Single-molecule fluorescence permits super-resolution imaging, but traditional algorithms for localizing these isolated fluorescent emitters assume stationary point light sources. Proposed here are two fitting functions that achieve similar nanometer-scale localization precision as the traditional symmetric Gaussian function, while allowing, and explicitly accounting for, directed motion. The precision of these methods is investigated through Fisher information analysis, simulation and experiments, and the new fitting functions are then used to measure, for the first time, the instantaneous velocity and direction of motion of live bacteria cells. These new methods increase the information content of single-molecule images of fast-moving molecules without sacrificing localization precision, thus permitting slower imaging speeds, and our new fitting functions promise to improve tracking algorithms by calculating velocity and direction during each image acquisition.
