Fundamental properties of light unavoidably impose features on images collected using fluorescence microscopes. Accounting for these features is often critical in quantitatively interpreting microscopy images, especially those gathering information at scales on par with or smaller than light's emission wavelength. Here the optics responsible for generating fluorescent images, fluorophore properties, and microscopy modalities leveraging properties of both light and fluorophores, in addition to the necessarily probabilistic modeling tools imposed by the stochastic nature of light and measurement, are reviewed.

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.

Methods that fuse multiple localization microscopy images of a single structure can improve signal-to-noise ratio and resolution, but they generally suffer from template bias or sensitivity to registration errors. We present a template-free particle-fusion approach based on an all-to-all registration that provides robustness against individual misregistrations and underlabeling. We achieved 3.3-nm Fourier ring correlation (FRC) image resolution by fusing 383 DNA origami nanostructures with 80% labeling density, and 5.0-nm resolution for structures with 30% labeling density.