Fig. 2.

Qualitative comparison of methods. Computer-generated images (15×15 pixels) like those illustrated were generated using 10-10⁴ emitter photons and different numbers of background photons (i.e., b = 0 or 10 photons/pixel) to give different signal-to-noise ratios (S:N); then, the root-mean-square error of localization in one dimension (1-D RMSE in nm or pixel units) was calculated (10⁴ localizations per data point) using the methods indicated. Photon counts (top) and S:N (bottom) are indicated in some typical images. The lower bound, LB (blue dashed line), is computed using Eq. (6) of Thompson et al. [14] and plotted here and in subsequent Figures as a reference. (a) With no background (b = 0), the ‘default’ version of JD returns the same results as CM, and both track the LB; MLS and MLE fail at low photon counts. The failure of MLS without background is examined more in Supplemental Fig. 1(b). In the presence of background (b = 10), all methods fail at low photon counts; at moderate counts, MLE performs best, and at high counts MLS is the worst as the others converge to the minimum error. (c) An ‘optimized’ version of JD increases precision at low S:N while retaining precision at high S:N. The grey region is analyzed further in Fig. 3. Arrows: conditions used in Fig. 4.