Model-independent machine learning approach for nanometric axial localization and tracking

Accuratelytrackingparticlesanddeterminingtheircoordinatealongtheopticalaxisisa majorchallengeinopticalmicroscopy,especiallywhenextremelyhighprecisionisneeded. Inthis study,weintroduceadeeplearningapproachusingconvolutionalneuralnetworks(CNNs)thatcan determine axial coordinates from dual-focal-plane images without relying on predefined models. Our method achieves an axiallocalizationprecision of40 nanometers — six times better than traditional single-focal-planetechniques. Themodel’ssimpledesignandstrongperformancemakeitsuitable for a wide range of uses, including dark matter detection, proton therapy for cancer, and radiation protection in space. It also shows promise in fields like biological imaging, materials science, and environmental monitoring. This work highlights how machine learning can turn complex image data into reliable, precise information, offering a flexible and powerful tool for many scientific applications.