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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 24461–24476

Accuracy of the Gaussian Point Spread Function model in 2D localization microscopy

Sjoerd Stallinga and Bernd Rieger  »View Author Affiliations

Optics Express, Vol. 18, Issue 24, pp. 24461-24476 (2010)

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The Gaussian function is simple and easy to implement as Point Spread Function (PSF) model for fitting the position of fluorescent emitters in localization microscopy. Despite its attractiveness the appropriateness of the Gaussian is questionable as it is not based on the laws of optics. Here we study the effect of emission dipole orientation in conjunction with optical aberrations on the localization accuracy of position estimators based on a Gaussian model PSF. Simulated image spots, calculated with all effects of high numerical aperture, interfaces between media, polarization, dipole orientation and aberrations taken into account, were fitted with a Gaussian PSF based Maximum Likelihood Estimator. For freely rotating dipole emitters it is found that the Gaussian works fine. The same, theoretically optimum, localization accuracy is found as if the true PSF were a Gaussian, even for aberrations within the usual tolerance limit of high-end optical imaging systems such as microscopes (Marechal’s diffraction limit). For emitters with a fixed dipole orientation this is not the case. Localization errors are found that reach up to 40 nm for typical system parameters and aberration levels at the diffraction limit. These are systematic errors that are independent of the total photon count in the image. The Gaussian function is therefore inappropriate, and more sophisticated PSF models are a practical necessity.

© 2010 Optical Society of America

OCIS Codes
(100.6640) Image processing : Superresolution
(110.2990) Imaging systems : Image formation theory
(180.2520) Microscopy : Fluorescence microscopy

ToC Category:
Imaging Systems

Original Manuscript: August 17, 2010
Revised Manuscript: October 18, 2010
Manuscript Accepted: October 24, 2010
Published: November 9, 2010

Sjoerd Stallinga and Bernd Rieger, "Accuracy of the Gaussian Point Spread Function model in 2D localization microscopy," Opt. Express 18, 24461-24476 (2010)

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  1. D. Evanko, "Primer: fluorescence imaging under the diffraction limit," Nat. Methods 6, 19-20 (2009). [CrossRef]
  2. S. W. Hell, "Microscopy and its focal switch," Nat. Methods 6, 24-32 (2009). [CrossRef] [PubMed]
  3. S. W. Hell, "Far-Field Optical Nanoscopy," Science 316, 1153-1158 (2007). [CrossRef] [PubMed]
  4. E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, "Imaging Intracellular Fluorescent Proteins at Nanometer Resolution," Science 313, 1643-1645 (2006). [CrossRef]
  5. K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, "Superresolution by localization of quantum dots using blinking statistics," Opt. Express 13, 7052-7062 (2005). [CrossRef] [PubMed]
  6. M. J. Rust, M. Bates, and X. Zhuang, "Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM)," Nat. Methods 3, 793-795 (2006). [CrossRef] [PubMed]
  7. J. Flling, M. Bossi, H. Bock, R. Medda, C. A. Wurm, B. Hein, S. Jakobs, C. Eggeling, and S. W. Hell, "Fluorescence nanoscopy by ground-state depletion and single-molecule return," Nat. Methods 5, 943-945 (2008). [CrossRef]
  8. A. Egner, C. Geisler, C. von Middendorff, H. Bock, D. Wenzel, R. Medda, M. Andresen, A. C. Stiel, S. Jakobs, C. Eggeling, A. Schnle, and S. W. Hell, "Fluorescence nanoscopy in whole cells by asynchronous localization of photoswitching emitters," Biophys. J. 93, 3285-3290 (2007). [CrossRef] [PubMed]
  9. M. Heilemann, S. van de Linde, M. Schttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, "Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes," Angew. Chem. Int. Ed. Engl. 47, 6172-6176 (2008). [CrossRef] [PubMed]
  10. A. P. Bartko, and R. M. Dickson, "Imaging three-dimensional single molecule orientations," J. Phys. Chem. B 103, 11237-11241 (1999). [CrossRef]
  11. P. Dedecker, B. Muls, J. Hofkens, J. Enderlein, and J. Hotta, "Orientational effects in the excitation and deexcitation of single molecules interacting with donut-mode laser beams," Opt. Express 15, 3372-3383 (2007). [CrossRef] [PubMed]
  12. T. Wilson, R. Juskaitis, and P. D. Higdon, "The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes," Opt. Commun. 141, 298-313 (1997). [CrossRef]
  13. P. Török, P. D. Higdon, and T. Wilson, "Theory for confocal and conventional microscopes imaging small dielectric scatterers," J. Mod. Opt. 45, 1681-1698 (1998). [CrossRef]
  14. O. Haeberlé, M. Ammar, H. Furukawa, K. Tenjimbayashi, and P. Török, "The point spread function of optical microscopes imaging through stratified media," Opt. Express 11, 2964-2969 (2003). [CrossRef] [PubMed]
  15. M. R. Foreman, C. M. Romero, and P. Török, "Determination of the three-dimensional orientation of single molecules," Opt. Lett. 33, 1020-1022 (2008). [CrossRef] [PubMed]
  16. J. Enderlein, E. Toprak, and P. R. Selvin, "Polarization effect on position accuracy of fluorophore localization," Opt. Express 14, 8111 (2006). [CrossRef] [PubMed]
  17. K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, "Optimized localization analysis for single molecule tracking and super-resolution microscopy," Nat. Methods 7, 377-381 (2010). [CrossRef] [PubMed]
  18. R. J. Ober, S. Ram, and E. S. Ward, "Localization Accuracy in Single-Molecule Microscopy," Biophys. J. 86, 1185-1200 (2004). [CrossRef] [PubMed]
  19. C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, "Fast, single-molecule localization that achieves theoretically minimum uncertainty," Nat. Methods 7, 373-375 (2010). [CrossRef] [PubMed]
  20. S. Stallinga, "Axial birefringence and the light distribution close to focus," J. Opt. Soc. Am. A 18, 2846-2859 (2001). [CrossRef]
  21. S. Stallinga, "Light distribution close to focus in biaxially birefringent media," J. Opt. Soc. Am. A 21, 1785-1798 (2004). [CrossRef]
  22. M. R. Foreman, S. S. Sherif, and P. Török, "Photon statistics in single molecule orientational imaging," Opt. Express 15, 13597-13606 (2007). [CrossRef] [PubMed]
  23. B. Zhang, J. Zerubia, and J.-C. Olivo-Marin, "Gaussian approximations of fluorescence microscope point-spread function models," Appl. Opt. 46, 1819-1829 (2007). [CrossRef] [PubMed]
  24. J. P. McGuire, Jr., and R. A. Chipman, "Polarization aberrations. 1. Rotationally symmetric optical systems," Appl. Opt. 33, 5080-5100 (1994). [CrossRef] [PubMed]
  25. J. P. McGuire, Jr., and R. A. Chipman, "Polarization aberrations. 2. Tilted and decentered optical systems," Appl. Opt. 33, 5101-5107 (1994). [CrossRef] [PubMed]
  26. S. Stallinga, "Compact description of substrate-related aberrations in high numerical aperture optical disk readout," Appl. Opt. 44, 949-958 (2005). [CrossRef]
  27. J. L. Bakx, "Efficient computation of optical disk readout by use of the chirp z transform," Appl. Opt. 41, 4879-4903 (2002). [CrossRef]
  28. A. van den Bos, Parameter Estimation for Scientists and Engineers (Wiley & Sons, New Jersey, 2007). [CrossRef]
  29. R. E. Thompson, D. R. Larson, and W. W. Webb, "Precise nanometer localization analysis for individual fluorescent probes," Biophys. J. 82, 2775-2783 (2002). [CrossRef] [PubMed]
  30. M. F. Kijewski, S. P. Müller, and S. C. Moore, "The Barankin bound: a model of detection with location uncertainty," Proc. SPIE 1768, 153-160 (1992). [CrossRef]
  31. S. P. Müller, C. K. Abbey, F. J. Rybicki, S. C. Moore, and M. F. Kijewski, "Measures of performance in nonlinear estimation tasks: prediction of estimation performance at low signal-to-noise ratio," Phys. Med. Biol. 50, 3697-3715 (2005). [CrossRef] [PubMed]
  32. L. Holtzer, T. Meckel, and T. Schmidt, "Nanometric three-dimensional tracking of individual quantum dots in cells," Appl. Phys. Lett. 90, 053902 (2007). [CrossRef]
  33. B. Huang, W. Wang, M. Bates, and X. Zhuang, "Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy," Science 319, 810-813 (2008). [CrossRef] [PubMed]
  34. E. Toprak, H. Balci, B. H. Blehm, and P. R. Selvin, "Three-dimensional particle tracking via bifocal imaging," Nano Lett. 7, 2043-2045 (2007). [CrossRef] [PubMed]
  35. M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, "Three-dimensional sub-100nmresolution fluorescence microscopy of thick samples," Nat. Methods 5, 527-530 (2008). [CrossRef] [PubMed]
  36. M. J. Mlodzianoski, M. F. Juette, G. L. Beane, and J. Bewersdorf, "Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy," Opt. Express 17, 8264-8277 (2009). [CrossRef] [PubMed]

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