Abstract

From an acquired image, single molecule microscopy makes possible the determination of the distance separating two closely spaced biomolecules in three-dimensional (3D) space. Such distance information can be an important indicator of the nature of the biomolecular interaction. Distance determination, however, is especially difficult when, for example, the imaged point sources are very close to each other or are located near the focal plane of the imaging setup. In the context of such challenges, we compare the limits of the distance estimation accuracy for several high resolution 3D imaging modalities. The comparisons are made using a Cramer-Rao lower bound-based 3D resolution measure which predicts the best possible accuracy with which a given distance can be estimated. Modalities which separate the detection of individual point sources (e.g., using photoactivatable fluorophores) are shown to provide the best accuracy limits when the two point sources are very close to each other and/or are oriented near parallel to the optical axis. Meanwhile, modalities which implement the simultaneous imaging of the point sources from multiple focal planes perform best when given a near-focus point source pair. We also demonstrate that the maximum likelihood estimator is capable of attaining the limit of the accuracy predicted for each modality.

© 2009 Optical Society of America

PDF Article
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References

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2009 (2)

2008 (5)

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

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[Crossref] [PubMed]

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[Crossref] [PubMed]

N. G. Walter, C. Huang, A. J. Manzo, and M. A. Sobhy, “Do-it-yourself guide: how to use the modern singlemolecule toolkit,” Nat. Methods 5, 475–489 (2008).
[Crossref] [PubMed]

2007 (4)

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. USA 104, 12596–12602 (2007).
[Crossref] [PubMed]

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D1–D7 (2007).

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

2006 (6)

S. Ram, E. S. Ward, and R. J. Ober, “A stochastic analysis of performance limits for optical microscopes,” Multidimens. Syst. Sig. Process. 17, 27–57 (2006).
[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. USA 103, 4457–4462 (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. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006).
[Crossref] [PubMed]

A. Sharonov and R. M. Hochstrasser, “Wide-field subdiffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103, 18911–18916 (2006).
[Crossref] [PubMed]

2005 (2)

S. Ram, E. S. Ward, and R. J. Ober, “How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?” Proc. SPIE 5699, 426–435 (2005).
[Crossref] [PubMed]

K. A. Lidke, B. Rieger, T. M. Jovin, and R. Heintzmann, “Superresolution by localization of quantum dots using blinking statistics,” Opt. Express 13, 7052–7062 (2005).
[Crossref] [PubMed]

2004 (3)

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. Nanobiosci. 3, 237–242 (2004).
[Crossref]

X. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 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. USA 101, 6462–6465 (2004).
[Crossref] [PubMed]

2003 (1)

O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,” Opt. Commun. 216, 55–63 (2003).
[Crossref]

2000 (1)

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[Crossref] [PubMed]

1999 (1)

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676–1683 (1999).
[Crossref] [PubMed]

1997 (1)

1995 (1)

L. Tao and C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[Crossref] [PubMed]

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]

1992 (1)

1988 (1)

M. Pluta, Advanced light microscopy, vol. 1: principles and basic properties (Elsevier, Amsterdam, 1988).

Abraham, A. V.

J. Chao, S. Ram, A. V. Abraham, E. S. Ward, and R. J. Ober, “A resolution measure for three-dimensional microscopy,” Opt. Commun. 282, 1751–1761 (2009).
[Crossref]

Agrawal, A.

A. Agrawal, R. Deo, G. D. Wang, M. D. Wang, and S. Nie, “Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes,” Proc. Natl. Acad. Sci. USA 105, 3298–3303 (2008).
[Crossref] [PubMed]

Alivisatos, A. P.

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[Crossref] [PubMed]

Andersson, S. B.

T. Sun and S. B. Andersson, “Precise 3-D localization of fluorescent probes without numerical fitting,” in Proceedings of the International Conference of IEEE Engineering in Medicine and Biology Society (IEEE, 2007) pp. 4181–4184.

Bates, M.

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

Beane, G. L.

Bennett, B. T.

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

Bewersdorf, J.

M. J. Mlodzianoski, M. F. Juette, G. L. Beane, and J. Bewersdorf, “Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy,” Opt. Express 17, 8264–8277 (2009).
[Crossref] [PubMed]

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999).

Chao, J.

J. Chao, S. Ram, A. V. Abraham, E. S. Ward, and R. J. Ober, “A resolution measure for three-dimensional microscopy,” Opt. Commun. 282, 1751–1761 (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, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D1–D7 (2007).

Chemla, D. S.

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[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]

Deo, R.

A. Agrawal, R. Deo, G. D. Wang, M. D. Wang, and S. Nie, “Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes,” Proc. Natl. Acad. Sci. USA 105, 3298–3303 (2008).
[Crossref] [PubMed]

Gan, Z.

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

Gibbons, S.

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

Gibson, S. F.

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. USA 101, 6462–6465 (2004).
[Crossref] [PubMed]

Gould, T. J.

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

Ha, T.

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

Haeberlé, O.

O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,” Opt. Commun. 216, 55–63 (2003).
[Crossref]

Heintzmann, R.

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.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. Nagpure, B. T. Bennett, S. T. Hess, and 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. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref] [PubMed]

Hochstrasser, R. M.

A. Sharonov and R. M. Hochstrasser, “Wide-field subdiffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103, 18911–18916 (2006).
[Crossref] [PubMed]

Holtzer, L.

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

Huang, C.

N. G. Walter, C. Huang, A. J. Manzo, and M. A. Sobhy, “Do-it-yourself guide: how to use the modern singlemolecule toolkit,” Nat. Methods 5, 475–489 (2008).
[Crossref] [PubMed]

Inoué, S.

S. Inoué “Foundations of confocal scanned imaging in light microscopy,” in “Handbook of Biological Confocal Microscopy,” J. B. Pawley, ed. (Springer Science+Business Media, LLC, New York, 2006), 3rd ed.

Jovin, T. M.

Juette, M. F.

M. J. Mlodzianoski, M. F. Juette, G. L. Beane, and J. Bewersdorf, “Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy,” Opt. Express 17, 8264–8277 (2009).
[Crossref] [PubMed]

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

Lacoste, T. D.

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[Crossref] [PubMed]

Lanni, F.

Lessard, M. D.

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

Lidke, K. A.

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.

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]

Manzo, A. J.

N. G. Walter, C. Huang, A. J. Manzo, and M. A. Sobhy, “Do-it-yourself guide: how to use the modern singlemolecule toolkit,” Nat. Methods 5, 475–489 (2008).
[Crossref] [PubMed]

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]

Meckel, T.

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

Mets, L.

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

Michalet, X.

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[Crossref] [PubMed]

Miller, M. I.

D. L. Snyder and M. I. Miller, Random point processes in time and space (Springer Verlag, New York, USA, 1991), 2nd ed.

Mlodzianoski, M. J.

M. J. Mlodzianoski, M. F. Juette, G. L. Beane, and J. Bewersdorf, “Experimental characterization of 3D localization techniques for particle-tracking and super-resolution microscopy,” Opt. Express 17, 8264–8277 (2009).
[Crossref] [PubMed]

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

Moerner, W. E.

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. USA 104, 12596–12602 (2007).
[Crossref] [PubMed]

Nagpure, B.

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

Nicholson, C.

L. Tao and C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[Crossref] [PubMed]

Nie, S.

A. Agrawal, R. Deo, G. D. Wang, M. D. Wang, and S. Nie, “Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes,” Proc. Natl. Acad. Sci. USA 105, 3298–3303 (2008).
[Crossref] [PubMed]

Ober, R. J.

J. Chao, S. Ram, A. V. Abraham, E. S. Ward, and R. J. Ober, “A resolution measure for three-dimensional microscopy,” Opt. Commun. 282, 1751–1761 (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, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D1–D7 (2007).

S. Ram, E. S. Ward, and R. J. Ober, “A stochastic analysis of performance limits for optical microscopes,” Multidimens. Syst. Sig. Process. 17, 27–57 (2006).
[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. USA 103, 4457–4462 (2006).
[Crossref] [PubMed]

S. Ram, E. S. Ward, and R. J. Ober, “How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?” Proc. SPIE 5699, 426–435 (2005).
[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. Nanobiosci. 3, 237–242 (2004).
[Crossref]

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]

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]

Pavani, S. R. P.

Piestun, R.

Pinaud, F.

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[Crossref] [PubMed]

Pluta, M.

M. Pluta, Advanced light microscopy, vol. 1: principles and basic properties (Elsevier, Amsterdam, 1988).

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]

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D1–D7 (2007).

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. Nanobiosci. 3, 237–242 (2004).
[Crossref]

Qu, X.

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

Ram, S.

J. Chao, S. Ram, A. V. Abraham, E. S. Ward, and R. J. Ober, “A resolution measure for three-dimensional microscopy,” Opt. Commun. 282, 1751–1761 (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. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D1–D7 (2007).

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

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. USA 103, 4457–4462 (2006).
[Crossref] [PubMed]

S. Ram, E. S. Ward, and R. J. Ober, “A stochastic analysis of performance limits for optical microscopes,” Multidimens. Syst. Sig. Process. 17, 27–57 (2006).
[Crossref]

S. Ram, E. S. Ward, and R. J. Ober, “How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?” Proc. SPIE 5699, 426–435 (2005).
[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. Nanobiosci. 3, 237–242 (2004).
[Crossref]

Rao, C. R.

C. R. Rao, Linear statistical inference and its applications (Wiley, New York, USA, 1965).

Rieger, B.

Rust, M.

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

Scherer, N. F.

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

Schmidt, T.

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

Selvin, P. R.

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

Sharonov, A.

A. Sharonov and R. M. Hochstrasser, “Wide-field subdiffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103, 18911–18916 (2006).
[Crossref] [PubMed]

Snyder, D. L.

D. L. Snyder and M. I. Miller, Random point processes in time and space (Springer Verlag, New York, USA, 1991), 2nd ed.

Sobhy, M. A.

N. G. Walter, C. Huang, A. J. Manzo, and M. A. Sobhy, “Do-it-yourself guide: how to use the modern singlemolecule toolkit,” Nat. Methods 5, 475–489 (2008).
[Crossref] [PubMed]

Sougrat, R.

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]

Sun, T.

T. Sun and S. B. Andersson, “Precise 3-D localization of fluorescent probes without numerical fitting,” in Proceedings of the International Conference of IEEE Engineering in Medicine and Biology Society (IEEE, 2007) pp. 4181–4184.

Tao, L.

L. Tao and C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[Crossref] [PubMed]

Török, P.

Vaccaro, C.

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

Varga, P.

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]

Walter, N. G.

N. G. Walter, C. Huang, A. J. Manzo, and M. A. Sobhy, “Do-it-yourself guide: how to use the modern singlemolecule toolkit,” Nat. Methods 5, 475–489 (2008).
[Crossref] [PubMed]

Wang, G. D.

A. Agrawal, R. Deo, G. D. Wang, M. D. Wang, and S. Nie, “Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes,” Proc. Natl. Acad. Sci. USA 105, 3298–3303 (2008).
[Crossref] [PubMed]

Wang, M. D.

A. Agrawal, R. Deo, G. D. Wang, M. D. Wang, and S. Nie, “Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes,” Proc. Natl. Acad. Sci. USA 105, 3298–3303 (2008).
[Crossref] [PubMed]

Ward, E. S.

J. Chao, S. Ram, A. V. Abraham, E. S. Ward, and R. J. Ober, “A resolution measure for three-dimensional microscopy,” Opt. Commun. 282, 1751–1761 (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, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

S. Ram, J. Chao, P. Prabhat, E. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D1–D7 (2007).

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. USA 103, 4457–4462 (2006).
[Crossref] [PubMed]

S. Ram, E. S. Ward, and R. J. Ober, “A stochastic analysis of performance limits for optical microscopes,” Multidimens. Syst. Sig. Process. 17, 27–57 (2006).
[Crossref]

S. Ram, E. S. Ward, and R. J. Ober, “How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?” Proc. SPIE 5699, 426–435 (2005).
[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. Nanobiosci. 3, 237–242 (2004).
[Crossref]

Weiss, S.

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[Crossref] [PubMed]

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676–1683 (1999).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999).

Wu, D.

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

Zacks, S.

S. Zacks, The theory of statistical inference (John Wiley and Sons, New York, USA, 1971).

Zhuang, X.

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

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

Biophys. J. (3)

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]

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. Nanobiosci. (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. Nanobiosci. 3, 237–242 (2004).
[Crossref]

J. Microsc. (1)

L. Tao and C. Nicholson, “The three-dimensional point spread functions of a microscope objective in image and object space,” J. Microsc. 178, 267–271 (1995).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Multidimens. Syst. Sig. Process. (1)

S. Ram, E. S. Ward, and R. J. Ober, “A stochastic analysis of performance limits for optical microscopes,” Multidimens. Syst. Sig. Process. 17, 27–57 (2006).
[Crossref]

Nat. Methods (3)

N. G. Walter, C. Huang, A. J. Manzo, and M. A. Sobhy, “Do-it-yourself guide: how to use the modern singlemolecule toolkit,” Nat. Methods 5, 475–489 (2008).
[Crossref] [PubMed]

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

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

Opt. Commun. (2)

J. Chao, S. Ram, A. V. Abraham, E. S. Ward, and R. J. Ober, “A resolution measure for three-dimensional microscopy,” Opt. Commun. 282, 1751–1761 (2009).
[Crossref]

O. Haeberlé, “Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy,” Opt. Commun. 216, 55–63 (2003).
[Crossref]

Opt. Express (3)

Proc. Natl. Acad. Sci. USA (8)

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. USA 104, 12596–12602 (2007).
[Crossref] [PubMed]

X. Qu, D. Wu, L. Mets, and N. F. Scherer, “Nanometer-localized multiple single-molecule fluorescence microscopy,” Proc. Natl. Acad. Sci. USA 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. USA 101, 6462–6465 (2004).
[Crossref] [PubMed]

T. D. Lacoste, X. Michalet, F. Pinaud, D. S. Chemla, A. P. Alivisatos, and S. Weiss, “Ultrahigh-resolution multi-color colocalization of single fluorescent probes,” Proc. Natl. Acad. Sci. USA 97, 9461–9466 (2000).
[Crossref] [PubMed]

A. Agrawal, R. Deo, G. D. Wang, M. D. Wang, and S. Nie, “Nanometer-scale mapping and single-molecule detection with color-coded nanoparticle probes,” Proc. Natl. Acad. Sci. USA 105, 3298–3303 (2008).
[Crossref] [PubMed]

P. Prabhat, Z. Gan, J. Chao, S. Ram, C. Vaccaro, S. Gibbons, R. J. Ober, and E. S. Ward, “Elucidation of intracellular recycling pathways leading to exocytosis of the Fc receptor, FcRn, by using multifocal plane microscopy,” Proc. Natl. Acad. Sci. USA 104, 5889–5894 (2007).
[Crossref] [PubMed]

A. Sharonov and R. M. Hochstrasser, “Wide-field subdiffraction imaging by accumulated binding of diffusing probes,” Proc. Natl. Acad. Sci. USA 103, 18911–18916 (2006).
[Crossref] [PubMed]

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. USA 103, 4457–4462 (2006).
[Crossref] [PubMed]

Proc. SPIE (2)

S. Ram, J. Chao, P. Prabhat, E. S. Ward, and R. J. Ober, “A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking,” Proc. SPIE 6443, 64430D1–D7 (2007).

S. Ram, E. S. Ward, and R. J. Ober, “How accurately can a single molecule be localized in three dimensions using a fluorescence microscope?” Proc. SPIE 5699, 426–435 (2005).
[Crossref] [PubMed]

Science (2)

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. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science 283, 1676–1683 (1999).
[Crossref] [PubMed]

Other (9)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, UK, 1999).

M. Pluta, Advanced light microscopy, vol. 1: principles and basic properties (Elsevier, Amsterdam, 1988).

S. Inoué “Foundations of confocal scanned imaging in light microscopy,” in “Handbook of Biological Confocal Microscopy,” J. B. Pawley, ed. (Springer Science+Business Media, LLC, New York, 2006), 3rd ed.

C. R. Rao, Linear statistical inference and its applications (Wiley, New York, USA, 1965).

T. Sun and S. B. Andersson, “Precise 3-D localization of fluorescent probes without numerical fitting,” in Proceedings of the International Conference of IEEE Engineering in Medicine and Biology Society (IEEE, 2007) pp. 4181–4184.

D. L. Snyder and M. I. Miller, Random point processes in time and space (Springer Verlag, New York, USA, 1991), 2nd ed.

“EstimationTool,” http://www4.utsouthwestern.edu/wardlab/estimationtool.

“FandPLimitTool,” http://www4.utsouthwestern.edu/wardlab/fandplimittool.

S. Zacks, The theory of statistical inference (John Wiley and Sons, New York, USA, 1971).

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