Design of axially super-resolving phase filters using the method of generalized projections

The design of pupil phase filters that super-resolve the axial intensity distribution with controlled side-lobe peak intensity under high numerical aperture conditions can be accomplished by incorporating the theory of electromagnetic diffraction in the method of generalized projections (MGP). The MGP results are however strongly dependent on the starting conditions and the applied constraints. In this report we study this dependence by investigating different starting pupil functions and introducing modifications to the applied constraints. Methods are described and implemented to generate a systematic set of starting conditions that enable a more thorough search of the solutions space. This approach generated results for which 95% have a super-resolved central-lobe, yet only a subset of those solutions offer a satisfactory compromise between super-resolution of the central-lobe and increased intensity of the axial side-lobes. These solutions are presented and discussed in the context of specific applications.