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.

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With the widespread uptake of 2D and 3D single molecule localization microscopy, a large set of different data analysis packages have been developed to generate super-resolution images. In a large community effort we designed a competition to extensively characterise and rank the performance of 2D and 3D single molecule localization microscopy software packages. We generated realistic simulated datasets for popular imaging modalities-2D, astigmatic 3D, biplane 3D, and double helix 3D-and evaluated 36 participant packages against these data. This provides the first broad assessment of 3D single molecule localization microscopy software and provides a holistic view of how the latest 2D and 3D single molecule localization software perform in realistic conditions. This resource allows researchers to identify optimal analytical software for their experiments, allows 3D SMLM software developers to benchmark new software against current state of the art, and provides insight into the current limits of the field. RESULTS Competition design We established a broad committee from the SMLM community, including experimentalists and software developers, to define the scope of the challenge, ensure realism of the datasets and define analysis metrics. We opened this discussion to all interested parties in an online discussion forum 17. In 2016, we ran a first round of the 3D SMLM competition with explicit submission deadlines, culminating in a special session at the 6th annual Single Molecule Localization Microscopy Symposium (SMLMS 2016). Since then, the challenge has been opened to continuously accept new entries. Thirtysix software packages have been entered in the competition thus far, including four packages used in commercial software (Table S1, Supplementary Note 1). Participation in the competition actually led at least eight teams to modify their software to support additional 3D SMLM modalities, showing how competition can foster microscopy software development. Realistic 3D simulations Testing super-resolution software on experimental data lacks the ground truth information required for rigorous quantification of software performance. Therefore, realistic simulated datasets are required. A critical challenge to in simulating 3D SMLM data was accurate modeling of the

SummaryOne of the most complex molecular machines of cells is the nuclear pore complex (NPC), which controls all trafficking of molecules in and out of the nucleus. Because of their importance for cellular processes such as gene expression and cytoskeleton organization, the structure of NPCs has been studied extensively during the last few decades, mainly by electron microscopy. We have used superresolution imaging by direct stochastic optical reconstruction microscopy (dSTORM) to investigate the structure of NPCs in isolated Xenopus laevis oocyte nuclear envelopes, with a lateral resolution of ,15 nm. By generating accumulated super-resolved images of hundreds of NPCs we determined the diameter of the central NPC channel to be 4167 nm and demonstrate that the integral membrane protein gp210 is distributed in an eightfold radial symmetry. Two-color dSTORM experiments emphasize the highly symmetric NPCs as ideal model structures to control the quality of corrections to chromatic aberration and to test the capability and reliability of superresolution imaging methods.

In microscopy, single fluorescence point sources can be localized with a precision several times greater than the resolution limit of the microscope. We show that the intermittent fluorescence or 'blinking' of quantum dots can analyzed by an Independent Component Analysis so as to identify the light emitted by each individual nanoparticle, localize it precisely, and thereby resolve groups of closely spaced (< lambda / 30) quantum dots. Both simulated and experimental data demonstrate that this technique is superior to localization based on Maximum Likelihood Estimation of the sum image under the assumption of point emitters. This technique has general application to any emitter with non-Gaussian temporal intensity distribution, including triplet state blinking. When applied to the labeling of structures, a high resolution "image" consisting of individually localized points may be reconstructed leading to the term "Pointillism".

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.

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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.