Sizing-up finite fluorescent particles with nanometer-scale precision by convolution and correlation image analysis

Determining the positions, shapes and sizes of finite living particles such as bacteria, mitochondria or vesicles is of interest in many biological processes. In fluorescence microscopy, algorithms that can simultaneously localize such particles as a function of time and determine the parameters of their shapes and sizes at the nanometer scale are not yet available. Here we develop two such algorithms based on convolution and correlation image analysis that take into account the position, orientation, shape and size of the object being tracked, and we compare the precision of the two algorithms using computer simulations. We show that the precision of both algorithms strongly depends on the object's size. In cases where the diameter of the object is larger than about four to five times the beam waist radius, the convolution algorithm gives a better precision than the correlation algorithm (it leads to more precise parameters), while for smaller object diameters, the correlation algorithm gives superior precision. We apply the convolution algorithm to sequences of confocal laser scanning micrographs of immobile Escherichia coli bacteria, and show that the centroid, the front end, the rear end, the left border and the right border of a bacterium can be determined with a signal-to-noise-dependent precision down to approximately 5 nm.