Design of superresolving continuous phase filters based on deformable mirror eigenmodes

The superresolving pupil filters are utilized to modulate amplitude or phase, which can compress the central main lobe of the diffracted spot below the diffraction limit. The mature pupil filter is mainly made by binary optical processing technology or liquid crystal spatial light modulators. Compared with these two types, the superresolving pupil filters based on deformable mirror(DM) have the advantages of programmability, no wavelength and polarization limitation. In this paper, the design of superresolving continuous phase filters using DM eigenmodes as the basis function is studied by simulation. The DM eigenmodes are constructed by the coupling relationship between the actuators, and the first, sixth, fifteenth and 30th order eigenmodes are selected for interpolation to obtain the continuous phase function. Superresolution gain factor (G^t), Strehl ratio (S) and axial displacement of focus (U^F) are chosen as performance evaluation index. Using multi-objective optimization genetic algorithm to solve the constrained multi-objective optimization problem, the spot size is reduced by approximately 30% compared to the diffraction-limited spot, and the corresponding Strehl ratio is approximately 0.4. Using DM as the continuous phase filter, we analyzed the effects of defocus and astigmatism on the super-resolution performance of the filter. The fitting accuracy of pupil filters designed by DM eigenmodes and Zernike polynomials are also compared, which proves that the eigenmode-based superresolving pupil filters are more suitable for fitting with a deformable mirror.