Image quality in single-molecule localization microscopy depends largely on the accuracy and precision of the localizations. While under ideal imaging conditions, the theoretically obtainable precision and accuracy are achieved; in practice, this changes if (field-dependent) aberrations are present. Currently, there is no simple way to measure and incorporate these aberrations into the point-spread function (PSF) fitting; therefore, the aberrations are often taken as constant or neglected altogether. Here we introduce a model-based approach to estimate the field-dependent aberration directly from single-molecule data without a calibration step. This is made possible by using nodal aberration theory to incorporate the field dependency of aberrations into our fully vectorial PSF model. This results in a limited set of aberration fit parameters that can be extracted from the raw frames without a bead calibration measurement, also in retrospect. The software implementation is computationally efficient, enabling the fitting of a full 2D or 3D dataset within a few minutes. We demonstrate our method on 2D and 3D localization data of microtubuli, nuclear pore complexes, and nuclear lamina over fields of view of up to 180 µm and compare it with Gaussian fitting, spline-based fitting, and a deep-learning-based approach.

Single-molecule localization microscopy super-resolution methods rely on stochastic blinking/binding events, which often occur multiple times from each emitter over the course of data acquisition. Typically, the blinking/binding events from each emitter are treated as independent events, without an attempt to assign them to a particular emitter. Here, we describe a Bayesian method of inferring the positions of the tagged molecules by exploring the possible grouping and combination of localizations from multiple blinking/binding events. The results are position estimates of the tagged molecules that have improved localization precision and facilitate nanoscale structural insights. The Bayesian framework uses the localization precisions to learn the statistical distribution of the number of blinking/binding events per emitter and infer the number and position of emitters. We demonstrate the method on a range of synthetic data with various emitter densities, DNA origami constructs and biological structures using DNA-PAINT and dSTORM data. We show that under some experimental conditions it is possible to achieve sub-nanometer precision.