Abstract

A technique has been developed to obtain three-dimensional structural information on a length scale well below the Rayleigh length with conventional far-field optics. By spectrally selecting a single molecule with high-resolution laser spectroscopy and using a CCD camera to register the spatial distribution of the emitted photons in three dimensions, one can determine the position of a molecule with unprecedented accuracy. One can resolve details in the specimen with sub-diffraction-limited resolution in three dimensions by applying this procedure to as many molecules as are present in the same diffraction-limited volume and obtaining their mutual positions. The feasibility of this technique is demonstrated for the system of pentacene in p-terphenyl at cryogenic temperatures for which molecules were localized with an accuracy of better than 40 nm in the lateral and 100 nm in the axial directions.

© 1999 Optical Society of America

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References

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  1. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9, 413–468 (1873).
    [CrossRef]
  2. Rayleigh, “On the manufacture and theory of diffraction-gratings,” Philos. Mag. 47, 81–93, 193–205 (1874).
  3. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274, 403–411, 477–486 (1879).
    [CrossRef]
  4. Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 9, 40–55 (1880) (continued from Vol. 8, p. 486).
    [CrossRef]
  5. J. W. Strutt( Rayleigh), “Investigations in optics, with special reference to the spectroscope,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1899), Vol. 1, 1869–1881, pp. 416–459 [originally published in Philos. Mag.3,4]
  6. D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Adv. Opt. Electron. Microsc. 12, 243–312 (1991).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. W. E. Moerner, “Low-temperature studies in solids,” in Single-Molecule Optical Detection, Imaging and Spectroscopy, T. Basché, W. E. Moerner, M. Orrit, U. P. Wild, eds. (VCH, Weinheim, Germany, 1997), Chap. 1.
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    [CrossRef]
  13. H. de Vries, D. A. Wiersma, “Fluorescence transient and optical free induction decay spectroscopy of pentacene in mixed crystals at 2 K. Determination of intersystem crossing and internal conversion rates,” J. Phys. Chem. 70, 5807–5822 (1979).
    [CrossRef]
  14. W. P. Ambrose, Th. Basché, W. E. Moerner, “Detection and spectroscopy of single pentacene molecules in a p-terphenyl crystal by means of fluorescence excitation,” J. Chem. Phys. 95, 7150–7163 (1991).
    [CrossRef]
  15. M. Orrit, J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
    [CrossRef] [PubMed]
  16. P. D. Reilly, J. L. Skinner, “Spectral diffusion of individual pentacene molecules in p-terphenyl crystal; stochastic theoretical model and analysis of experimental data,” J. Chem. Phys. 102, 1540–1552 (1995).
    [CrossRef]
  17. J. L. Skinner, W. E. Moerner, “Structure and dynamics in solids as probed by optical spectroscopy,” J. Phys. Chem. 100, 13,251–13,262 (1996).
    [CrossRef]
  18. M. Orrit, J. Bernard, A. Zumbusch, R. I. Personov, “Stark effect on single molecules in a polymer matrix,” Chem. Phys. Lett. 196, 595–600 (1992).
    [CrossRef]

1996

J. L. Skinner, W. E. Moerner, “Structure and dynamics in solids as probed by optical spectroscopy,” J. Phys. Chem. 100, 13,251–13,262 (1996).
[CrossRef]

1995

P. D. Reilly, J. L. Skinner, “Spectral diffusion of individual pentacene molecules in p-terphenyl crystal; stochastic theoretical model and analysis of experimental data,” J. Chem. Phys. 102, 1540–1552 (1995).
[CrossRef]

E. Betzig, “Proposed method for molecular optical imaging,” Opt. Lett. 20, 237–239 (1995).
[CrossRef] [PubMed]

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

1994

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Appl. Phys. A: Solids Surf. 59, 89–101 (1994).
[CrossRef]

1992

M. Orrit, J. Bernard, A. Zumbusch, R. I. Personov, “Stark effect on single molecules in a polymer matrix,” Chem. Phys. Lett. 196, 595–600 (1992).
[CrossRef]

1991

D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Adv. Opt. Electron. Microsc. 12, 243–312 (1991).

W. P. Ambrose, Th. Basché, W. E. Moerner, “Detection and spectroscopy of single pentacene molecules in a p-terphenyl crystal by means of fluorescence excitation,” J. Chem. Phys. 95, 7150–7163 (1991).
[CrossRef]

1990

M. Orrit, J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
[CrossRef] [PubMed]

1985

1979

H. de Vries, D. A. Wiersma, “Fluorescence transient and optical free induction decay spectroscopy of pentacene in mixed crystals at 2 K. Determination of intersystem crossing and internal conversion rates,” J. Phys. Chem. 70, 5807–5822 (1979).
[CrossRef]

1976

J. L. Baudour, “Transition structurale dans les polyphenyles. I. Structure crystalline de la phase basse temperature du p-terphenyl a 113 K,” Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 32, 150–154 (1976).
[CrossRef]

1880

Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 9, 40–55 (1880) (continued from Vol. 8, p. 486).
[CrossRef]

1879

Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274, 403–411, 477–486 (1879).
[CrossRef]

1874

Rayleigh, “On the manufacture and theory of diffraction-gratings,” Philos. Mag. 47, 81–93, 193–205 (1874).

1873

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9, 413–468 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9, 413–468 (1873).
[CrossRef]

Ambrose, W. P.

W. P. Ambrose, Th. Basché, W. E. Moerner, “Detection and spectroscopy of single pentacene molecules in a p-terphenyl crystal by means of fluorescence excitation,” J. Chem. Phys. 95, 7150–7163 (1991).
[CrossRef]

Basché, Th.

W. P. Ambrose, Th. Basché, W. E. Moerner, “Detection and spectroscopy of single pentacene molecules in a p-terphenyl crystal by means of fluorescence excitation,” J. Chem. Phys. 95, 7150–7163 (1991).
[CrossRef]

Baudour, J. L.

J. L. Baudour, “Transition structurale dans les polyphenyles. I. Structure crystalline de la phase basse temperature du p-terphenyl a 113 K,” Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 32, 150–154 (1976).
[CrossRef]

Bernard, J.

M. Orrit, J. Bernard, A. Zumbusch, R. I. Personov, “Stark effect on single molecules in a polymer matrix,” Chem. Phys. Lett. 196, 595–600 (1992).
[CrossRef]

M. Orrit, J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
[CrossRef] [PubMed]

Betzig, E.

Brouwer, A. C. J.

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

Burns, D. H.

Callis, J. B.

Christian, G. D.

Davidson, E. R.

de Vries, H.

H. de Vries, D. A. Wiersma, “Fluorescence transient and optical free induction decay spectroscopy of pentacene in mixed crystals at 2 K. Determination of intersystem crossing and internal conversion rates,” J. Phys. Chem. 70, 5807–5822 (1979).
[CrossRef]

Disselhorst, J. A. J. M.

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

Groenen, E. J. J.

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

Heinzelmann, H.

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Appl. Phys. A: Solids Surf. 59, 89–101 (1994).
[CrossRef]

Köhler, J.

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

Moerner, W. E.

J. L. Skinner, W. E. Moerner, “Structure and dynamics in solids as probed by optical spectroscopy,” J. Phys. Chem. 100, 13,251–13,262 (1996).
[CrossRef]

W. P. Ambrose, Th. Basché, W. E. Moerner, “Detection and spectroscopy of single pentacene molecules in a p-terphenyl crystal by means of fluorescence excitation,” J. Chem. Phys. 95, 7150–7163 (1991).
[CrossRef]

W. E. Moerner, “Low-temperature studies in solids,” in Single-Molecule Optical Detection, Imaging and Spectroscopy, T. Basché, W. E. Moerner, M. Orrit, U. P. Wild, eds. (VCH, Weinheim, Germany, 1997), Chap. 1.

Orrit, M.

M. Orrit, J. Bernard, A. Zumbusch, R. I. Personov, “Stark effect on single molecules in a polymer matrix,” Chem. Phys. Lett. 196, 595–600 (1992).
[CrossRef]

M. Orrit, J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
[CrossRef] [PubMed]

Personov, R. I.

M. Orrit, J. Bernard, A. Zumbusch, R. I. Personov, “Stark effect on single molecules in a polymer matrix,” Chem. Phys. Lett. 196, 595–600 (1992).
[CrossRef]

Pohl, D. W.

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Appl. Phys. A: Solids Surf. 59, 89–101 (1994).
[CrossRef]

D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Adv. Opt. Electron. Microsc. 12, 243–312 (1991).

Rayleigh,

Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 9, 40–55 (1880) (continued from Vol. 8, p. 486).
[CrossRef]

Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274, 403–411, 477–486 (1879).
[CrossRef]

Rayleigh, “On the manufacture and theory of diffraction-gratings,” Philos. Mag. 47, 81–93, 193–205 (1874).

J. W. Strutt( Rayleigh), “Investigations in optics, with special reference to the spectroscope,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1899), Vol. 1, 1869–1881, pp. 416–459 [originally published in Philos. Mag.3,4]

Reilly, P. D.

P. D. Reilly, J. L. Skinner, “Spectral diffusion of individual pentacene molecules in p-terphenyl crystal; stochastic theoretical model and analysis of experimental data,” J. Chem. Phys. 102, 1540–1552 (1995).
[CrossRef]

Schmidt, J.

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

Skinner, J. L.

J. L. Skinner, W. E. Moerner, “Structure and dynamics in solids as probed by optical spectroscopy,” J. Phys. Chem. 100, 13,251–13,262 (1996).
[CrossRef]

P. D. Reilly, J. L. Skinner, “Spectral diffusion of individual pentacene molecules in p-terphenyl crystal; stochastic theoretical model and analysis of experimental data,” J. Chem. Phys. 102, 1540–1552 (1995).
[CrossRef]

Strutt, J. W.

J. W. Strutt( Rayleigh), “Investigations in optics, with special reference to the spectroscope,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1899), Vol. 1, 1869–1881, pp. 416–459 [originally published in Philos. Mag.3,4]

van der Meer, H.

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

Wiersma, D. A.

H. de Vries, D. A. Wiersma, “Fluorescence transient and optical free induction decay spectroscopy of pentacene in mixed crystals at 2 K. Determination of intersystem crossing and internal conversion rates,” J. Phys. Chem. 70, 5807–5822 (1979).
[CrossRef]

Zumbusch, A.

M. Orrit, J. Bernard, A. Zumbusch, R. I. Personov, “Stark effect on single molecules in a polymer matrix,” Chem. Phys. Lett. 196, 595–600 (1992).
[CrossRef]

Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem.

J. L. Baudour, “Transition structurale dans les polyphenyles. I. Structure crystalline de la phase basse temperature du p-terphenyl a 113 K,” Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 32, 150–154 (1976).
[CrossRef]

Adv. Opt. Electron. Microsc.

D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Adv. Opt. Electron. Microsc. 12, 243–312 (1991).

Appl. Opt.

Appl. Phys. A: Solids Surf.

H. Heinzelmann, D. W. Pohl, “Scanning near-field optical microscopy (SNOM),” Appl. Phys. A: Solids Surf. 59, 89–101 (1994).
[CrossRef]

Arch. Mikrosc. Anat. Entwicklungsmech.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9, 413–468 (1873).
[CrossRef]

Chem. Phys. Lett.

M. Orrit, J. Bernard, A. Zumbusch, R. I. Personov, “Stark effect on single molecules in a polymer matrix,” Chem. Phys. Lett. 196, 595–600 (1992).
[CrossRef]

J. Chem. Phys.

W. P. Ambrose, Th. Basché, W. E. Moerner, “Detection and spectroscopy of single pentacene molecules in a p-terphenyl crystal by means of fluorescence excitation,” J. Chem. Phys. 95, 7150–7163 (1991).
[CrossRef]

P. D. Reilly, J. L. Skinner, “Spectral diffusion of individual pentacene molecules in p-terphenyl crystal; stochastic theoretical model and analysis of experimental data,” J. Chem. Phys. 102, 1540–1552 (1995).
[CrossRef]

J. Phys. Chem.

J. L. Skinner, W. E. Moerner, “Structure and dynamics in solids as probed by optical spectroscopy,” J. Phys. Chem. 100, 13,251–13,262 (1996).
[CrossRef]

H. de Vries, D. A. Wiersma, “Fluorescence transient and optical free induction decay spectroscopy of pentacene in mixed crystals at 2 K. Determination of intersystem crossing and internal conversion rates,” J. Phys. Chem. 70, 5807–5822 (1979).
[CrossRef]

Opt. Lett.

Philos. Mag.

Rayleigh, “On the manufacture and theory of diffraction-gratings,” Philos. Mag. 47, 81–93, 193–205 (1874).

Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274, 403–411, 477–486 (1879).
[CrossRef]

Rayleigh, “Investigations in optics, with special reference to the spectroscope,” Philos. Mag. 9, 40–55 (1880) (continued from Vol. 8, p. 486).
[CrossRef]

Phys. Rev. Lett.

M. Orrit, J. Bernard, “Single pentacene molecules detected by fluorescence excitation in a p-terphenyl crystal,” Phys. Rev. Lett. 65, 2716–2719 (1990).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

H. van der Meer, J. A. J. M. Disselhorst, J. Köhler, A. C. J. Brouwer, E. J. J. Groenen, J. Schmidt, “An insert for single-molecule magnetic-resonance spectroscopy in an external magnetic field,” Rev. Sci. Instrum. 66, 4853–4856 (1995).
[CrossRef]

Other

W. E. Moerner, “Low-temperature studies in solids,” in Single-Molecule Optical Detection, Imaging and Spectroscopy, T. Basché, W. E. Moerner, M. Orrit, U. P. Wild, eds. (VCH, Weinheim, Germany, 1997), Chap. 1.

J. W. Strutt( Rayleigh), “Investigations in optics, with special reference to the spectroscope,” in Scientific Papers by John William Strutt, Baron Rayleigh (Cambridge U. Press, Cambridge, 1899), Vol. 1, 1869–1881, pp. 416–459 [originally published in Philos. Mag.3,4]

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Figures (7)

Fig. 1
Fig. 1

Schematic of the experimental setup: ADC, analog-to-digital converter; DAC, digital-to-analog converter; PCI, peripheral component interconnect bus; MCS, multichannel scaling card; other abbreviations defined in text.

Fig. 2
Fig. 2

Part of the fluorescence-excitation spectrum of pentacene in p-terphenyl taken at a wavelength of 592.20 nm. The laser frequency has been detuned by 20 GHz to the red with respect to the center of the O2 ensemble line. The features marked with asterisks result from two or more molecules and are not considered in the evaluation.

Fig. 3
Fig. 3

Inset, fluorescence image of a single pentacene molecule. From the width of the Airy-function-like shape, the lateral resolution of the microscope is determined to be δrexp=880 nm. The circles represent the accuracies of the position determination of a single molecule as a function of acquisition time. These data points are fitted (solid curve) by the sum of the accuracy given by Poisson statistics (dotted curve) and the mechanical drift in the setup (described by a random walk; dashed curve).

Fig. 4
Fig. 4

(a) Diffraction-limited image of molecule 3. Its lateral position is determined as x3=(1.357±0.040)µm and y3=(1.420±0.040)µm. (b) Diffraction-limited image of molecule 5. Here x5=(1.741±0.040)µm and y5=(1.410±0.040)µm. Both images were obtained with an accumulation time of 15 s on the CCD camera. The total image covers 4.7 µm×4.7 µm in object space. (c) Sum of the images shown in (a) and (b).

Fig. 5
Fig. 5

Dependence of radial spot size on the axial position of the CCD camera for molecule 2 (filled circles) and molecule 3 (open circles). Horizontal and vertical scales are given in object space dimensions. We obtained spot size w(z) by taking the radial average of the photon distribution on the CCD camera with respect to the lateral position of the molecule and determining the radius of the area that contains 50% of the total intensity. The solid curve corresponds to a fit of a focused Gaussian beam waist according to Eq. (1). The axial positions of molecule 2 and molecule 3 are, respectively, z2=(1.82±0.12)µm and z3=(0.49±0.05)µm. For illustration, six photon distribution patterns are shown for molecule 2 at the indicated focal positions.

Fig. 6
Fig. 6

Relative positions of molecules 1–7 (bright dots) together with the experimentally obtained total three-dimensional photon distribution summed in computer memory and projected into object space. Each molecule contributes one cigar-shaped photon distribution, whose intensity distribution is given by the gray scale. The size of each single distribution corresponds to the diffraction-limited resolution of the microscope, and the intensity is determined by the orientation of the transition-dipole moment of the molecule, the saturation characteristics of the optical transition, and the laser intensity at the location of the molecule. In a conventional experiment in which all seven molecules are excited simultaneously, the total cloud is observed without information on the mutual position of the contributing molecules.

Fig. 7
Fig. 7

(a) Relative lateral positions of molecules from three different areas in the sample studied (each data set is indicated by a different symbol). The gray area denotes the size of the diffraction-limited spot. The positions of molecules from different data sets obtained from different sample positions are all given relative to the statistical center of the distribution within each data set. (b) Relative axial positions of the molecules studied.

Equations (1)

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w2(z)=w021+(zi-z)2λ2π2w04,

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