Abstract

We demonstrate a new method of determining the three-dimensional dipole orientations of single molecules by direct imaging of the emission patterns in the back focal plane of a high-numerical-aperture objective lens. We compare the reconstructed emission-dipole orientations with a previously established method of absorption-dipole mapping. We find that, for a given number of emitted photons, emission pattern imaging provides better accuracy (1°–2°) than absorption-dipole mapping of single molecules. Compared with some other methods for emission-dipole mapping, the presented method is (1) less sensitive to optical aberrations and adjustment and (2) data analysis is simplified because radiation patterns can be expressed in a simple analytical form.

© 2004 Optical Society of America

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  4. J. Hofkens, W. Verheijen, R. Shukla, W. Dehaen, and F. C. De Schryver, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopyrroledione (DPP) core embedded in a thin polystyrene polymer film,” Macromolecules 31, 4493–4497 (1998).
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2003

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. T. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature (London) 422, 399–404 (2003).
[CrossRef]

M. Prummer, B. Sick, B. Hecht, and U. P. Wild, “Three-dimensional optical polarization tomography of single molecules,” J. Chem. Phys. 118, 9824–9829 (2003).
[CrossRef]

M. Vacha and M. Kotani, “Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy,” J. Chem. Phys. 118, 5279–5282 (2003).
[CrossRef]

M. Böhmer and J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B 20, 554–559 (2003).
[CrossRef]

2001

S. Quabis, R. Dorn, O. Glöckl, M. Reichle, and M. Eberler, “Reduction of the spot size by using a radially polarized laser beam,” in International Seminar on Novel Trends in Nonlinear Laser Spectroscopy and High-Precision Measurements in Optics, S. N. Bagaev, V. N. Zadkov, and S. M. Arakelian, eds., Proc. SPIE 4429, 105–111 (2001).
[CrossRef]

J. T. Fourkas, “Rapid determination of the three-dimensional orientation of single molecules,” Opt. Lett. 26, 211–213 (2001).
[CrossRef]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

L. A. Deschenes and D. A. Van den Bout, “Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition,” Science 292, 255–258 (2001).
[CrossRef] [PubMed]

2000

S. Weiss, “Measuring conformational dynamics of biomolecules by single molecule fluorescence spectroscopy,” Nature Struct. Biol. 7, 724–729 (2000).
[CrossRef] [PubMed]

Ph. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Ten years of single-molecule spectroscopy,” J. Phys. Chem. A 104, 1–16 (2000).
[CrossRef]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

1999

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single molecule orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Three-dimensional orientations of polymer-bound single molecules,” J. Phys. Chem. B 103, 3053–3056 (1999).
[CrossRef]

1998

J. Hofkens, W. Verheijen, R. Shukla, W. Dehaen, and F. C. De Schryver, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopyrroledione (DPP) core embedded in a thin polystyrene polymer film,” Macromolecules 31, 4493–4497 (1998).
[CrossRef]

1997

J. Sepiol, J. Jasny, J. Keller, and U. Wild, “Single molecules observed by immersion mirror objective. The orientation of Terrylene molecules via the direction of its transition dipole moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

1996

L. Novotny, “Single molecule fluorescence in inhomogeneous environments,” Appl. Phys. Lett. 69, 3806–3808 (1996).
[CrossRef]

1993

E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

1987

1984

Ch. Fattinger and W. Lukosz, “Optical-environment-dependent lifetimes and radiation patterns of luminescent centers in very thin films,” J. Lumin. 31/32, 933–935 (1984).
[CrossRef]

1977

1926

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 81, 1135–1153 (1926).
[CrossRef]

1919

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).
[CrossRef]

1911

H. v. Hörschelmann, “Über die Wirkungsweise des geknickten Marconischen Senders in der drahtlosen Telegraphie,” Jahrbuch drahtlos. Telegr. Teleph. 5, 14–34, 188–211 (1911).

1909

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).
[CrossRef]

Axelrod, D.

Bartko, A. P.

A. P. Bartko and R. M. Dickson, “Three-dimensional orientations of polymer-bound single molecules,” J. Phys. Chem. B 103, 3053–3056 (1999).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single molecule orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[CrossRef]

Betzig, E.

E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Böhmer, M.

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Chichester, R. J.

E. Betzig and R. J. Chichester, “Single molecules observed by near-field scanning optical microscopy,” Science 262, 1422–1425 (1993).
[CrossRef] [PubMed]

Corrie, J. E. T.

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. T. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature (London) 422, 399–404 (2003).
[CrossRef]

De Schryver, F. C.

J. Hofkens, W. Verheijen, R. Shukla, W. Dehaen, and F. C. De Schryver, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopyrroledione (DPP) core embedded in a thin polystyrene polymer film,” Macromolecules 31, 4493–4497 (1998).
[CrossRef]

Dehaen, W.

J. Hofkens, W. Verheijen, R. Shukla, W. Dehaen, and F. C. De Schryver, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopyrroledione (DPP) core embedded in a thin polystyrene polymer film,” Macromolecules 31, 4493–4497 (1998).
[CrossRef]

Deschenes, L. A.

L. A. Deschenes and D. A. Van den Bout, “Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition,” Science 292, 255–258 (2001).
[CrossRef] [PubMed]

Dickson, R. M.

A. P. Bartko and R. M. Dickson, “Imaging three-dimensional single molecule orientations,” J. Phys. Chem. B 103, 11237–11241 (1999).
[CrossRef]

A. P. Bartko and R. M. Dickson, “Three-dimensional orientations of polymer-bound single molecules,” J. Phys. Chem. B 103, 3053–3056 (1999).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, O. Glöckl, M. Reichle, and M. Eberler, “Reduction of the spot size by using a radially polarized laser beam,” in International Seminar on Novel Trends in Nonlinear Laser Spectroscopy and High-Precision Measurements in Optics, S. N. Bagaev, V. N. Zadkov, and S. M. Arakelian, eds., Proc. SPIE 4429, 105–111 (2001).
[CrossRef]

Eberler, M.

S. Quabis, R. Dorn, O. Glöckl, M. Reichle, and M. Eberler, “Reduction of the spot size by using a radially polarized laser beam,” in International Seminar on Novel Trends in Nonlinear Laser Spectroscopy and High-Precision Measurements in Optics, S. N. Bagaev, V. N. Zadkov, and S. M. Arakelian, eds., Proc. SPIE 4429, 105–111 (2001).
[CrossRef]

Enderlein, J.

Fattinger, Ch.

Ch. Fattinger and W. Lukosz, “Optical-environment-dependent lifetimes and radiation patterns of luminescent centers in very thin films,” J. Lumin. 31/32, 933–935 (1984).
[CrossRef]

Forkey, J. N.

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. T. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature (London) 422, 399–404 (2003).
[CrossRef]

Fourkas, J. T.

Gerken, U.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Glöckl, O.

S. Quabis, R. Dorn, O. Glöckl, M. Reichle, and M. Eberler, “Reduction of the spot size by using a radially polarized laser beam,” in International Seminar on Novel Trends in Nonlinear Laser Spectroscopy and High-Precision Measurements in Optics, S. N. Bagaev, V. N. Zadkov, and S. M. Arakelian, eds., Proc. SPIE 4429, 105–111 (2001).
[CrossRef]

Goldman, Y. E.

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. T. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature (London) 422, 399–404 (2003).
[CrossRef]

Hecht, B.

M. Prummer, B. Sick, B. Hecht, and U. P. Wild, “Three-dimensional optical polarization tomography of single molecules,” J. Chem. Phys. 118, 9824–9829 (2003).
[CrossRef]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

Hellen, E. H.

Hofkens, J.

J. Hofkens, W. Verheijen, R. Shukla, W. Dehaen, and F. C. De Schryver, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopyrroledione (DPP) core embedded in a thin polystyrene polymer film,” Macromolecules 31, 4493–4497 (1998).
[CrossRef]

Jasny, J.

J. Sepiol, J. Jasny, J. Keller, and U. Wild, “Single molecules observed by immersion mirror objective. The orientation of Terrylene molecules via the direction of its transition dipole moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Jelezko, F.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Keller, J.

J. Sepiol, J. Jasny, J. Keller, and U. Wild, “Single molecules observed by immersion mirror objective. The orientation of Terrylene molecules via the direction of its transition dipole moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Kotani, M.

M. Vacha and M. Kotani, “Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy,” J. Chem. Phys. 118, 5279–5282 (2003).
[CrossRef]

Kunz, R. E.

Lounis, B.

Ph. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Ten years of single-molecule spectroscopy,” J. Phys. Chem. A 104, 1–16 (2000).
[CrossRef]

Lukosz, W.

Ch. Fattinger and W. Lukosz, “Optical-environment-dependent lifetimes and radiation patterns of luminescent centers in very thin films,” J. Lumin. 31/32, 933–935 (1984).
[CrossRef]

W. Lukosz and R. E. Kunz, “Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power,” J. Opt. Soc. Am. 67, 1607–1615 (1977).
[CrossRef]

Maali, A.

Ph. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Ten years of single-molecule spectroscopy,” J. Phys. Chem. A 104, 1–16 (2000).
[CrossRef]

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

L. Novotny, “Single molecule fluorescence in inhomogeneous environments,” Appl. Phys. Lett. 69, 3806–3808 (1996).
[CrossRef]

Orrit, M.

Ph. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Ten years of single-molecule spectroscopy,” J. Phys. Chem. A 104, 1–16 (2000).
[CrossRef]

Prummer, M.

M. Prummer, B. Sick, B. Hecht, and U. P. Wild, “Three-dimensional optical polarization tomography of single molecules,” J. Chem. Phys. 118, 9824–9829 (2003).
[CrossRef]

Quabis, S.

S. Quabis, R. Dorn, O. Glöckl, M. Reichle, and M. Eberler, “Reduction of the spot size by using a radially polarized laser beam,” in International Seminar on Novel Trends in Nonlinear Laser Spectroscopy and High-Precision Measurements in Optics, S. N. Bagaev, V. N. Zadkov, and S. M. Arakelian, eds., Proc. SPIE 4429, 105–111 (2001).
[CrossRef]

Quinlan, M. E.

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. T. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature (London) 422, 399–404 (2003).
[CrossRef]

Reichle, M.

S. Quabis, R. Dorn, O. Glöckl, M. Reichle, and M. Eberler, “Reduction of the spot size by using a radially polarized laser beam,” in International Seminar on Novel Trends in Nonlinear Laser Spectroscopy and High-Precision Measurements in Optics, S. N. Bagaev, V. N. Zadkov, and S. M. Arakelian, eds., Proc. SPIE 4429, 105–111 (2001).
[CrossRef]

Rogl, H.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Schubert, A.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Schuler, S.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Sepiol, J.

J. Sepiol, J. Jasny, J. Keller, and U. Wild, “Single molecules observed by immersion mirror objective. The orientation of Terrylene molecules via the direction of its transition dipole moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Shaw, M. A.

J. N. Forkey, M. E. Quinlan, M. A. Shaw, J. E. T. Corrie, and Y. E. Goldman, “Three-dimensional structural dynamics of myosin V by single-molecule fluorescence polarization,” Nature (London) 422, 399–404 (2003).
[CrossRef]

Shukla, R.

J. Hofkens, W. Verheijen, R. Shukla, W. Dehaen, and F. C. De Schryver, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopyrroledione (DPP) core embedded in a thin polystyrene polymer film,” Macromolecules 31, 4493–4497 (1998).
[CrossRef]

Sick, B.

M. Prummer, B. Sick, B. Hecht, and U. P. Wild, “Three-dimensional optical polarization tomography of single molecules,” J. Chem. Phys. 118, 9824–9829 (2003).
[CrossRef]

B. Sick, B. Hecht, and L. Novotny, “Orientational imaging of single molecules by annular illumination,” Phys. Rev. Lett. 85, 4482–4485 (2000).
[CrossRef] [PubMed]

Sommerfeld, A.

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 81, 1135–1153 (1926).
[CrossRef]

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).
[CrossRef]

Tamarat, Ph.

Ph. Tamarat, A. Maali, B. Lounis, and M. Orrit, “Ten years of single-molecule spectroscopy,” J. Phys. Chem. A 104, 1–16 (2000).
[CrossRef]

Tietz, C.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

v. Hörschelmann, H.

H. v. Hörschelmann, “Über die Wirkungsweise des geknickten Marconischen Senders in der drahtlosen Telegraphie,” Jahrbuch drahtlos. Telegr. Teleph. 5, 14–34, 188–211 (1911).

Vacha, M.

M. Vacha and M. Kotani, “Three-dimensional orientation of single molecules observed by far- and near-field fluorescence microscopy,” J. Chem. Phys. 118, 5279–5282 (2003).
[CrossRef]

Van den Bout, D. A.

L. A. Deschenes and D. A. Van den Bout, “Single-molecule studies of heterogeneous dynamics in polymer melts near the glass transition,” Science 292, 255–258 (2001).
[CrossRef] [PubMed]

Verheijen, W.

J. Hofkens, W. Verheijen, R. Shukla, W. Dehaen, and F. C. De Schryver, “Detection of a single dendrimer macromolecule with a fluorescent dihydropyrrolopyrroledione (DPP) core embedded in a thin polystyrene polymer film,” Macromolecules 31, 4493–4497 (1998).
[CrossRef]

Weiss, S.

S. Weiss, “Measuring conformational dynamics of biomolecules by single molecule fluorescence spectroscopy,” Nature Struct. Biol. 7, 724–729 (2000).
[CrossRef] [PubMed]

Weyl, H.

H. Weyl, “Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter,” Ann. Phys. (Leipzig) 60, 481–500 (1919).
[CrossRef]

Wild, U.

J. Sepiol, J. Jasny, J. Keller, and U. Wild, “Single molecules observed by immersion mirror objective. The orientation of Terrylene molecules via the direction of its transition dipole moment,” Chem. Phys. Lett. 273, 444–448 (1997).
[CrossRef]

Wild, U. P.

M. Prummer, B. Sick, B. Hecht, and U. P. Wild, “Three-dimensional optical polarization tomography of single molecules,” J. Chem. Phys. 118, 9824–9829 (2003).
[CrossRef]

Wrachtrup, J.

C. Tietz, F. Jelezko, U. Gerken, S. Schuler, A. Schubert, H. Rogl, and J. Wrachtrup, “Single-molecule spectroscopy on the light-harvesting complex II of higher plants,” Biophys. J. 81, 556–562 (2001).
[CrossRef] [PubMed]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Ann. Phys. (Leipzig)

A. Sommerfeld, “Über die Ausbreitung der Wellen in der drahtlosen Telegraphie,” Ann. Phys. (Leipzig) 28, 665–736 (1909).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Coordinate system used for calculations: p, dipole moment; ob, the objective lens; ba, the back aperture of the objective lens.

Fig. 2
Fig. 2

Calculated emission patterns of a dipole at an air–glass interface (nair=1.0, nglass=1.52) in the back-aperture plane of a NA=1.4 objective lens: (a) Θ=90°, Φ=0° (horizontal dipole); (b) Θ=90°, Φ=90° (horizontal dipole); (c) Θ=0°, Φ=0° (vertical dipole); (d) Θ=45°, Φ=45°.

Fig. 3
Fig. 3

Experimental setup consisting of an inverted microscope, a green excitation laser (λ=532 nm), a polarization optics box containing a half-wave plate, a quarter-wave plate, and a mode converter (see Ref. 29). DBS, dichroic mirror; FM, flip mirror; APD, avalanche photodiode; CCD, a cooled CCD camera.

Fig. 4
Fig. 4

Example of an observed emission pattern: (a) measured data; (b) fitted pattern; (c), (d), cross sections along a horizontal and a vertical line through the center of the pattern, respectively.

Fig. 5
Fig. 5

Comparison of the orientations of emission dipoles and absorption dipoles: (a)–(c) Fluorescence-rate images recorded by the raster scanning of a single-molecule sample in the focal plane of a strongly focused excitation beam. The excitation beam is (a) a Gaussian beam polarized in x (horizontal polarization); (b) a Gaussian beam polarized in y (vertical polarization); and (c) a radially polarized beam. (d) Orientations of 16 molecules determined from the emission patterns. (e) Emission patterns of six selected molecules [as marked in (d)] for different excitation polarizations. The left-hand images are measured data, the right-hand images are best fits. Numbers in the top centers are maximum intensities. lx (ly) denotes excitation with an x-polarized (y-polarized) Gaussian beam and r denotes excitation with a radially polarized beam. (f) Comparison of corresponding fluorescence-rate images extracted from (a)–(c) (left-hand images) with calculated patterns for dipole orientations as determined from the emission patterns (right-hand images). The arrows mark the centers of the molecules to watch. Note the close proximity of other molecules for molecules 1, 4, and 5. In the images marked with N.A., the molecules were already photobleached.

Equations (11)

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I(r, φ, Θ, Φ)1cos θ(EpEp*+EsEs*),
Ep=[c1(θ)cos Θ sin θ+c2(θ)sin Θ cos θ cos(φ-Φ)],
Es=c3(θ)sin Θ sin(φ-Φ),
c1(θ)=n2cos θcos θstp(θs)(θs),
c2(θ)=ntp(θs)(θs),
c3(θ)=-ncos θcos θsts(θs)(θs),
(θs)=exp(ikn1 cosθsδ)
c1(θ)=-1(θ)+rp(θ)(θ),
c2(θ)=-1(θ)-rp(θ)(θ),
c3(θ)=-[-1(θ)+rs(θ)(θ)],
(θ)=exp(-ikn2 cos θδ),

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