Design of three-dimensional superresolving binary amplitude filters by using the analytical method

An analytical method known for phase filters is applied to amplitude filters. The method is based on the use of a series of figures of merit, such as the axial and the transverse gains and the Strehl ratio, which characterize the point-spread-function distribution near the focal region. As a practical implementation, we have applied this method to analytically design the superresolving three-zone amplitude filters and obtained a complete reshaping of the spatial intensity distribution. Regions of the radii of the filters with the transverse, axial or three-dimensional superresolutions are shown analytically. The maximum possible transverse or axial gain is derived for the certain Strehl ratio.