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.
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