Abstract
resolution in optical nanoscopy (or super-resolution microscopy) depends on the localization uncertainty and density of single fluorescent labels and on the sample's spatial structure. currently there is no integral, practical resolution measure that accounts for all factors. We introduce a measure based on Fourier ring correlation (Frc) that can be computed directly from an image. We demonstrate its validity and benefits on two-dimensional (2d) and 3d localization microscopy images of tubulin and actin filaments. our Frc resolution method makes it possible to compare achieved resolutions in images taken with different nanoscopy methods, to optimize and rank different emitter localization and labeling strategies, to define a stopping criterion for data acquisition, to describe image anisotropy and heterogeneity, and even to estimate the average number of localizations per emitter. our findings challenge the current focus on obtaining the best localization precision, showing instead how the best image resolution can be achieved as fast as possible. The first and foremost law of conventional optical imaging science is that resolution is limited to a value on the order of $łambda$/NA, with $łambda$ equal to the wavelength of light and NA to the numerical aperture of the imaging lens. Rayleigh and Sparrow captured this law through empirical resolution criteria. These criteria were placed on solid foundations by Abbe and Nyquist, who defined resolution as the inverse of the spatial bandwidth of the imaging system. This diffraction limit, however, can be overcome by numerous optical nanoscopy techniques, notably stimulated emission depletion (STED) 1 , reversible saturable optical fluorescence transitions (RESOLFT) 2 , the family of localization microscopy techniques such as photoactivated localization microscopy (PALM), stochas-tic optical reconstruction microscopy (STORM), ground state depletion microscopy followed by individual molecule return (GSDIM) and direct STORM 3-6 and statistical methods such as blinking fluorescence localization and super-resolution optical fluctuation imaging (SOFI) 7,8. These revolutionary developments raise the question: what is resolution in diffraction-unlimited imaging? The resolving power of the instrument is often coupled to the uncertainty of localizing
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