Localization microscopy is an imaging technique in which the positions of individual point emitters (e.g. fluorescent molecules) are precisely determined from their images. This is a key ingredient in single/multiple-particle-tracking and super-resolution microscopy. 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 to vary distinctively with emitter depth, using additional optical elements. 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 localize multiple emitters with densely overlapping PSFs over a large axial range. Furthermore, we then use the network to design the optimal PSF for the multi-emitter case. We demonstrate our approach experimentally with super-resolution reconstructions of mitochondria and volumetric imaging of fluorescently labeled telomeres in cells.

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