Design and performance analysis of super-resolving continuous phase pupil filters based on deformable mirror eigenmodes

We proposed a superresolving pupil filter based on deformable mirror (DM) eigenmodes in this paper. A set of superresolving pupil filters containing the first, sixth, fifteenth and 28th order DM eigenmodes are designed by solving a multi-objective optimization problem. Simulations show that the pupil filter can make the transverse spot size be reduced by approximately 30% compared to the diffraction-limited one, and the corresponding Strehl ratio is approximately 0.4. Moreover, pupil filters based on different order eigenmodes are designed and their superresolution performances are discussed respectively, the results show that it is possible to obtain superresolution even if the order of eigenmodes drops to 2. Finally, we analyze the influence of sampling rate of influence functions(IF) and system noise when using DM to fit the designed filters, which is significant for choosing the appropriate filter in practical applications.