Imaging performance of annular apertures

Images formed by aberration free optical systems with annular apertures are investigated in the whole range of central obstruction ratios. Annular apertures form images with central and surrounding ring groups, and the number of rings in each group is given by the outer diameter of the annular aperture divided by the width of the annulus. The theoretical energy fraction of 0.838 in the Airy disk of the unobstructed aperture increases to 0.903 in the central ring groups. Furthermore it is shown that the energy fractions for the central and surrounding ring groups are constant for all obstruction ratios and in each fractional energy level. The central image spot in the central ring group contains only a small energy fraction and therefore the central ring group as a whole is the effective image element.