Fig. 4

Model-based validation of MLE for the fluorophore distribution on a single nanoparticle. a Simulated fluorophore locations (solid points) on a spherical nanoparticle (grey sphere) with a stochastically homogeneous spatial distribution. The number of fluorophores is a realization of the introduced negative binomial distribution. The spatial locations are realizations of a uniform distribution over the surface of the sphere. b Simulated clusters of localizations (crosses) based on the generated fluorophore locations in Fig. 4a. The simulations of the dSTORM imaging process are generated realizations of the probabilistic model described in detail in the Supplementary Methods. c Measurement uncertainties for each localization, dependent on brightness and z-position. The uncertainty is graphically depicted as an ellipsoid of one standard deviation in three dimensions (transparent surface). Only localizations associated with the fluorophore colour-coded in blue are depicted. d Measurement uncertainties viewed along the z-axis. e Final MLE estimates of the fluorophore locations (solid triangles), resulting from the EM-algorithm based on the simulated localizations and associated uncertainties. The actual locations of simulated fluorophores are indicated for reference (solid points). f Matching of estimated and actual simulated fluorophore locations, using the Hungarian algorithm given the real number of dyes. Matched pairs are indicated by identical colours. The average distance between pairs is a measure of the estimation error in the MLE procedure