Abstract

Single molecule localization based super-resolution imaging techniques require repeated localization of many single emitters. We describe a method that uses the maximum likelihood estimator to localize multiple emitters simultaneously within a single, two-dimensional fitting sub-region, yielding an order of magnitude improvement in the tolerance of the analysis routine with regards to the single-frame active emitter density. Multiple-emitter fitting enables the overall performance of single-molecule super-resolution to be improved in one or more of several metrics that result in higher single-frame density of localized active emitters. For speed, the algorithm is implemented on Graphics Processing Unit (GPU) architecture, resulting in analysis times on the order of minutes. We show the performance of multiple emitter fitting as a function of the single-frame active emitter density. We describe the details of the algorithm that allow robust fitting, the details of the GPU implementation, and the other imaging processing steps required for the analysis of data sets.

© 2011 OSA

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G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61, 345–367 (2010).
[CrossRef] [PubMed]

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190, 165–175 (2010).
[CrossRef] [PubMed]

J. Vogelsang, C. Steinhauer, C. Forthmann, I. H. Stein, B. Person-Skegro, T. Cordes, and P. Tinnefeld, “Make them blink: probes for super-resolution microscopy,” Chemphyschem 11, 2475–2490 (2010).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

S. Stallinga and B. Rieger, “Accuracy of the gaussian point spread function model in 2d localization microscopy,” Opt. Express 18, 24461–24476 (2010).
[CrossRef] [PubMed]

2009

J. Chao, S. Ram, E. S. Ward, and R. J. Ober, “A comparative study of high resolution microscopy imaging modalities using a three-dimensional resolution measure,” Opt. Express 17, 24377–24402 (2009).
[CrossRef]

A. R. Small, “Theoretical limits on errors and acquisition rates in localizing switchable fluorophores,” Biophys. J. 96, L16–L18 (2009).
[CrossRef] [PubMed]

K. R. Chi, “Microscopy: ever-increasing resolution,” Nature 462, 675–678 (2009).
[CrossRef] [PubMed]

B. Huang, M. Bates, and X. W. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[CrossRef] [PubMed]

2008

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5, 687–694 (2008).
[CrossRef] [PubMed]

M. Heilemann, S. van de Linde, M. Schuttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. 47, 6172–6176 (2008).
[CrossRef]

2007

A. Van den Bos and C. Ebooks, Parameter Estimation for Scientists and Engineers (Wiley Online Library, 2007).

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]

S. W. Hell, “Far-field optical nanoscopy,” Science 316, 1153–1158 (2007).
[CrossRef] [PubMed]

2006

S. Ram, E. S. Ward, and R. J. Ober, “Beyond rayleigh’s criterion: A resolution measure with application to single-molecule microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103, 4457–4462 (2006).
[CrossRef] [PubMed]

B. C. Lagerholm, L. Averett, G. E. Weinreb, K. Jacobson, and N. L. Thompson, “Analysis method for measuring submicroscopic distances with blinking quantum dots,” Biophys. J. 91, 3050–3060 (2006).
[CrossRef] [PubMed]

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, 1642–1645 (2006).
[CrossRef] [PubMed]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3, 793–795 (2006).
[CrossRef] [PubMed]

2005

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution with quantum dots: enhanced localization in fluorescence microscopy by exploitation of quantum dot blinking,” Biophys. J. 88, 346a–346a (2005).

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U. S. A. 102, 13081–13086 (2005).
[CrossRef] [PubMed]

2004

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101, 11298–11303 (2004).
[CrossRef] [PubMed]

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101, 6462–6465 (2004).
[CrossRef] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 1185–1200 (2004).
[CrossRef] [PubMed]

2001

P. Stoica and T. L. Marzetta, “Parameter estimation problems with singular information matrices,” IEEE Trans. Sig. Process. 49, 87–90 (2001).
[CrossRef]

1994

1992

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4pi-confocal fluorescence microscope using 2-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

1990

W. H. Press, S. L. A. Teukolsky, B. N. P. Flannery, and W. M. T. Vetterling, Numerical Recipes: FORTRAN (Cambridge University Press, 1990).

1974

J. A. Högbom, “Aperture synthesis with a non-regular distribution of interferometer baselines,” Astron. Astrophys. Suppl. 15, 417 (1974).

Averett, L.

B. C. Lagerholm, L. Averett, G. E. Weinreb, K. Jacobson, and N. L. Thompson, “Analysis method for measuring submicroscopic distances with blinking quantum dots,” Biophys. J. 91, 3050–3060 (2006).
[CrossRef] [PubMed]

Bates, M.

B. Huang, M. Bates, and X. W. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3, 793–795 (2006).
[CrossRef] [PubMed]

Bertaux, N.

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5, 687–694 (2008).
[CrossRef] [PubMed]

Betzig, E.

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Bonifacino, J. S.

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Chao, J.

Chi, K. R.

K. R. Chi, “Microscopy: ever-increasing resolution,” Nature 462, 675–678 (2009).
[CrossRef] [PubMed]

Cordes, T.

J. Vogelsang, C. Steinhauer, C. Forthmann, I. H. Stein, B. Person-Skegro, T. Cordes, and P. Tinnefeld, “Make them blink: probes for super-resolution microscopy,” Chemphyschem 11, 2475–2490 (2010).
[CrossRef] [PubMed]

Davidson, M.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61, 345–367 (2010).
[CrossRef] [PubMed]

Davidson, M. W.

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Ebooks, C.

A. Van den Bos and C. Ebooks, Parameter Estimation for Scientists and Engineers (Wiley Online Library, 2007).

Flannery, B. N. P.

W. H. Press, S. L. A. Teukolsky, B. N. P. Flannery, and W. M. T. Vetterling, Numerical Recipes: FORTRAN (Cambridge University Press, 1990).

Forthmann, C.

J. Vogelsang, C. Steinhauer, C. Forthmann, I. H. Stein, B. Person-Skegro, T. Cordes, and P. Tinnefeld, “Make them blink: probes for super-resolution microscopy,” Chemphyschem 11, 2475–2490 (2010).
[CrossRef] [PubMed]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[CrossRef] [PubMed]

Gordon, M. P.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101, 6462–6465 (2004).
[CrossRef] [PubMed]

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. U. S. A. 102, 13081–13086 (2005).
[CrossRef] [PubMed]

Ha, T.

M. P. Gordon, T. Ha, and P. R. Selvin, “Single-molecule high-resolution imaging with photobleaching,” Proc. Natl. Acad. Sci. U.S.A. 101, 6462–6465 (2004).
[CrossRef] [PubMed]

Heilemann, M.

M. Heilemann, S. van de Linde, M. Schuttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. 47, 6172–6176 (2008).
[CrossRef]

Heintzmann, R.

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190, 165–175 (2010).
[CrossRef] [PubMed]

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution with quantum dots: enhanced localization in fluorescence microscopy by exploitation of quantum dot blinking,” Biophys. J. 88, 346a–346a (2005).

Hell, S.

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4pi-confocal fluorescence microscope using 2-photon excitation,” Opt. Commun. 93, 277–282 (1992).
[CrossRef]

Hell, S. W.

Hess, H. F.

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[CrossRef] [PubMed]

Högbom, J. A.

J. A. Högbom, “Aperture synthesis with a non-regular distribution of interferometer baselines,” Astron. Astrophys. Suppl. 15, 417 (1974).

Huang, B.

B. Huang, M. Bates, and X. W. Zhuang, “Super-resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[CrossRef] [PubMed]

Jacobson, K.

B. C. Lagerholm, L. Averett, G. E. Weinreb, K. Jacobson, and N. L. Thompson, “Analysis method for measuring submicroscopic distances with blinking quantum dots,” Biophys. J. 91, 3050–3060 (2006).
[CrossRef] [PubMed]

Joseph, N.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7, 373–U52 (2010).
[CrossRef] [PubMed]

Jovin, T. M.

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution with quantum dots: enhanced localization in fluorescence microscopy by exploitation of quantum dot blinking,” Biophys. J. 88, 346a–346a (2005).

Kasper, R.

M. Heilemann, S. van de Linde, M. Schuttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. 47, 6172–6176 (2008).
[CrossRef]

Lagerholm, B. C.

B. C. Lagerholm, L. Averett, G. E. Weinreb, K. Jacobson, and N. L. Thompson, “Analysis method for measuring submicroscopic distances with blinking quantum dots,” Biophys. J. 91, 3050–3060 (2006).
[CrossRef] [PubMed]

Leonhardt, H.

L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190, 165–175 (2010).
[CrossRef] [PubMed]

Lidke, K. A.

C. S. Smith, N. Joseph, B. Rieger, and K. A. Lidke, “Fast, single-molecule localization that achieves theoretically minimum uncertainty,” Nat. Methods 7, 373–U52 (2010).
[CrossRef] [PubMed]

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution with quantum dots: enhanced localization in fluorescence microscopy by exploitation of quantum dot blinking,” Biophys. J. 88, 346a–346a (2005).

Lindwasser, O. W.

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61, 345–367 (2010).
[CrossRef] [PubMed]

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Manley, S.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61, 345–367 (2010).
[CrossRef] [PubMed]

Marguet, D.

A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5, 687–694 (2008).
[CrossRef] [PubMed]

Marzetta, T. L.

P. Stoica and T. L. Marzetta, “Parameter estimation problems with singular information matrices,” IEEE Trans. Sig. Process. 49, 87–90 (2001).
[CrossRef]

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[CrossRef] [PubMed]

Mets, L.

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101, 11298–11303 (2004).
[CrossRef] [PubMed]

Mukherjee, A.

M. Heilemann, S. van de Linde, M. Schuttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. 47, 6172–6176 (2008).
[CrossRef]

Ober, R. J.

J. Chao, S. Ram, E. S. Ward, and R. J. Ober, “A comparative study of high resolution microscopy imaging modalities using a three-dimensional resolution measure,” Opt. Express 17, 24377–24402 (2009).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, “Beyond rayleigh’s criterion: A resolution measure with application to single-molecule microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103, 4457–4462 (2006).
[CrossRef] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 1185–1200 (2004).
[CrossRef] [PubMed]

Olenych, S.

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Olivo-Marin, J. C.

Patterson, G.

G. Patterson, M. Davidson, S. Manley, and J. Lippincott-Schwartz, “Superresolution imaging using single-molecule localization,” Annu. Rev. Phys. Chem. 61, 345–367 (2010).
[CrossRef] [PubMed]

Patterson, G. H.

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, 1642–1645 (2006).
[CrossRef] [PubMed]

Person-Skegro, B.

J. Vogelsang, C. Steinhauer, C. Forthmann, I. H. Stein, B. Person-Skegro, T. Cordes, and P. Tinnefeld, “Make them blink: probes for super-resolution microscopy,” Chemphyschem 11, 2475–2490 (2010).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, S. L. A. Teukolsky, B. N. P. Flannery, and W. M. T. Vetterling, Numerical Recipes: FORTRAN (Cambridge University Press, 1990).

Qu, X. H.

X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101, 11298–11303 (2004).
[CrossRef] [PubMed]

Ram, S.

J. Chao, S. Ram, E. S. Ward, and R. J. Ober, “A comparative study of high resolution microscopy imaging modalities using a three-dimensional resolution measure,” Opt. Express 17, 24377–24402 (2009).
[CrossRef]

S. Ram, E. S. Ward, and R. J. Ober, “Beyond rayleigh’s criterion: A resolution measure with application to single-molecule microscopy,” Proc. Natl. Acad. Sci. U.S.A. 103, 4457–4462 (2006).
[CrossRef] [PubMed]

R. J. Ober, S. Ram, and E. S. Ward, “Localization accuracy in single-molecule microscopy,” Biophys. J. 86, 1185–1200 (2004).
[CrossRef] [PubMed]

Rieger, B.

S. Stallinga and B. Rieger, “Accuracy of the gaussian point spread function model in 2d localization microscopy,” Opt. Express 18, 24461–24476 (2010).
[CrossRef] [PubMed]

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L. Schermelleh, R. Heintzmann, and H. Leonhardt, “A guide to super-resolution fluorescence microscopy,” J. Cell Biol. 190, 165–175 (2010).
[CrossRef] [PubMed]

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M. Heilemann, S. van de Linde, M. Schuttpelz, R. Kasper, B. Seefeldt, A. Mukherjee, P. Tinnefeld, and M. Sauer, “Subdiffraction-resolution fluorescence imaging with conventional fluorescent probes,” Angew. Chem. Int. Ed. 47, 6172–6176 (2008).
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B. C. Lagerholm, L. Averett, G. E. Weinreb, K. Jacobson, and N. L. Thompson, “Analysis method for measuring submicroscopic distances with blinking quantum dots,” Biophys. J. 91, 3050–3060 (2006).
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X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101, 11298–11303 (2004).
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A. Serge, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes,” Nat. Methods 5, 687–694 (2008).
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X. H. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. U.S.A. 101, 11298–11303 (2004).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Proximity of emitters as a function of emitter density. The probabilities of finding N=1–5 emitters within a 8σ PSF×8σ PSF square sub-region (σ PSF = 127 nm) at different densities were calculated for a uniformly distributed population of emitters and plotted as a function of density. As the emitter density increases beyond 1 μm−2, the fraction of subregions containing single emitters reduces dramatically (red line), emphasizing the need for fitting algorithms that can accommodate multiple emitters within a single sub-region.

Fig. 2
Fig. 2

Illustration of execution steps in the multi-emitter estimation task. (a) Fitting algorithm flowchart. For a given sub-region, MFA is performed sequentially from the N = 1 emitter model to either the N max emitter model or is terminated if the maximum pixel counts in the residuum image is lower than 10 counts. (b) through (e): Demonstration of the results from each estimation task from the 1 emitter model through the 4 emitter model. The 5 emitter model fitting is not performed by the algorithm, because of the low photon counts in the deflated image.

Fig. 3
Fig. 3

Single fluorophore intensity distribution of the organic fluorophore Alexa Fluor 647 obtained from the data set described in section 4.4.1 taken in TIRF condition. The distribution is modeled as a normal distribution with μ = 800, σ = 100.

Fig. 4
Fig. 4

Performance of the precision estimate. (a) A comparison between the precision predicted from the CRLB and from the modified Fisher information matrix. A series of simulated images of two emitters at varoius separations between their centers were generated. MFA was performed on these images and the precision estimates calculated by the modified Fisher information matrices (F(θ) Estimated Std. Dev.) were compared with that obtained from the CRLB (Estimated Uncertainty CRLB), precisions obtained from the CRLB generated by emitter’s true position (Theoretical Uncertainty CRLB), and the observed standard deviation of the estimates (Observed Std. Dev.). (b) The CDF (integral of histogram) of the uncertainty estimator accuracy obtained using the modified Fisher information matrices for random placements of multiple emitters.

Fig. 5
Fig. 5

Performance versus active emitter density and intensity distribution. Shown are the results of MFA analysis of images with spatially random distributed emitters with normally distributed intensities of 300 ± 30 (a), (b), 800 ± 100 (c), (d), and 5000 ± 30 (e), (f). Localization error is calculated as the distance from the estimated position to the found position and in all cases assumes N max = 5. The median localization error is where the cumulative distribution reaches 0.5. Localization fraction is the fraction of emitters that are correctly localized as determined by being found within either 20 nm or 50 nm from the known position.

Fig. 6
Fig. 6

(a) The emitter position histogram used in generating synthetic data. (b) Sum projection of the generated image. (c) Single emitter fitting result at a density of 1 μm−2 with N max = 1. (d) Multiple emitter fitting result at a density of 1 μm−2 with N max = 5. (e) Single emitter fitting result at a density of 6 μm−2 with N max = 1. (f) Multiple emitter fitting result at a density of 6 μm−2 with N max = 5. At 1 μm−2 case, N max = 1 resulted in 12848 emitters localized while N max = 5 localized 30354 emitters. While in 6 μm−2 case, N max = 1 resulted in 519 emitters localized while N max = 5 localized 33580 emitters. The contrast of images (c) to (f) were globally adjusted across all images for optimal display.

Fig. 7
Fig. 7

Comparison of SM-SR fitting routines for imaging the actin mesh-work within a HeLa cell labeled with Alexa 647 phalloidin. Conventional TIRF microscopy, (a) and (b), compared with SM-SR images generated using both a N max = 1, (c) and (d), and N max = 5, (e) and (f). Actin rich regions, seen in top right of (b),(d),(f) are missing using single emitter routines (N max = 1) (d), but successfully fit using the MFA (N max = 5) (f). The increase in molecular density found using the MFA (N max = 5) routine also reveals a more complete depiction of the underlying actin structure, outlining possible actin corrals seen in the center of (f). Scales bars represent 5 μm in (a), (c), (e) and 1 μm in (b), (d), (f).

Tables (1)

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Table 1 Time Consumption and Performance*

Equations (13)

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PSF( x , y ) = 1 2 π σ 0 2 e ( x 2 + y 2 ) 2 σ 0 2
μ k ( x , y ) = I 0 Δ E x ( x , y ) Δ E y ( x , y ) + b 0
Δ E x ( x , y ) = 1 2 ( erf ( x x 0 + 1 2 ) 2 σ 0 erf ( x x 0 1 2 ) 2 σ 0 )
Δ E y ( x , y ) = 1 2 ( erf ( y y 0 + 1 2 ) 2 σ 0 erf ( y y 0 1 2 ) 2 σ 0 )
μ k ( x , y ) = i N I 0 Δ E x i ( x , y ) Δ E y i ( x , y ) + b 0
L ( θ | D ) = k μ k ( x , y ) d k e μ k ( x , y ) d k !
θ i θ i [ k μ k ( θ i ) θ i ( d k μ k ( θ i ) 1 ) ] [ k 2 μ k ( θ i ) θ i 2 ( d k μ k ( θ i ) 1 ) μ k ( θ i ) 2 θ i d k μ k ( θ i ) 2 ] 1
A 1 = uniform [ I , ( 2 σ P S F + 1 ) ] uniform [ I , ( 2 × ( 2 σ PSF + 1 ) ) ]
A 2 = max [ A 1 , ( 5 σ PSF ) ]
A 3 = { if A 1 A 2 1 if A 1 = A 2
LLR = 2 ln [ L ( θ ^ | D ) L ( D | D ) ]
F ( θ ) i , j = { A A + 1 I ( θ ) i , j ( i , odd ) & ( j , odd ) & ( i 1 , j 1 ) & ( i j ) A A + 1 I ( θ ) i , j ( i , even ) & ( j , even ) & ( i j ) I ( θ ) i , j other
ρ active = ρ 0 × k on k off + k on

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