The existence of multiple local solutions makes it very difficult to search for filter parameters to achieve a desired side lobe level during the design of superresolution pupil filters. To deal with the difficult issue of side lobe control in the designing process, a convex objective function-based design method is developed through phase rotation and variable replacement to transform the complicated solving process with multiextreme subintervals into a simple optimization process with a convex interval. A group of constant annular complex superresolving filters are designed using the developed method. The comparison of the superresolving filters designed in this way with the well-known continuous phase filter and 3-zone multiphase diffractive superresolution filters proves the validity of the developed method.
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