Abstract

In recent years three-dimensional (3D) super-resolution fluorescence imaging by single-molecule localization (localization microscopy) has gained considerable interest because of its simple implementation and high optical resolution. Astigmatic and biplane imaging are experimentally simple methods to engineer a 3D-specific point spread function (PSF), but existing evaluation methods have proven problematic in practical application. Here we introduce the use of cubic B-splines to model the relationship of axial position and PSF width in the above mentioned approaches and compare the performance with existing methods. We show that cubic B-splines are the first method that can combine precision, accuracy and simplicity.

© 2014 Optical Society of America

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2012

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

2011

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, H. Shroff, “Confined activation and subdiffractive localization enables whole-cell palm with genetically expressed probes,” Nat. Methods 8, 327–333 (2011).
[CrossRef] [PubMed]

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

D. Baddeley, M. Cannell, C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4, 589–598 (2011).
[CrossRef]

2010

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (2010).
[CrossRef] [PubMed]

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

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

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

2009

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

2008

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

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[CrossRef] [PubMed]

2007

M. Bates, B. Huang, G. T. Dempsey, X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

L. Holtzer, T. Meckel, T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

2006

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

S. T. Hess, T. P. Girirajan, 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, X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (storm),” Nat. Methods 3, 793–795 (2006).
[CrossRef] [PubMed]

2002

R. E. Thompson, D. R. Larson, W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

2001

M. K. Cheezum, W. F. Walker, W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

1994

H. Kao, A. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

1965

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Aufmkolk, S.

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

S. Wolter, S. Proppert, S. Aufmkolk, A. Lampe, T. Klein, “rapid STORM manual,” http://www.super-resolution.de/home/rapidstorm/ (2012).

Baddeley, D.

D. Baddeley, M. Cannell, C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4, 589–598 (2011).
[CrossRef]

Bates, M.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

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

Bennett, B. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Betzig, E.

H. Shroff, C. G. Galbraith, J. A. Galbraith, E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Bewersdorf, J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Biteen, J. S.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[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, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Booth, M.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

Cannell, M.

D. Baddeley, M. Cannell, C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4, 589–598 (2011).
[CrossRef]

Cheezum, M. K.

M. K. Cheezum, W. F. Walker, W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Churchman, L. S.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Dabauvalle, M.-C.

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

Davidson, M. W.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, H. Shroff, “Confined activation and subdiffractive localization enables whole-cell palm with genetically expressed probes,” Nat. Methods 8, 327–333 (2011).
[CrossRef] [PubMed]

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (2010).
[CrossRef] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Davies, J.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

de Boor, C.

C. de Boor, A Practical Guide to Splines, Applied Mathematical Sciences (Springer, 1978).
[CrossRef]

Dempsey, G. T.

M. Bates, B. Huang, G. T. Dempsey, X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

Fetter, R. D.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

Flyvbjerg, H.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Fornasiero, E. F.

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

Galassi, M.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

Galbraith, C. G.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[CrossRef] [PubMed]

Galbraith, J. A.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[CrossRef] [PubMed]

Ghitani, A.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, H. Shroff, “Confined activation and subdiffractive localization enables whole-cell palm with genetically expressed probes,” Nat. Methods 8, 327–333 (2011).
[CrossRef] [PubMed]

Gillette, J. M.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

Girirajan, T. P.

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

Gough, B.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

Gould, T. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Guilford, W. H.

M. K. Cheezum, W. F. Walker, W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Heidbreder, M.

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

Heilemann, M.

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

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

Henriques, R.

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

Hess, H. F.

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (2010).
[CrossRef] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Hess, S. T.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

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

Holm, T.

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

Holtzer, L.

L. Holtzer, T. Meckel, T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Huang, B.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

Juette, M. F.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Jungman, G.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

Kanchanawong, P.

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (2010).
[CrossRef] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

Kao, H.

H. Kao, A. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

Kasper, R.

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

Klein, T.

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

S. Wolter, S. Proppert, S. Aufmkolk, A. Lampe, T. Klein, “rapid STORM manual,” http://www.super-resolution.de/home/rapidstorm/ (2012).

Lampe, A.

S. Wolter, S. Proppert, S. Aufmkolk, A. Lampe, T. Klein, “rapid STORM manual,” http://www.super-resolution.de/home/rapidstorm/ (2012).

Larson, D. R.

R. E. Thompson, D. R. Larson, W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

Lelek, M.

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

Lessard, M. D.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Levine, M.

S. McKinley, M. Levine, Cubic Spline Interpolation (College of the Redwoods, 1999).

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Liu, N.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Lord, S. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Löschberger, A.

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

Manley, S.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

Mason, M. D.

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

McKinley, S.

S. McKinley, M. Levine, Cubic Spline Interpolation (College of the Redwoods, 1999).

Mead, R.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Meckel, T.

L. Holtzer, T. Meckel, T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Mhlanga, M. M.

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

Mlodzianoski, M. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Moerner, W. E.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Mortensen, K. I.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Mukherjee, A.

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

Nagpure, B. S.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods 5, 527–529 (2008).
[CrossRef] [PubMed]

Nelder, J. A.

J. A. Nelder, R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Pasapera, A. M.

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (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, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Pavani, S. R. P.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Piestun, R.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Proppert, S.

S. Wolter, S. Proppert, S. Aufmkolk, A. Lampe, T. Klein, “rapid STORM manual,” http://www.super-resolution.de/home/rapidstorm/ (2012).

Ramko, E. B.

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (2010).
[CrossRef] [PubMed]

Rieger, B.

Rossi, F.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

Rust, M. J.

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

Sauer, M.

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

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

Schmidt, T.

L. Holtzer, T. Meckel, T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Schüttpelz, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

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

Seefeldt, B.

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

Shroff, H.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, H. Shroff, “Confined activation and subdiffractive localization enables whole-cell palm with genetically expressed probes,” Nat. Methods 8, 327–333 (2011).
[CrossRef] [PubMed]

H. Shroff, C. G. Galbraith, J. A. Galbraith, E. Betzig, “Live-cell photoactivated localization microscopy of nanoscale adhesion dynamics,” Nat. Methods 5, 417–423 (2008).
[CrossRef] [PubMed]

Shtengel, G.

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (2010).
[CrossRef] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

Soeller, C.

D. Baddeley, M. Cannell, C. Soeller, “Three-dimensional sub-100 nm super-resolution imaging of biological samples using a phase ramp in the objective pupil,” Nano Res. 4, 589–598 (2011).
[CrossRef]

Sougrat, R.

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[CrossRef] [PubMed]

Spudich, J. A.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7, 377–381 (2010).
[CrossRef] [PubMed]

Stallinga, S.

Theiler, J.

M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi, Gnu Scientific Library: Reference Manual (Network Theory Ltd., 2003).

Thompson, M. A.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Thompson, R. E.

R. E. Thompson, D. R. Larson, W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

Tinnefeld, P.

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

Tscherepanow, M.

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

Twieg, R. J.

S. R. P. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, W. E. Moerner, “Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function,” Proc. Natl. Acad. Sci. U. S. A. 106, 2995–2999 (2009).
[CrossRef] [PubMed]

Valtorta, F.

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

van de Linde, S.

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

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

Vaziri, A.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, H. Shroff, “Confined activation and subdiffractive localization enables whole-cell palm with genetically expressed probes,” Nat. Methods 8, 327–333 (2011).
[CrossRef] [PubMed]

Verkman, A.

H. Kao, A. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

Walker, W. F.

M. K. Cheezum, W. F. Walker, W. H. Guilford, “Quantitative comparison of algorithms for tracking single fluorescent particles,” Biophys. J. 81, 2378–2388 (2001).
[CrossRef] [PubMed]

Wang, W.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

Waterman, C. M.

P. Kanchanawong, G. Shtengel, A. M. Pasapera, E. B. Ramko, M. W. Davidson, H. F. Hess, C. M. Waterman, “Nanoscale architecture of integrin-based cell adhesions,” Nature 468, 580–584 (2010).
[CrossRef] [PubMed]

G. Shtengel, J. A. Galbraith, C. G. Galbraith, J. Lippincott-Schwartz, J. M. Gillette, S. Manley, R. Sougrat, C. M. Waterman, P. Kanchanawong, M. W. Davidson, R. D. Fetter, H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. U. S. A. 106, 3125–3130 (2009).
[CrossRef] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J. 82, 2775–2783 (2002).
[CrossRef] [PubMed]

Wolter, S.

S. Wolter, A. Löschberger, T. Holm, S. Aufmkolk, M.-C. Dabauvalle, S. van de Linde, M. Sauer, “rapid STORM: accurate, fast open-source software for localization microscopy,” Nat. Methods 9, 1040–1041 (2012).
[CrossRef] [PubMed]

S. van de Linde, A. Löschberger, T. Klein, M. Heidbreder, S. Wolter, M. Heilemann, M. Sauer, “Direct stochastic optical reconstruction microscopy with standard fluorescent probes,” Nat. Protoc. 6, 991–1009 (2011).
[CrossRef] [PubMed]

S. Wolter, M. Schüttpelz, M. Tscherepanow, S. van de Linde, M. Heilemann, M. Sauer, “Real-time computation of subdiffraction-resolution fluorescence images,” J. Microsc. 237, 12–22 (2010).
[CrossRef] [PubMed]

S. Wolter, S. Proppert, S. Aufmkolk, A. Lampe, T. Klein, “rapid STORM manual,” http://www.super-resolution.de/home/rapidstorm/ (2012).

York, A. G.

A. G. York, A. Ghitani, A. Vaziri, M. W. Davidson, H. Shroff, “Confined activation and subdiffractive localization enables whole-cell palm with genetically expressed probes,” Nat. Methods 8, 327–333 (2011).
[CrossRef] [PubMed]

Zhuang, X.

B. Huang, W. Wang, M. Bates, X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science 319, 810–813 (2008).
[CrossRef] [PubMed]

M. Bates, B. Huang, G. T. Dempsey, X. Zhuang, “Multicolor super-resolution imaging with photo-switchable fluorescent probes,” Science 317, 1749–1753 (2007).
[CrossRef] [PubMed]

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

Zimmer, C.

R. Henriques, M. Lelek, E. F. Fornasiero, F. Valtorta, C. Zimmer, M. M. Mhlanga, “QuickPALM: 3D real-time photoactivation nanoscopy image processing in ImageJ,” Nat. Methods 7, 339–340 (2010).
[CrossRef] [PubMed]

Angew. Chem. Int. Ed.

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

Appl. Phys. Lett.

L. Holtzer, T. Meckel, T. Schmidt, “Nanometric three-dimensional tracking of individual quantum dots in cells,” Appl. Phys. Lett. 90, 053902 (2007).
[CrossRef]

Biophys. J.

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

H. Kao, A. Verkman, “Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position,” Biophys. J. 67, 1291–1300 (1994).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematic view of the microscope setups used in our experiments. The laser is focused on the back focal plane of a high NA objective to achieve epi-fluorescence illumination. The fluorescence signal passes the 45° dichroic, is imaged on the EMCCD camera by lenses L1 and L2 (setup 1) or directly imaged on a sCMOS camera (setup 2). The PSF is shaped by a cylindrical lens (CL).

Fig. 2
Fig. 2

Construction of a cubic B-spline. The black crosses represent data points that are to be interpolated. The rainbow-colored functions at the bottom of the diagram are unscaled instances of the cubic B-spline basis functions si,4(x) (i = 0, 1,...,11) with the n = 9 knots indicated by black circles. Evaluation of Eq. (6) leads to amplitude factors for each basis function, and their sum is the interpolation represented by the red curve.

Fig. 3
Fig. 3

Typical sigma plots as obtained with (a) oil-immersion objectives or (b) water-immersion objectives. (a) shows localizations of a single TetraSpeck, and (b) shows a superposition of 27 TetraSpecks. Sample 1 and 2 in Fig. 4 were evaluated with the splines shown in (a) and (b), respectively. Note the strong axial asymmetry in (a), which originates from the different diffractive indices of oil and water at the glass-specimen-interface. Both samples show the typical oscillation behavior of the polynomial fits around the better-fitting cubic B-splines.

Fig. 4
Fig. 4

Axial localization performance. The figure shows data for two samples. The PSF snapshots (top of figure) were taken from the data presented and correspond to the z-position indicated on the abscissa. Sample 1 is a bright microsphere imaged with oil immersion, and Sample 2 is an emitter with fluorophore-like photon yield in water immersion. In Sample 1, the same bead was used for calibration and testing. In Sample 2, one bead was calibrated, and a different bead from the same acquisition tested. In each subplot, the fitted z position was plotted against the z ground-truth extracted from the piezo movement, and data within 100 nm intervals was averaged. The table shows the root mean square deviation (RMSD) of points and ground truth, and the autocorrelation of the deviation at a lag time of one frame (R(1)). Highly autocorrelated deviations indicate systematic errors, i.e., a low accuracy.

Fig. 5
Fig. 5

Comparison of complexity and axial localization error for the 3D inference methods. The complexity is given comparatively in arbitrary units, determined from a difficulty ranking of the steps in each procedure. We judged user-visible complexity as steps that have a high likelihood of error or require manual intervention. The values were chosen on a relative scale according to our experience with the methods’ application during the preparation of this article. The axial localization error, given as the RMSD of localizations from the z ground truth, characterizes the precision achievable with the method. The cubic B-spline method combines the good precision of the polynomial method with the simpleness of the sigma difference calibration.

Fig. 6
Fig. 6

Difference between the fitted z-coordinate and the known z-position of the objective-piezo. The calibration measurement was obtained with a Nikon N-STORM and calibrated according to the Nikon routine (red squares). For comparison, we calibrated the same measurement with the fit algorithm of rapidSTORM and cubic B-spline interpolation (gray dots). For both evaluations, the standard deviation is indicated by the respective red and gray regions. We suppose, that the data acquisition was corrupted by sample drift and multi-bead conglomerates. Thus we assume that the mean real zero-plane is around z = −50 nm (solid black line, coined “apparent zero” in the plot).

Equations (6)

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G = B + A 2 π σ x σ y exp [ 1 2 ( ( x x 0 ) 2 σ x 2 + ( y y 0 ) 2 σ y 2 ) ]
σ ( x , y ) 2 = σ 0 , ( x , y ) 2 + a ( x , y ) ( z z 0 , ( x , y ) ) 2
σ ( x , y ) 2 = σ 0 , ( x , y ) 2 ( 1 + i = 1 4 ( z z 0 , ( x , y ) Δ σ i , ( x , y ) ) i ) i )
S ( z ) = i s i ( z ) c i
X j i = s i ( z j )
c = ( X T X ) 1 X T σ

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