A Bayesian approach towards atomically-precise localization in fluorescence microscopy.

Super-resolution microscopy has revolutionized the imaging of complex physical and biological systems by surpassing the Abbe diffraction limit. Recent advancements, particularly in single-molecule localization microscopy, have pushed localization below nanometer precision, by applying prior knowledge of correlated fluorescence emission from single emitters. However, achieving a refinement from 1 nm to 1 Ångström demands a hundred-fold increase in collected photon signal. This quadratic resource scaling imposes a fundamental barrier in single-molecule localization microscopy, where the intense photon collection is challenged by photo-bleaching, prolonged integration times, and inherent practical constraints. Here, we break this limit by harnessing the periodic nature of the atomic lattice structure. Applying this discrete grid imaging technique (DIGIT) in a quantum emitter system, we observe an exponential collapse of localization uncertainty once surpassing the host crystal's atomic lattice constant. We further applied DIGIT to a large-scale quantum emitter array, enabling parallel positioning of each emitter through wide-field imaging. Collectively, these advancements establish DIGIT as a competitive tool for achieving unprecedented, precise measurements, ultimately paving the way to direct optical resolution of crystal and atomic features within quantum and biological systems.