A binary annular phase mask to regulate spherical aberration and allow super-localization in single-particle tracking over extended depth-of-focus

Important applications of single-particle tracking (SPT) aim at deciphering the diffusion properties single fluorescent nanoparticles immersed in heterogeneous environments, such as multi-cellular biological tissues. To maximize particle localization precision complex high numerical aperture objectives are often required, which intrinsically restrict depth-of-focus (DOF) to less than a micrometer and impedes recording long trajectories when particles escape plane focus. In this work, we show that simple binary phase mask can work with spherical aberration inevitably induced by thick sample inhomogeneities, extend DOF single-molecule fluorescence microscope over more 4 {\mu}m. The effect point-spread-function (PSF) engineering regularizes inhomogeneities PSF along optical axis restricting it narrow distribution. This allows use fitting function (i.e. Gaussian function) localize emitters whole extended DOF. Application approach on diffusing demonstrate SPT be recorded significantly longer times.