In our recently published Letter [1], the code used to perform the maximum likelihood estimation (MLE) contained an error. Our code did not properly vary all the fitting parameters ($x_0$, $I_0$, and $b$) simultaneously. We have corrected the code to fix this error and have replicated the results of both figures with the corrected code. The results are shown in Fig. 1 and Fig. 2. The corrected code is available online [2]. Although a few cases have slightly higher or lower precision than in the original version, all cases remain clustered in the same range, i.e., within about 16% of the theoretical limit (labeled PLAM, for Practical Localization Accuracy Measure, calculated with code from the Ober Lab [3]).

 

Fig. 1. Revised version of Fig. 1 from our original paper.

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Fig. 2. Revised version of Fig. 2 from our original paper.

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Although the corrected and original codes give essentially identical results in all cases studied in the original Letter, we further tested the code by reducing the signal to noise ratio, in order to identify cases in which the errors in the code might be problematic and verify that the corrected code is in fact superior. When we considered cases analogous to Fig. 2 but with a substantially lower photon count per molecule (88 photons), we verified that the original code gave poor reconstruction, while the corrected code gave spurious results that remained close to the theoretical limit.