focus are also presented.