Abstract
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.