  Localization microscopy is an imaging technique in which the positions of
individual nanoscale point emitters (e.g. fluorescent molecules) are determined
at high precision from their images. This is the key ingredient in
single/multiple-particle-tracking and several super-resolution microscopy
approaches. Localization in three-dimensions (3D) can be performed by modifying
the image that a point-source creates on the camera, namely, the point-spread
function (PSF). The PSF is engineered using additional optical elements to vary
distinctively with the depth of the point-source. However, localizing multiple
adjacent emitters in 3D poses a significant algorithmic challenge, due to the
lateral overlap of their PSFs. Here, we train a neural network to receive an
image containing densely overlapping PSFs of multiple emitters over a large
axial range and output a list of their 3D positions. Furthermore, we then use
the network to design the optimal PSF for the multi-emitter case. We
demonstrate our approach numerically as well as experimentally by 3D STORM
imaging of mitochondria, and volumetric imaging of dozens of
fluorescently-labeled telomeres occupying a mammalian nucleus in a single
snapshot.
