Achieving an axial superresolved focus with a single lens by simply inserting a modulation mask in the pupil plane is preferred due to its compact configuration and general applicability. However, lack of a universal theoretical model to manifest the superresolved focusing mechanism vastly complicates the mask design and hinders optimal resolution. Here we establish an interference model and find out that the axial resolution closely relates to the Gouy phase gradient (GPG) at the focal point. Using a GPG tuning-based optimization approach, the axial resolution of a ring-mask-modulated beam is readily improved to attain superresolved focal depth for multiple types of pupil function and polarization. In experiment, a focus with an axial resolution of 27% improved from the diffraction limit and 11% finer than the previously reported record is demonstrated for the radially polarized beam. In simulations, a spherical focus with 3D isotropic resolution and a superoscillation-like axial modulation behavior toward extremely high axial resolution is also presented. This approach can be applied for varied types of pupil function, wavelength, and polarization, and can be easily transferred to other traditional or superresolution microscopes to upgrade their axial resolution.

Cathodoluminescence (CL) as a radiative light produced by an electron beam exciting a luminescent material, has been widely used in imaging and spectroscopic detection of semiconductor, mineral and biological samples with an ultrahigh spatial resolution. Conventional CL spectroscopy shows an excellent performance in characterization of traditional material luminescence, such as spatial composition variations and fluorescent displays. With the development of nanotechnology, advances of modern microscopy enable CL technique to obtain deep valuable insight of the testing sample, and further extend its applications in the material science, especially for opto-electronic investigations at nanoscale. In this article, we review the study of CL microscopy applied in semiconductor nanostructures for the dislocation, carrier diffusion, band structure, doping level and exciton recombination. Then advantages of CL in revealing and manipulating surface plasmon resonances of metallic nanoantennas are discussed. Finally, the challenge of CL technology is summarized, and potential CL applications for the future opto-electronic study are proposed.