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