Optimizing Super Resolution Microscopy

Abstract

Super-resolution microscopy is often done by imaging isolated fluorescent probes as diffraction-limited spots with objective-type total internal fluorescence (TIRF) microscopy. The centers of these spots are commonly, sub-optimally located by least-squares fitting a 2D Gaussian to each spot's intensity distribution. Here we give the optimal localization procedure based on the true point spread function (PSF) known from wave optics. From a single focused image of a fluorophore molecule with fixed or time-resolved spatial orientation, we estimate the fluorophore's position and orientation using maximum likelihood estimation. We achieve the highest possible precision, given by Fisher's information limit. In the same manner, optimal localization is demonstrated for isotropic distributions of dipoles, e.g. fluorescent beads, excited by the evanescent wave produced in TIRF. Using this as a baseline, we compare a number of estimators and demonstrate that (i) for a 2D Gaussian, the unweighted least-squares fitting squanders one third of the available information, and weighted least-squares fitting is unreliable; (ii) a popular formula for the localization error of a 2D Gaussian fit exaggerates its precision beyond Fisher's information limit; (iii) maximum likelihood fitting of a 2D Gaussian is, on the other hand, practically optimal. We also present new, reliable formulae for the precisions of the various localization methods.