Fig. 2: Characterization of the planar localization and tracking uncertainties.

a–c Lateral localization uncertainty maps σ_xy(x_e, y_e). The CRB is calculated using an experimental PSF, SBR_p = 5 and N_p = 100 photons, and assuming a fixed acquisition time. The uncertainty maps of the MLE and centroid estimator are measured by using a common dataset obtained by scanning 20 times a 20 nm fluorescent bead replicating the same conditions of the CRB. λ_exc = 561 nm. Scale bar = 100 nm. d–f Axial localization uncertainty maps σ_xz(x_e, z_e). The CRB is calculated using an experimental PSF, SBR_p = 5 and N_p = 100 photons, and assuming a fixed acquisition time. The uncertainty maps of the MLE and normalized difference estimator are measured by using a common dataset obtained by scanning 33 times a 20 nm fluorescent bead replicating the same conditions of the CRB. λ_exc = 561 nm. Scale bar = 100 nm. g Imposed and tracked trajectories of a single 20 nm fluorescent bead (λ_exc = 561 nm) moved at an average tangential speed of 5.5 μm/s along a 3D Lissajous pattern. The scanning position is updated simultaneously in the lateral direction with the centroid estimator and in the axial direction with the normalized difference estimator every 100 photons (〈Δt_rc〉 = 1.9 ± 0.4 ms). The color is used to visualize time, and black lines on the colormap mark the end of each complete turn of the periodic pattern. Extended time trace of the trajectory in Supplementary Fig. 14. h Histograms of the difference between the imposed and tracked trajectories along the three directions for the experiment in (g). σ_x = 34.60 ± 0.04 nm, σ_y = 30.36 ± 0.04 nm, and σ_z = 39.13 ± 0.07 nm.