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Licensed Unlicensed Requires Authentication Published by De Gruyter February 14, 2023

Computational resolution in single molecule localization – impact of noise level and emitter density

  • Mathias Hockmann EMAIL logo , Stefan Kunis ORCID logo EMAIL logo and Rainer Kurre EMAIL logo
From the journal Biological Chemistry

Abstract

Classical fluorescence microscopy is a powerful technique to image biological specimen under close-to-native conditions, but light diffraction limits its optical resolution to 200–300 nm-two orders of magnitude worse than the size of biomolecules. Assuming single fluorescent emitters, the final image of the optical system can be described by a convolution with the point spread function (PSF) smearing out details below the size of the PSF. In mathematical terms, fluorescence microscopy produces bandlimited space-continuous images that can be recovered from their spatial samples under the conditions of the classical Shannon-Nyquist theorem. During the past two decades, several single molecule localization techniques have been established and these allow for the determination of molecular positions with sub-pixel accuracy. Without noise, single emitter positions can be recovered precisely – no matter how close they are. We review recent work on the computational resolution limit with a sharp phase transition between two scenarios: 1) where emitters are well-separated with respect to the bandlimit and can be recovered up to the noise level and 2) closely distributed emitters which results in a strong noise amplification in the worst case. We close by discussing additional pitfalls using single molecule localization techniques based on structured illumination.


Corresponding authors: Mathias Hockmann, Stefan Kunis and Rainer Kurre, Department of Mathematics and Center for Cellular Nanoanalytics, Osnabrück University, Barbarastrasse 113, D-49076 Osnabruck, Germany, E-mail: (M. Hockmann), (S. Kunis), (R. Kurre)

Funding source: Volkswagen Foundation

Award Identifier / Grant number: Stability of Moment Problems and Super-Resolution

Award Identifier / Grant number: CRC944

  1. Author contributions: All authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This work was funded within the Collaborative Research Center 944 “Physiology and Dynamics of Cellular Microcompartments” (Project Z: Advanced imaging techniques) and by the Volkswagen Foundation project “Stability of Moment Problems and Super-Resolution Imaging”.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2022-09-30
Accepted: 2023-01-24
Published Online: 2023-02-14
Published in Print: 2023-04-25

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