Resolution of annular-pupil optical systems

The resolution of optical systems with annular pupil objectives is discussed, particularly with respect to the imaging properties of soft-x-ray imaging optical systems. Images of two dark bars in a bright field and knife-edge responses, which are calculated with partially coherent transfer functions, were used to estimate the resolution. Resolution for two bright points in a dark field, which is conventionally used in Rayleigh's analysis, is also discussed for comparison. It was found that annular systems with obstruction ratios of more than 0.6 show resolution properties different from those of systems with low-obstruction-ratios. The high-obstruction-ratio systems show lower resolution for the two-dark-bar objects and higher resolution for the two-bright-point objects, whereas the low-obstruction-ratio system show almost the same resolution for both objects.