Resolution in optical nanoscopy depends on the localization uncertainty of single fluorescent labels, the density of labels covering the sample, and the sample’s spatial structure. Currently there is no integral, practical resolution measure that takes all factors into account. Here we introduce such a measure that can be computed directly from the image. We demonstrate its validity and benefits on 2D and 3D localization microscopy images of tubulin and actin filaments. Our approach makes it possible to compare achieved resolutions in images taken with different nanoscopy methods, optimize and rank different emitter localization and labeling strategies, define a stopping criterion for data acquisition, describe image anisotropy and heterogeneity, and, surprisingly, estimate the average number of localizations per emitter. Our findings challenge the current focus on obtaining the best localization precision, but instead show how the best image resolution can be achieved as fast as possible.

Conventional acquisition of three-dimensional (3D) microscopy data requires sequential z-scanning and is often too slow to capture biological events. We report a new aberration-corrected multi-focus microscopy method capable of producing an instant focal stack of nine 2D images. Appended to an epifluorescence microscope, the multi-focus system enables high-resolution 3D imaging in multiple colors with single molecule sensitivity, at speeds limited by the camera readout time of a single image.

Abstract:The Gaussian function is simple and easy to implement as Point Spread Function (PSF) model for fitting the position of fluorescent emitters in localization microscopy. Despite its attractiveness the appropriateness of the Gaussian is questionable as it is not based on the laws of optics. Here we study the effect of emission dipole orientation in conjunction with optical aberrations on the localization accuracy of position estimators based on a Gaussian model PSF. Simulated image spots, calculated with all effects of high numerical aperture, interfaces between media, polarization, dipole orientation and aberrations taken into account, were fitted with a Gaussian PSF based Maximum Likelihood Estimator. For freely rotating dipole emitters it is found that the Gaussian works fine. The same, theoretically optimum, localization accuracy is found as if the true PSF were a Gaussian, even for aberrations within the usual tolerance limit of high-end optical imaging systems such as microscopes (Marechal's diffraction limit). For emitters with a fixed dipole orientation this is not the case. Localization errors are found that reach up to 40 nm for typical system parameters and aberration levels at the diffraction limit. These are systematic errors that are independent of the total photon count in the image. The Gaussian function is therefore inappropriate, and more sophisticated PSF models are a practical necessity.

Abstract:We present a new super-resolution technique, Re-scan Confocal Microscopy (RCM), based on standard confocal microscopy extended with an optical (re-scanning) unit that projects the image directly on a CCDcamera. This new microscope has improved lateral resolution and strongly improved sensitivity while maintaining the sectioning capability of a standard confocal microscope. This simple technology is typically useful for biological applications where the combination high-resolution and highsensitivity is required. Toomre, and J. Bewersdorf, "Video-rate nanoscopy using sCMOS camera-specific single-molecule localization algorithms," Nat. Methods 10(7), 653-658 (2013).

A study of the uncertainty of localizing single-molecule emitters for super-resolution light microscopy is presented. Maximum likelihood estimation (MLE) is found to be superior to least-squares fitting for low background levels, but the performance difference between the two methods decreases to a few percent for practical background levels. It is shown that the performance limit of MLE, the Cramér-Rao lower bound, is well described by a concise analytical formula with only spot width and signal and background photon count as input parameters. These predictions for the lateral localization uncertainty are compared with the localization error obtained from repeated localizations of the same single-molecule emitter. Agreement within a few percent is found, thus verifying the validity of the fitting model and the concise analytical approximation. The analysis is extended by novel analytical results for the dependence of the axial localization uncertainty on background level for the astigmatic, bifocal, and double-helix methods.

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.

MINFLUX offers a breakthrough in single molecule localization precision, but is limited in fieldof-view. Here, we combine centroid estimation and illumination pattern induced photon count variations in a conventional widefield imaging setup to extract position information over a typical micron sized field-of-view. We show a near twofold improvement in precision over standard localization with the same photon count on DNA-origami nano-structures and tubulin in cells, using DNA-PAINT and STORM imaging. Single-molecule localization microscopy 1,2,3 circumvents the diffraction limit using centroid estimation of sparsely activated, stochastically switching, single-molecule fluorescence images. Improvement over state-of-the-art image resolutions of around 20 nm towards values below 5 nm is desired for truly imaging at the molecular scale. This needs improvements in labelling strategy to reduce linker sizes 4,5,6,7 and methods to overcome low labelling density such as data fusion 8 , but also a step in localization precision. Efforts so far have targeted an increase in the number of detected photons N by chemical engineering of brighter fluorophores 9 , or by avoiding photo-bleaching via e.g. cryogenic techniques 10,11,12. Users may view, print, copy, and download text and data-mine the content in such documents, for the purposes of academic research, subject always to the full Conditions of use:

Quantification in localization microscopy with reversibly switchable fluorophores is severely hampered by the unknown number of switching cycles a fluorophore undergoes and the unknown stoichiometry of fluorophores on a marker such as an antibody. We overcome this problem by measuring the average number of localizations per fluorophore, or generally per fluorescently labeled site from the build-up of spatial image correlation during acquisition. To this end we employ a model for the interplay between the statistics of activation, bleaching, and labeling stoichiometry. We validated our method using single fluorophore labeled DNA oligomers and multiple-labeled neutravidin tetramers where we find a counting error of less than 17% without any calibration of transition rates. Furthermore, we demonstrated our quantification method on nanobody- and antibody-labeled biological specimens.