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The Lateral and Axial Localization Uncertainty in Super‐Resolution Light Microscopy
Author(s) -
Rieger Bernd,
Stallinga Sjoerd
Publication year - 2014
Publication title -
chemphyschem
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.016
H-Index - 140
eISSN - 1439-7641
pISSN - 1439-4235
DOI - 10.1002/cphc.201300711
Subject(s) - resolution (logic) , microscopy , common emitter , optics , limit (mathematics) , physics , measurement uncertainty , least squares function approximation , image resolution , computational physics , mathematics , chemistry , statistics , molecular physics , mathematical analysis , computer science , estimator , optoelectronics , artificial intelligence
A study of the uncertainty of localizing single‐molecule emitters for super‐resolution light microscopy is presented. Maximum likelihood estimation (MLE) is found to be superior to least‐squares fitting for low background levels, but the performance difference between the two methods decreases to a few percent for practical background levels. It is shown that the performance limit of MLE, the Cramér–Rao lower bound, is well described by a concise analytical formula with only spot width and signal and background photon count as input parameters. These predictions for the lateral localization uncertainty are compared with the localization error obtained from repeated localizations of the same single‐molecule emitter. Agreement within a few percent is found, thus verifying the validity of the fitting model and the concise analytical approximation. The analysis is extended by novel analytical results for the dependence of the axial localization uncertainty on background level for the astigmatic, bifocal, and double‐helix methods.