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Localization microscopy is an imaging technique in which the positions ofindividual nanoscale point emitters (e.g. fluorescent molecules) are determinedat high precision from their images. This is the key ingredient insingle/multiple-particle-tracking and several super-resolution microscopyapproaches. Localization in three-dimensions (3D) can be performed by modifyingthe image that a point-source creates on the camera, namely, the point-spreadfunction (PSF). The PSF is engineered using additional optical elements to varydistinctively with the depth of the point-source. However, localizing multipleadjacent emitters in 3D poses a significant algorithmic challenge, due to thelateral overlap of their PSFs. Here, we train a neural network to receive animage containing densely overlapping PSFs of multiple emitters over a largeaxial range and output a list of their 3D positions. Furthermore, we then usethe network to design the optimal PSF for the multi-emitter case. Wedemonstrate our approach numerically as well as experimentally by 3D STORMimaging of mitochondria, and volumetric imaging of dozens offluorescently-labeled telomeres occupying a mammalian nucleus in a singlesnapshot.

DeepSTORM3D: dense three dimensional localization microscopy and point spread function design by deep learning