Abstract

Multifocal plane microscopy (MUM) can be used to visualize biological samples in three dimensions over large axial depths and provides for the high axial localization accuracy that is needed in applications such as the three-dimensional tracking of single particles and super-resolution microscopy. This report analyzes the performance of intensity-based axial localization approaches as applied to MUM data using Fisher information calculations. In addition, a new non-parametric intensity-based axial location estimation method, Multi-Intensity Lookup Algorithm (MILA), is introduced that, unlike typical intensity-based methods that make use of a single intensity value per data image, utilizes multiple intensity values per data image in determining the axial location of a point source. MILA is shown to be robust against potential bias induced by differences in the sub-pixel location of the imaged point source. The method’s effectiveness on experimental data is also evaluated.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref] [PubMed]
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2013 (1)

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

2012 (1)

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103, 1594–1603 (2012).
[Crossref] [PubMed]

2011 (3)

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8, 1027–1036 (2011).
[Crossref] [PubMed]

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36, 202–204 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (3)

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

A. V. Abraham, S. Ram, J. Chao, E. S. Ward, and R. J. Ober, “Quantitative study of single molecule location estimation techniques,” Opt. Express 17, 23352–23373 (2009).
[Crossref]

2008 (1)

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

2007 (2)

T. M. Watanabe, T. Sato, K. Gonda, and H. Higuchi, “Three-dimensional nanometry of vesicle transport in living cells using dual-focus imaging optics,” Biochem. Biophys. Res. Commun. 359, 1–7 (2007).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. Ward, and R. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[Crossref]

2004 (1)

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans. Nanobioscience 3, 237–242 (2004).
[Crossref]

1994 (1)

H. P. Kao and A. S. 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]

Abraham, A. V.

Abrahamsson, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Agard, D. A.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Badieirostami, M.

Bargmann, C. I.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Bates, M.

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8, 1027–1036 (2011).
[Crossref] [PubMed]

Biteen, J. S.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

Chao, J.

A. V. Abraham, S. Ram, J. Chao, E. S. Ward, and R. J. Ober, “Quantitative study of single molecule location estimation techniques,” Opt. Express 17, 23352–23373 (2009).
[Crossref]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. Ward, and R. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[Crossref]

Chen, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Chen, K. H.

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8, 1027–1036 (2011).
[Crossref] [PubMed]

Dada, A. C.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

Dahan, M.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Dalgarno, H. I.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

P. A. Dalgarno, H. I. Dalgarno, A. Putoud, R. Lambert, L. Paterson, D. C. Logan, D. P. Towers, R. J. Warburton, and A. H. Greenaway, “Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy,” Opt. Express 18, 877–884 (2010).
[Crossref] [PubMed]

Dalgarno, P. A.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

P. A. Dalgarno, H. I. Dalgarno, A. Putoud, R. Lambert, L. Paterson, D. C. Logan, D. P. Towers, R. J. Warburton, and A. H. Greenaway, “Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy,” Opt. Express 18, 877–884 (2010).
[Crossref] [PubMed]

Darzacq, C. D.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Darzacq, X.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Davidson, M. W.

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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Davis, I.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

Dempsey, G. T.

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8, 1027–1036 (2011).
[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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Gibson, G. J.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Gonda, K.

T. M. Watanabe, T. Sato, K. Gonda, and H. Higuchi, “Three-dimensional nanometry of vesicle transport in living cells using dual-focus imaging optics,” Biochem. Biophys. Res. Commun. 359, 1–7 (2007).
[Crossref] [PubMed]

Greenaway, A. H.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

P. A. Dalgarno, H. I. Dalgarno, A. Putoud, R. Lambert, L. Paterson, D. C. Logan, D. P. Towers, R. J. Warburton, and A. H. Greenaway, “Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy,” Opt. Express 18, 877–884 (2010).
[Crossref] [PubMed]

Gustafsson, M. G. L.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Hajj, B.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Hess, H. F.

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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Higuchi, H.

T. M. Watanabe, T. Sato, K. Gonda, and H. Higuchi, “Three-dimensional nanometry of vesicle transport in living cells using dual-focus imaging optics,” Biochem. Biophys. Res. Commun. 359, 1–7 (2007).
[Crossref] [PubMed]

Kanchanawong, P.

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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Kao, H. P.

H. P. Kao and A. S. 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]

Katsov, A. Y.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Kim, D.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103, 1594–1603 (2012).
[Crossref] [PubMed]

Lambert, R.

Lee, S. F.

Lew, M. D.

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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Liu, N.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Logan, D. C.

Lord, S. J.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Mizuguchi, G.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Moerner, W. E.

M. D. Lew, S. F. Lee, M. Badieirostami, and W. E. Moerner, “Corkscrew point spread function for far-field three-dimensional nanoscale localization of pointlike objects,” Opt. Lett. 36, 202–204 (2011).
[Crossref] [PubMed]

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Mueller, F.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Ober, R.

S. Ram, J. Chao, P. Prabhat, E. Ward, and R. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[Crossref]

Ober, R. J.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103, 1594–1603 (2012).
[Crossref] [PubMed]

A. V. Abraham, S. Ram, J. Chao, E. S. Ward, and R. J. Ober, “Quantitative study of single molecule location estimation techniques,” Opt. Express 17, 23352–23373 (2009).
[Crossref]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans. Nanobioscience 3, 237–242 (2004).
[Crossref]

Parton, R. M.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

Paterson, L.

Pavani, S. R.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Piestun, R.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Prabhat, P.

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. Ward, and R. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[Crossref]

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans. Nanobioscience 3, 237–242 (2004).
[Crossref]

Putoud, A.

Ram, S.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103, 1594–1603 (2012).
[Crossref] [PubMed]

A. V. Abraham, S. Ram, J. Chao, E. S. Ward, and R. J. Ober, “Quantitative study of single molecule location estimation techniques,” Opt. Express 17, 23352–23373 (2009).
[Crossref]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. Ward, and R. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[Crossref]

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans. Nanobioscience 3, 237–242 (2004).
[Crossref]

Sato, T.

T. M. Watanabe, T. Sato, K. Gonda, and H. Higuchi, “Three-dimensional nanometry of vesicle transport in living cells using dual-focus imaging optics,” Biochem. Biophys. Res. Commun. 359, 1–7 (2007).
[Crossref] [PubMed]

Shtengel, 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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Soule, P.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Stallinga, S.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Thompson, M. A.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Towers, C. E.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

Towers, D. P.

Twieg, R. J.

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Vaughan, J. C.

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8, 1027–1036 (2011).
[Crossref] [PubMed]

Verkman, A. S.

H. P. Kao and A. S. 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]

Warburton, R. J.

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

P. A. Dalgarno, H. I. Dalgarno, A. Putoud, R. Lambert, L. Paterson, D. C. Logan, D. P. Towers, R. J. Warburton, and A. H. Greenaway, “Multiplane imaging and three dimensional nanoscale particle tracking in biological microscopy,” Opt. Express 18, 877–884 (2010).
[Crossref] [PubMed]

Ward, E.

S. Ram, J. Chao, P. Prabhat, E. Ward, and R. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[Crossref]

Ward, E. S.

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103, 1594–1603 (2012).
[Crossref] [PubMed]

A. V. Abraham, S. Ram, J. Chao, E. S. Ward, and R. J. Ober, “Quantitative study of single molecule location estimation techniques,” Opt. Express 17, 23352–23373 (2009).
[Crossref]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans. Nanobioscience 3, 237–242 (2004).
[Crossref]

Watanabe, T. M.

T. M. Watanabe, T. Sato, K. Gonda, and H. Higuchi, “Three-dimensional nanometry of vesicle transport in living cells using dual-focus imaging optics,” Biochem. Biophys. Res. Commun. 359, 1–7 (2007).
[Crossref] [PubMed]

Waterman, C. 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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

Wisniewski, J.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

Wu, C.

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Zhuang, X.

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8, 1027–1036 (2011).
[Crossref] [PubMed]

Biochem. Biophys. Res. Commun. (1)

T. M. Watanabe, T. Sato, K. Gonda, and H. Higuchi, “Three-dimensional nanometry of vesicle transport in living cells using dual-focus imaging optics,” Biochem. Biophys. Res. Commun. 359, 1–7 (2007).
[Crossref] [PubMed]

Biophys. J. (3)

S. Ram, D. Kim, R. J. Ober, and E. S. Ward, “3D single molecule tracking with multifocal plane microscopy reveals rapid intercellular transferrin transport at epithelial cell barriers,” Biophys. J. 103, 1594–1603 (2012).
[Crossref] [PubMed]

S. Ram, P. Prabhat, J. Chao, E. S. Ward, and R. J. Ober, “High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells,” Biophys. J. 95, 6025–6043 (2008).
[Crossref] [PubMed]

H. P. Kao and A. S. 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]

IEEE Trans. Nanobioscience (1)

P. Prabhat, S. Ram, E. S. Ward, and R. J. Ober, “Simultaneous imaging of different focal planes in fluorescence microscopy for the study of cellular dynamics in three dimensions,” IEEE Trans. Nanobioscience 3, 237–242 (2004).
[Crossref]

J. R. Soc. Interface (1)

H. I. Dalgarno, P. A. Dalgarno, A. C. Dada, C. E. Towers, G. J. Gibson, R. M. Parton, I. Davis, R. J. Warburton, and A. H. Greenaway, “Nanometric depth resolution from multi-focal images in microscopy,” J. R. Soc. Interface 8, 942–951 (2011).
[Crossref] [PubMed]

Nat. Methods (2)

G. T. Dempsey, J. C. Vaughan, K. H. Chen, M. Bates, and X. Zhuang, “Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging,” Nat. Methods 8, 1027–1036 (2011).
[Crossref] [PubMed]

S. Abrahamsson, J. Chen, B. Hajj, S. Stallinga, A. Y. Katsov, J. Wisniewski, G. Mizuguchi, P. Soule, F. Mueller, C. D. Darzacq, X. Darzacq, C. Wu, C. I. Bargmann, D. A. Agard, M. Dahan, and M. G. L. Gustafsson, “Fast multicolor 3D imaging using aberration-corrected multifocus microscopy,” Nat. Methods 10, 60–63 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Proc. Natl. Acad. Sci. USA. (2)

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, and H. F. Hess, “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” Proc. Natl. Acad. Sci. USA. 106, 3125–3130 (2009).
[Crossref] [PubMed]

S. R. Pavani, M. A. Thompson, J. S. Biteen, S. J. Lord, N. Liu, R. J. Twieg, R. Piestun, and 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. USA. 106, 2995–2999 (2009).
[Crossref] [PubMed]

Proc. SPIE (1)

S. Ram, J. Chao, P. Prabhat, E. Ward, and R. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D (2007).
[Crossref]

Other (3)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

“FandPLimitTool,” http://wardoberlab.com/software/fandplimittool .

“EstimationTool,” http://wardoberlab.com/software/estimationtool .

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Figures (8)

Fig. 1
Fig. 1

A: Schematic representation of the method of extracting multiple summed intensity values from MUM images of a point source. B: Plot of normalized intensities for a typical point source as a function of its axial position. Vertical dotted lines indicate the position of the focal planes in the object space (focal plane 1 is the dotted line on the left).

Fig. 2
Fig. 2

Plots of the standard PLAM and SPB-PLAMs for the axial location of a simulated point source as a function of its axial location. The standard deviation of 1000 axial location estimates obtained using the ratiometric method is also shown. Sub-panels show plots of these values in simulations with different focal plane spacings in a two-plane MUM configuration. PLAM calculations were performed with the following numerical values: magnification M = 100, numerical aperture na = 1.45, pixel size: 16 µm 16 µm, ROI size: 13 × 13 pixels. Here, the 16-µm, 48-µm and 80-µm sizes of the summed-pixels × correspond to areas that cover sub-ROIs of 1 × 1, 3 × 3 and 5 × 5 pixels, respectively, that are centered in the 13 × 13-pixel ROI. The point source was simulated such that a mean of 4000 photons were detected per image. The ratiometric method utilizes the entire 13 × 13-pixel ROI for its Gaussian fitting and its calibration data was generated using data from one simulated point source with all the same parameters except that a mean of 10000 photons were detected per image. Standard deviation values for the ratiometric method are only plotted for axial positions where the mean of the estimates does not deviate more than 50 nm from the simulated axial position. Vertical lines mark the positions of the focal planes in the object space.

Fig. 3
Fig. 3

A: The top panel shows the standard deviation of axial location estimates, obtained from 3 non-parametric algorithms when applied to 1000 pairs of simulated two-plane MUM images of a point source from which a mean of 4000 photons were detected per image, as a function of the axial position of the point source. The bottom panel shows the deviation of the mean of the same estimates from the true axial position of the simulated point source. The red line shows the values obtained using MILA (r = 1, 2) and the green line represents values obtained using the ratiometric method. The blue line shows values obtained using MILA (r = 1), which uses only one sub-ROI. B: Plots of the SPB-PLAM and the standard deviation of MILA estimates for the axial location of a simulated point source calculated for r = 1, 2 (top) and r = 1 (bottom). C: Plots of SPB-PLAM curves for different sub-ROI combinations as indicated in the legend. D: Plots of the standard deviation of MILA estimates for the axial location of a simulated point source for different sub-ROI combinations as indicated in the legend. The dashed black line in B, C and D indicates the standard PLAM for axial localization from the full ROI. The simulations were performed with the following numerical values: magnification M = 100, numerical aperture na = 1.45, pixel size: 16 µm × 16 µm, ROI size: 15 × 15 pixels. The calibration data was generated using data from one simulated point source with all the same parameters except that a mean of 10000 photons were detected per image. Vertical dotted lines mark the positions of the focal planes in the object space.

Fig. 4
Fig. 4

A: Schematic representation of a MUM configuration that simultaneously images four focal planes using independent detectors. Sample ROIs of a typical point source are also shown, along with a representation of the sub-ROIs that are used for intensity calculations. B: The top panel shows a plot of the accuracy reached by MILA (r = 0, 1, 2, 3, 4, 5) in the estimation of the axial location of a point source using four-plane MUM data. 1000 sets of four images corresponding to the four focal planes of a point source from which a mean of 2000 photons were detected per image were simulated and the point source’s axial location was estimated using MILA. The standard deviation of these estimates is plotted as a function of the axial position of the simulated point source. The corresponding SPB-PLAM and standard PLAM for the axial location of the point source are also plotted. The bottom panel shows a plot of the SPB-PLAM calculated for different sub-ROI sequences for the same data as a function of the point source’s axial location. The axial location range shown is restricted to one-half of the simulation range and the y-axis is depicted in log10 scale for display purposes. The simulations were performed using the following numerical values: magnification M = 100, numerical aperture na = 1.45, pixel size: 16 µm 16 µm, ROI size: 15 × 15 pixels. The calibration data was generated using data from one simulated point source with all the same parameters except that a mean of 10000 photons were detected per image. Vertical lines mark the positions of the focal planes in the object space.

Fig. 5
Fig. 5

A: Example images of four simulated point sources that differ only in their locations within the center pixel of the ROI. B: Histogram of 10000 axial location estimates of a point source obtained using MILA when the calibration point source used to generate the lookup table is located at a different sub-pixel location. Red line indicates the true axial position. C: Plot of the bias in the axial location estimates of four different point sources as a function axial location. The lateral positions of these point sources are shown in A. Each colored line represents bias in the estimates of one of the point sources. Bias is calculated as the difference between the mean of 1000 axial location estimates and the true axial location. The axial location was estimated using MILA from simulated four-plane MUM data. The point sources were simulated such that a mean of 2000 photons were detected per image. Simulations and estimations were performed using the following numerical values: magnification M = 40, numerical aperture na = 1.45, pixel size: 13 µm × 13 µm, ROI size: 11 × 11 pixels, sub-ROI sequence r = 0, 1, 2. The calibration data was generated as a series of images of a fifth point source located at another random position within the center pixel of the ROI, from which a mean of 10000 photons were detected per image. Vertical dotted lines mark the positions of the focal planes in the object space.

Fig. 6
Fig. 6

A: Plots of the difference between the mean of 1000 axial location estimates and the true axial location as a function of the axial location for five simulated point sources that are imaged using a four-plane MUM setup. Calibration data from 50 different point sources were used. Each colored line represents bias in the estimates of one of the five test point sources. Simulations and estimations were performed using the following numerical values: focal-plane separation: 1.5 µm, magnification M = 40, numerical aperture na = 1.45, pixel size: 13 µm × 13 µm, ROI size: 11 × 11 pixels, sub-ROI sequence r = 0, 1, 2. The five test point sources were positioned in various locations within the center pixel of the ROI and the calibration data was generated as a series of images of 50 different point sources located in random locations within the same center pixel. A mean of 2000 photons were detected per image from each of the five test point sources, and a mean of 10000 photons were detected per image from each calibration point source. B: Plot of the mean modulus bias in the obtained axial location estimates as a function of the number of calibration point sources used. Test and calibration data were simulated similar to A, but calibration curves were generated with different numbers of point sources whose positions within the center pixel were randomized every time. For each test point source, datasets were simulated that differ by the axial location of the point source. The mean modulus bias is the average of the modulus bias of the axial estimates obtained for each dataset. All simulation parameters were maintained as above, except the magnification and pixel size were varied as indicated in the legend.

Fig. 7
Fig. 7

A: Standard deviation of z estimates, obtained using MILA from 50 sets of four images (each corresponding to a distinct focal plane) per axial position of a typical 100-nm TetraSpeck fluorescent bead, as a function of the relative axial position of the bead. B: Deviation of the mean estimated z value from the expected z value for the same bead as a function of its relative axial position. The expected z value is determined based on the step size used for the piezo nanopositioner. The following estimation parameter values were used: ROI size: 13 × 13 pixels, sub-ROI sequence r = 2, 3, 4. Calibration data and test data were both generated using beads from the same sample but in different fields of view. For calibration data, 10 images of the beads were acquired per detector, followed by moving the piezo nanopositioner 25 nm and repeating the process over a wide axial range. Data from six beads was used for calibration. For the test data, 50 images of the beads were acquired per detector, followed by moving the piezo nanopositioner 100 nm similarly. Per acquisition, a combined total of at least 4000 photons were detected from each calibration bead, and approximately 6000 photons were detected from the test bead, within the ROIs from the four detector images. Vertical dotted lines indicate the calculated positions of the focal planes.

Fig. 8
Fig. 8

Example illustrations of different sub-ROI shapes.

Equations (3)

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A d , r p = A d , r p   max { A d 1 , r p 1   | d 1 = 1 , , D , p 1 = 1 , , P } , d = 1 , , D , p = 1 , , P .
z ^ = arg min z ( z 1 , , z J ) { p = 1 P d = 1 D ( A z , d , r p l o o k u p A d , r p ) 2 } .
z c = arg min z ( z 1 , , z J ) { p = 1 P d = 1 D ( A z , d , r p , c l o o k u p A d , r p ) 2 } , c = 1 , C .

Metrics