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We present a fast and model-free 2D and 3D single-molecule localization algorithm that allows more than 3 million localizations per second on a standard multi-core CPU with localization accuracies in line with the most accurate algorithms currently available. Our algorithm converts the region of interest around a point spread function (PSF) to two phase vectors (phasors) by calculating the first Fourier coefficients in both x- and y-direction. The angles of these phasors are used to localize the center of the single fluorescent emitter, and the ratio of the magnitudes of the two phasors is a measure for astigmatism, which can be used to obtain depth information (z-direction). Our approach can be used both as a stand-alone algorithm for maximizing localization speed and as a first estimator for more time consuming iterative algorithms.
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