Three-dimensional control of the focal light intensity distribution by analytically designed phase masks

An analytical method for a total control of the light-intensity distribution at the focus of an optical system by simple pupil-plane phase mask is presented. The masks are composed of three annuli that only reach 0 or π values. A relevant advantage of this method is that the parameters of the mask are analytically obtained from the figures of merit that characterize the focal intensity distribution, as the Strehl ratio, the axial and the transverse gains. As a consequence, the method allows an easy and complete analysis of the masks performance. We demonstrate that these masks allow us to attain a complete reshaping of the spatial intensity distribution, including apodization or superresolution in the axial or transverse directions and, especially, three-dimensional superresolution. Finally, we derive the Strehl limit in the superresolution regime.