Hybrid super-resolving pupils with smooth profile

One form of achieving super-resolution consists in reducing the size of the Point Spread Function (PSF) of a diffraction-limited optical system. For this end, good results have been obtained by means of pupils with discontinuous profiles. When devices such as deformable mirrors are used to generate such pupils, however, these cannot be accurately reproduced. To overcome this limitation, we developed a method based on a Bessel series expansion to design pupils with smooth profiles, and found that, properly designed, pupils with continuous profiles will perform equally well, and in some respects better, than pupils with discontinuous ones.