A Bayesian Approach to Angstrom-Level Super-Resolution Microscopy with Color Centers in Diamond

Super-resolution microscopy enables imaging beyond the diffraction limit by reconstructing far-field emission patterns, achieving sub-nanometer precision. However, conventional methods are limited by the Cramér-Rao lower bound, where precision scales inversely with the square root of the number of collected photons. This means further improvements require quadratically longer acquisition times. In this talk, we introduce the Discrete-Grid Imaging Technique (DIGIT), which surpasses this scaling law by incorporating prior knowledge of emitters' underlying spatial structure into a Bayesian framework. We demonstrate this by implementing DIGIT on an angstrom-level super-resolution microscope using color centers in diamond. Additionally, we highlight the broader applications of our method and its potential impact on high-precision measurements in quantum and biological systems.