Abstract

The 3D orientation and location of individual molecules is an important marker for the local environment and the state of a molecule. Therefore dipole localization and orientation estimation is important for biological sensing and imaging. Precise dipole localization is also critical for superresolution imaging. We propose and analyze wide field microscope configurations to simultaneously measure these parameters for multiple fixed dipole emitters. Examination of the images of radiating dipoles reveals how information transfer and precise detection can be improved. We use an information theoretic analysis to quantify the performance limits of position and orientation estimation through comparison of the Cramer-Rao lower bounds in a photon limited environment. We show that bi-focal and double-helix polarization-sensitive systems are attractive candidates for simultaneously estimating the 3D dipole location and orientation.

© 2012 OSA

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2012 (1)

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A.109(3), 675–679 (2012).
[CrossRef] [PubMed]

2011 (3)

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

M. R. Foreman and P. Török, “Fundamental limits in single-molecule orientation measurements,” New J. Phys.13(9), 093013 (2011).
[CrossRef]

G. Grover, S. Quirin, C. Fiedler, and R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express2(11), 3010–3020 (2011).
[CrossRef] [PubMed]

2010 (3)

2009 (3)

2008 (3)

M. R. Foreman, C. M. Romero, and P. Török, “Determination of the three-dimensional orientation of single molecules,” Opt. Lett.33(9), 1020–1022 (2008).
[CrossRef] [PubMed]

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 527–529 (2008).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science319(5864), 810–813 (2008).
[CrossRef] [PubMed]

2007 (3)

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. SPIE6443, 64430D (2007).
[CrossRef]

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A.104(31), 12596–12602 (2007).
[CrossRef] [PubMed]

E. Toprak and P. R. Selvin, “New fluorescent tools for watching nanometer-scale conformational changes of single molecules,” Annu. Rev. Biophys. Biomol. Struct.36(1), 349–369 (2007).
[CrossRef] [PubMed]

2006 (5)

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,” Science313(5793), 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(11), 4258–4272 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express14(18), 8111–8120 (2006).
[CrossRef] [PubMed]

2004 (2)

M. A. Lieb, J. M. Zavislan, and L. Novotny, “Single-molecule orientations determined by direct emission pattern imaging,” J. Opt. Soc. Am. B21(6), 1210 (2004).
[CrossRef]

D. Patra, I. Gregor, and J. Enderlein, “Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies,” J. Phys. Chem. A108(33), 6836–6841 (2004).
[CrossRef]

2003 (1)

1999 (1)

A. P. Bartko and R. M. Dickson, “Imaging Three-Dimensional Single Molecule Orientations,” J. Phys. Chem. B103(51), 11237–11241 (1999).
[CrossRef]

Aguet, F.

Bartko, A. P.

A. P. Bartko and R. M. Dickson, “Imaging Three-Dimensional Single Molecule Orientations,” J. Phys. Chem. B103(51), 11237–11241 (1999).
[CrossRef]

Bates, M.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science319(5864), 810–813 (2008).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 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,” Science313(5793), 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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 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, 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

Böhmer, M.

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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Chao, J.

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. SPIE6443, 64430D (2007).
[CrossRef]

Churchman, L. S.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

DeLuca, J. G.

Dickson, R. M.

A. P. Bartko and R. M. Dickson, “Imaging Three-Dimensional Single Molecule Orientations,” J. Phys. Chem. B103(51), 11237–11241 (1999).
[CrossRef]

Enderlein, J.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express14(18), 8111–8120 (2006).
[CrossRef] [PubMed]

D. Patra, I. Gregor, and J. Enderlein, “Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies,” J. Phys. Chem. A108(33), 6836–6841 (2004).
[CrossRef]

M. Böhmer and J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B20(3), 554 (2003).
[CrossRef]

Engelhardt, J.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

Fiedler, C.

Flyvbjerg, H.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

Foreman, M. R.

M. R. Foreman and P. Török, “Fundamental limits in single-molecule orientation measurements,” New J. Phys.13(9), 093013 (2011).
[CrossRef]

M. R. Foreman, C. M. Romero, and P. Török, “Determination of the three-dimensional orientation of single molecules,” Opt. Lett.33(9), 1020–1022 (2008).
[CrossRef] [PubMed]

Geissbühler, S.

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(11), 4258–4272 (2006).
[CrossRef] [PubMed]

Goldman, Y. E.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

Gould, T. J.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 527–529 (2008).
[CrossRef] [PubMed]

Gregor, I.

D. Patra, I. Gregor, and J. Enderlein, “Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies,” J. Phys. Chem. A108(33), 6836–6841 (2004).
[CrossRef]

Grover, G.

Ha, T.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

Hell, S. W.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

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,” Science313(5793), 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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 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(11), 4258–4272 (2006).
[CrossRef] [PubMed]

Hoyer, P.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

Huang, B.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science319(5864), 810–813 (2008).
[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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 527–529 (2008).
[CrossRef] [PubMed]

Keller, J.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

Lasser, T.

Lessard, M. D.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 527–529 (2008).
[CrossRef] [PubMed]

Lieb, M. 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,” Science313(5793), 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,” Science313(5793), 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, 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. U.S.A.106(9), 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, 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

Märki, I.

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(11), 4258–4272 (2006).
[CrossRef] [PubMed]

McKinney, S. A.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[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, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 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, 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A.104(31), 12596–12602 (2007).
[CrossRef] [PubMed]

Mortensen, K. I.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

Nagpure, B. S.

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 527–529 (2008).
[CrossRef] [PubMed]

Novotny, L.

Ober, R. J.

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. SPIE6443, 64430D (2007).
[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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Patra, D.

D. Patra, I. Gregor, and J. Enderlein, “Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies,” J. Phys. Chem. A108(33), 6836–6841 (2004).
[CrossRef]

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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Pavani, S. R. P.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A.109(3), 675–679 (2012).
[CrossRef] [PubMed]

G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett.35(19), 3306–3308 (2010).
[CrossRef] [PubMed]

S. R. P. Pavani, J. G. DeLuca, and R. Piestun, “Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system,” Opt. Express17(22), 19644–19655 (2009).
[CrossRef] [PubMed]

S. R. P. 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

Petschek, R. G.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

Piestun, R.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A.109(3), 675–679 (2012).
[CrossRef] [PubMed]

G. Grover, S. Quirin, C. Fiedler, and R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express2(11), 3010–3020 (2011).
[CrossRef] [PubMed]

G. Grover, S. R. P. Pavani, and R. Piestun, “Performance limits on three-dimensional particle localization in photon-limited microscopy,” Opt. Lett.35(19), 3306–3308 (2010).
[CrossRef] [PubMed]

S. R. P. Pavani, J. G. DeLuca, and R. Piestun, “Polarization sensitive, three-dimensional, single-molecule imaging of cells with a double-helix system,” Opt. Express17(22), 19644–19655 (2009).
[CrossRef] [PubMed]

S. R. P. 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

Prabhat, P.

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. SPIE6443, 64430D (2007).
[CrossRef]

Quirin, S.

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A.109(3), 675–679 (2012).
[CrossRef] [PubMed]

G. Grover, S. Quirin, C. Fiedler, and R. Piestun, “Photon efficient double-helix PSF microscopy with application to 3D photo-activation localization imaging,” Biomed. Opt. Express2(11), 3010–3020 (2011).
[CrossRef] [PubMed]

Ram, S.

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. SPIE6443, 64430D (2007).
[CrossRef]

Reuss, M.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

Rieger, B.

Romero, C. M.

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Selvin, P. R.

E. Toprak and P. R. Selvin, “New fluorescent tools for watching nanometer-scale conformational changes of single molecules,” Annu. Rev. Biophys. Biomol. Struct.36(1), 349–369 (2007).
[CrossRef] [PubMed]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express14(18), 8111–8120 (2006).
[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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Spudich, J. A.

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

Stallinga, S.

Staudt, T.

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

Syed, S.

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

Thompson, M. A.

S. R. P. 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

Toprak, E.

E. Toprak and P. R. Selvin, “New fluorescent tools for watching nanometer-scale conformational changes of single molecules,” Annu. Rev. Biophys. Biomol. Struct.36(1), 349–369 (2007).
[CrossRef] [PubMed]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

J. Enderlein, E. Toprak, and P. R. Selvin, “Polarization effect on position accuracy of fluorophore localization,” Opt. Express14(18), 8111–8120 (2006).
[CrossRef] [PubMed]

Török, P.

M. R. Foreman and P. Török, “Fundamental limits in single-molecule orientation measurements,” New J. Phys.13(9), 093013 (2011).
[CrossRef]

M. R. Foreman, C. M. Romero, and P. Török, “Determination of the three-dimensional orientation of single molecules,” Opt. Lett.33(9), 1020–1022 (2008).
[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, 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

Unser, M.

Wang, W.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science319(5864), 810–813 (2008).
[CrossRef] [PubMed]

Ward, E. S.

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. SPIE6443, 64430D (2007).
[CrossRef]

Zavislan, J. M.

Zhuang, X.

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science319(5864), 810–813 (2008).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

E. Toprak and P. R. Selvin, “New fluorescent tools for watching nanometer-scale conformational changes of single molecules,” Annu. Rev. Biophys. Biomol. Struct.36(1), 349–369 (2007).
[CrossRef] [PubMed]

Biomed. Opt. Express (1)

Biophys. J. (1)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J.91(11), 4258–4272 (2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (2)

J. Phys. Chem. A (1)

D. Patra, I. Gregor, and J. Enderlein, “Image Analysis of Defocused Single-Molecule Images for Three-Dimensional Molecule Orientation Studies,” J. Phys. Chem. A108(33), 6836–6841 (2004).
[CrossRef]

J. Phys. Chem. B (1)

A. P. Bartko and R. M. Dickson, “Imaging Three-Dimensional Single Molecule Orientations,” J. Phys. Chem. B103(51), 11237–11241 (1999).
[CrossRef]

Nano Lett. (1)

J. Engelhardt, J. Keller, P. Hoyer, M. Reuss, T. Staudt, and S. W. Hell, “Molecular orientation affects localization accuracy in superresolution far-field fluorescence microscopy,” Nano Lett.11(1), 209–213 (2011).
[CrossRef] [PubMed]

Nat. Methods (3)

K. I. Mortensen, L. S. Churchman, J. A. Spudich, and H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods7(5), 377–381 (2010).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods3(10), 793–796 (2006).
[CrossRef] [PubMed]

M. F. Juette, T. J. Gould, M. D. Lessard, M. J. Mlodzianoski, B. S. Nagpure, B. T. Bennett, S. T. Hess, and J. Bewersdorf, “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples,” Nat. Methods5(6), 527–529 (2008).
[CrossRef] [PubMed]

New J. Phys. (1)

M. R. Foreman and P. Török, “Fundamental limits in single-molecule orientation measurements,” New J. Phys.13(9), 093013 (2011).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. U.S.A. (4)

W. E. Moerner, “New directions in single-molecule imaging and analysis,” Proc. Natl. Acad. Sci. U.S.A.104(31), 12596–12602 (2007).
[CrossRef] [PubMed]

S. Quirin, S. R. P. Pavani, and R. Piestun, “Optimal 3D single-molecule localization for superresolution microscopy with aberrations and engineered point spread functions,” Proc. Natl. Acad. Sci. U.S.A.109(3), 675–679 (2012).
[CrossRef] [PubMed]

E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, “Defocused orientation and position imaging (DOPI) of myosin V,” Proc. Natl. Acad. Sci. U.S.A.103(17), 6495–6499 (2006).
[CrossRef] [PubMed]

S. R. P. 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. U.S.A.106(9), 2995–2999 (2009).
[CrossRef] [PubMed]

Proc. SPIE (1)

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. SPIE6443, 64430D (2007).
[CrossRef]

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,” Science313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

B. Huang, W. Wang, M. Bates, and X. Zhuang, “Three-dimensional super-resolution imaging by stochastic optical reconstruction microscopy,” Science319(5864), 810–813 (2008).
[CrossRef] [PubMed]

Other (3)

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Chap. 10.

A. Agrawal, S. Quirin, G. Grover, and R. Piestun, “Limits of 3D Dipole Localization and Orientation Estimation with Application to Single-Molecule Imaging - OSA Technical Digest (CD),” in Computational Optical Sensing and Imaging (Optical Society of America, 2011), p. CWA4.

S. M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (v. 1) (Prentice Hall, 1993), Chap. 3.

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Figures (7)

Fig. 1
Fig. 1

Point Spread Function Engineering versus Green’s tensor engineering: (a) The PSF is the response of the system to a point source whereas the Green’s tensor is the response of the system to a dipole input. The output of the Green’s tensor system is a vector function of the dipole orientation. Each of the rows, shown at the output, corresponds to a unique dipole orientation, showing the total intensity and the intensity of two transverse orthogonal components of the electric field. (b) The position and orientation of a dipole with respect to an objective lens defines the input space. The origin (0,0,0) is at the focal point of the objective lens with the z-axis parallel to the optical axis. Here (x0, y0, z0) represent the position of the dipole and (Θ,Φ) represent the polar and azimuthal orientation angles respectively.

Fig. 2
Fig. 2

Simulation of the dipole spread function along three representative orientations: (I) is the detected total Intensity (single channel system), |Ex|2, |Ey|2, |E1|2, and |E2|2 (left to right) correspond to images obtained in two-channel systems when using either orthogonal polarizers (|Ex|2, |Ey|2) or a quarter waveplate with orthogonal polarizer (see text for details), whereas | E x DH | 2 and | E y DH | 2 represent the intensity distributions of the two orthogonal linear polarizations using the double-helix phase mask (DH). In (a), the dipole is at the focal plane, while in (b) it is located 0.2 μm from the focal plane. The dipole is oriented along (from top to bottom) y ^ (Θ = 90° Φ = 90°), z ^ (Θ = 0° Φ = 0°) and Θ = 45° Φ = 45°

Fig. 3
Fig. 3

Schematic of the systems considered for dipole location and orientation estimation: (a) A traditional microscope system with a signal processing unit for Green’s function engineering. Category A shows three signal processing units that focus at the same plane whereas Category B shows the three signal processing units that focus at two different planes leading to a bifocal system. Parts (b) and (e), represent systems that measures the total intensity, parts (c) and (f) represent systems with two orthogonal polarization channels, imaging the intensities |Ex|2 and |Ey|2 separately, and parts (d) and (g) represent the systems with two polarization channels imaging the intensities of the elliptical polarizations components, (|Ex + iEy|2)/2 and (|iEx + Ey|2)/2 separately. (h) Shows the linear polarization system with a double-helix phase mask in the Fourier plane. (i) Shows the five dipole orientations used to compare these six systems on a unit sphere. TL - tube lens, L1, L2 -relay lenses, OL1 - objective lens, DM – dichroic mirror, PBS – polarizing beam splitter, QWP – Quarter wave plates with fast axis along 45° from x-axis.

Fig. 4
Fig. 4

Estimation error bounds as a function of defocus: (a) Average of volume localization - σ 3D ( 4π /3 σ x σ y σ z ) (b) Average of Solid angle error - σ Ω (sinΘ σ Θ σ Φ ) for the five representative dipole orientations with respect to the axial position of the dipole. For the bifocal systems, the two focal planes were offset by 0.4 μm and the x-axis represents the center of the two planes. The legends represent the systems compared here, namely single measurement-total intensity (TI np: solid blue), linear polarization (Lin pol: green o), elliptical polarization (Elp pol: red dash-dot), bi-focal total intensity (Bf-TI np: solid cyan), bi-focal with linear polarization (Bf-Lin pol: magenta dash), bi-focal with elliptical polarization (Bf-Elp pol: yellow + ), and linear polarization system that used a double helix phase mask in the Fourier plane (PS-DH-Lin pol: black ∆).

Fig. 5
Fig. 5

Estimation error bounds as a function of dipole orientation angle: (a) Volume localization - σ 3D ( 4π /3 σ x σ y σ z ) and (b) Solid angle error - σ Ω (sinΘ σ Θ σ Φ ) as a function of the azimuthal angle Φ (top row) and polar angle Θ (bottom plot). For the plots of category A, where system collects information from a single focal plane chosen at a defocus z0 = 0.1μm. For plot against Φ the angle Θ = 90 and for the plots against Θ the angle Φ was chosen to be 0°. For the bifocal systems, the two focal planes were offset by 0.4μm and the x-axis represents the center of the two planes. The legends represent the systems compared here, namely single measurement- total intensity (TI np: solid blue), linear polarization (Lin pol: green o), elliptical polarization (Elp pol: red dash-dot), bi-focal total intensity (Bf-TI np: solid cyan), bi-focal with linear polarization (Bf-Lin pol: magenta dash), bi-focal with elliptical polarization (Bf-Elp pol: yellow + ), and linear polarization system that used a double helix phase mask in the Fourier plane (PS-DH-Lin pol: black ∆).

Fig. 6
Fig. 6

3D localization and orientation estimation design via the CRLB: Parts (a) and (c) show the volume localization lower bound- σ 3D ( 4π /3 σ x σ y σ z ) . Parts (b) and (d) show the solid angle lower bound error - σ Ω (sinΘ σ Θ σ Φ ) as a function of the polar angle Θ and defocus (z0). The systems compared in the above plots are the single channel total intensity system (TI np: blue surface), Linear polarization system (Lin Pol: green surface), bifocal linear polarization system (Bf-Lin Pol: red surface), bifocal elliptical polarization system (Bf-Elp Pol: brown surface), linear polarization with the DH mask (PS-DH: yellow surface), and the DH system for the isotropic emitter (Iso-DH: cyan surface). For the bifocal system, the two focal planes are separated by the distance dz = 0.4 μm and z0 represents the center of the two planes.

Fig. 7
Fig. 7

Comparison of CRLB for 3D localization for a fixed dipole and an isotropic emitter: The 3D volume localization lower bound- σ 3D ( 4π /3 σ x σ y σ z ) is plotted as a function of the polar angle Θ and defocus distance (z0). The systems compared in the above plots are the linear polarization with the DH mask (PS-DH: blue surface), and the DH system for the isotropic emitter (Iso-DH: green surface). For this comparison it is assumed that both emitters emit the same number of photons leading to varying number of detected photons.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

E θ o =Π(θ)[cosΘsinθ+sinΘcosθcos(φΦ)]
E φ o =Π(θ)sinΘsin(φΦ)]
Π(θ)=exp[ik n 1 ( x 0 sinθcosφ+ y 0 sinθsinφ z 0 cosθ)]
[ E φ b E ρ b ]=[ E φ o E θ o ] n 2 n 1 cosθ
E y b = E ρ b sinφ+ E φ b cosφ
E x b = E ρ b cosφ E φ b sinφ
[ E x b ' E y b ' ]= J OE [ E x b E y b ]
I(r,φ,Θ,Φ)( E x E x * + E y E y * )
E 1 b = ( E x b +i E y b ) / 2
E 2 b = ( E x b i E y b ) / 2
σ LB = CRLB
σ 3D = 4π 3 σ x σ y σ z
σ Ω =sinΘ σ Θ σ Φ
Dipole Photon Count Point source Photon Count =1+cos t m + cos 2 t m
CRL B ψ [ m ]=F I ψ 1 [ m,m ]
F I ψ [ m,n ]= i,j E[ ln p i,j ( k|ψ ) ψ[ m ] ln p i,j ( k|ψ ) ψ[ n ] ]

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