Optimized localization analysis for single-molecule tracking and super-resolution microscopy

Abstract

A theoretical and experimental treatment of fitting methods for localizing the centers of diffraction-limited spots is presented. Use of an analytical point spread function shows that maximum likelihood fitting is superior to both unweighted and weighted least squares Gaussian fitting. We optimally localized isolated fluorescent beads and molecules imaged as diffraction-limited spots, determined the orientation of molecules and present reliable formulas for the precision of various localization methods. Both theory and experimental data showed that unweighted least-squares fitting of a Gaussian squanders one-third of the available information, a popular formula for its precision exaggerates beyond Fisher's information limit, and weighted least-squares may do worse, whereas maximum-likelihood fitting is practically optimal.