Design of binary phase filters for depth-of-focus extension via binarization of axisymmetric aberrations

We present a novel design approach for a binary phase mask with depth-of-focus (DoF) extension ability. Our method considers that the binarized version of an axisymmetric continuous phase pupil generates twin-intensity profiles that are symmetric with respect to the focal plane, each of which resembles the focal behavior of its continuous original. The DoF extension is realized by repositioning and coherently summing the twin foci to achieve an elongated focus along the axial direction. The shift of the two foci towards the focal plane can be handled by superimposing the defocus term in the continuous pupil function. We demonstrate our proposed design approach for two representative axisymmetric aberration functions, i.e., defocused phase axicon and spherical aberration. The manipulation of topological parameters in the phase axicon and spherical aberration, along with the defocus strength, enables the multiple binary phase-filter designs of DoF extension of 3.2-7.1 fold with a phase axicon and 2.8-14.8 fold with a spherical aberration, compared to the case with a clear aperture.