Localization uncertainty

Let \sigma be the standard deviation of a fitted Gaussian PSF in nm, a is the (backprojected) pixel size in nm, N is the number of photons detected for a given molecule, and b is the background signal level in photons calculated as the standard deviation of the residuals between the raw data and the fitted PSF model [1]. The uncertainty in the lateral position of a molecule can be approximated by the formula [3]

\left\langle(\Delta x)^{2}\right\rangle=\frac{\sigma^{2}+a^{2}/12}{N}+\frac{8% \pi\sigma^{4}b^{2}}{a^{2}N^{2}}\,. (1)

The previous equation can be further adjusted to take EM gain of EMCCD cameras into account [2], giving the expression

\left\langle(\Delta x)^{2}\right\rangle=\frac{2\sigma^{2}+a^{2}/12}{N}+\frac{8% \pi\sigma^{4}b^{2}}{a^{2}N^{2}}\,. (2)

In the 3D case, the localization uncertainty of molecular positions in the lateral direction is determined according to Equations (2) or (1), where we use \sigma^{2}=\sigma_{1}\left(\theta_{z}\right)\sigma_{2}\left(\theta_{z}\right). In the axial direction, we use a constant, user-specified value.

References

  • [1] P. Křížek, I. Raška and G. M. Hagen(2011) Minimizing detection errors in single molecule localization microscopy, Optics Express 19 (4), pp. 3226–35. External Links: Document. Cited by: Localization uncertainty.
  • [2] T. Quan, S. Zeng and Z.-L. Huang(2010) Localization capability and limitation of electron-multiplying charge-coupled, scientific complementary metal-oxide semiconductor, and charge-coupled devices for superresolution imaging, Journal of Biomedical Optics 15 (6), pp. 066005. External Links: Document. Cited by: Localization uncertainty.
  • [3] R. E. Thompson, D. R. Larson and W. W. Webb(2002) Precise nanometer localization analysis for individual fluorescent probes, Biophysical Journal 82 (5), pp. 2775–83. External Links: Document. Cited by: Localization uncertainty.