Fast Fourier domain localization algorithm of a single molecule with nanometer precision

We present an algorithm to determine the location of a fluorescent molecule with nanometer-scale accuracy. A Fourier domain localization scheme based on zero-padded fast Fourier transform and phase gradient operators is used to obtain a powerful mathematical model for localizing the molecule without numerical fitting. Compared with conventional algorithms, our position estimator does not require prior background information or initial parameter estimation. Numerical simulations indicate that the proposed method exhibits high localization precision and small bias while executing almost as fast as the fluoroBancroft algorithm.