Abstract

In this paper we present a scheme for the acquisition of high temporal resolution images of single particles with enhanced lateral localization accuracy. The scheme, which is implementable as a part of the illumination system of a standard confocal microscope, is based on the generation of a vector beam that is manipulated by polarimetry techniques to create a set of illumination PSFs with different spatial profiles. The combination of data collected in different illumination states enables the extraction of spatial information obscured by diffraction in the standard imaging system. An implementation of the scheme based on the utilization of the unique phenomenon of conical diffraction is presented, and the basic strategy it provides for enhanced localization in the diffraction limited region is demonstrated.

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  1. M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Annu. Rev. Biophys. Biomol. Struct.26(1), 373–399 (1997).
    [CrossRef] [PubMed]
  2. M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol.9(12), 929–943 (2008).
    [CrossRef] [PubMed]
  3. 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]
  4. G. B. Airy, “On the diffraction of an object-glass with circular aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).
  5. N. Bobroff, “Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum.57(6), 1152 –1157(1986).
    [CrossRef]
  6. R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
    [CrossRef] [PubMed]
  7. J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd Ed. (Springer Science + Business Media, LLC, 2006).
  8. G. Y. Sirat, Patent application PCT/FR2011/000555.
  9. W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. Royal Irish. Acad.1–144 (1833).
  10. H. Llyold, “On the phenomena presented by light in its passage along the axes of biaxal crystals,” Phil. Mag. 1,112–120 and 207–210 (1833).
  11. J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann.124(11), 461–462 (1839).
  12. C. V. Raman, “'Conical refraction in biaxial crystals,” Nature107(2702), 747–747 (1921).
    [CrossRef]
  13. A. M. Belsky and A. P. Khapalyuk, “Internal conical refraction of limited light-beams in 2-axes crystals,” Opt. Spectrosc.44, 746–751 (1978).
  14. M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt.6(4), 289–300 (2004).
    [CrossRef]
  15. M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A. 462(2070), 1629–1642 (2006).
    [CrossRef]
  16. M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Optics50, 13–50 (2007).
    [CrossRef]
  17. B. Boulanger and J. Zyss, Physical Properties of Crystals. Vol. D of International Tables for Crystallography, A. Authier, Ed. (Kluwer, Dordrecht, 1997).
  18. G. Y. Sirat, Patent application US 2009/0168613 A1.
  19. P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci.96(1-3), 108–140 (1980).
    [CrossRef]
  20. S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
    [CrossRef]

2008 (1)

M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol.9(12), 929–943 (2008).
[CrossRef] [PubMed]

2007 (1)

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Optics50, 13–50 (2007).
[CrossRef]

2006 (1)

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]

2004 (1)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt.6(4), 289–300 (2004).
[CrossRef]

2002 (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
[CrossRef] [PubMed]

2001 (1)

S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
[CrossRef]

1997 (1)

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Annu. Rev. Biophys. Biomol. Struct.26(1), 373–399 (1997).
[CrossRef] [PubMed]

1986 (1)

N. Bobroff, “Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum.57(6), 1152 –1157(1986).
[CrossRef]

1980 (1)

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci.96(1-3), 108–140 (1980).
[CrossRef]

1978 (1)

A. M. Belsky and A. P. Khapalyuk, “Internal conical refraction of limited light-beams in 2-axes crystals,” Opt. Spectrosc.44, 746–751 (1978).

1921 (1)

C. V. Raman, “'Conical refraction in biaxial crystals,” Nature107(2702), 747–747 (1921).
[CrossRef]

1839 (1)

J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann.124(11), 461–462 (1839).

1835 (1)

G. B. Airy, “On the diffraction of an object-glass with circular aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).

1833 (1)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. Royal Irish. Acad.1–144 (1833).

Airy, G. B.

G. B. Airy, “On the diffraction of an object-glass with circular aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).

Belsky, A. M.

A. M. Belsky and A. P. Khapalyuk, “Internal conical refraction of limited light-beams in 2-axes crystals,” Opt. Spectrosc.44, 746–751 (1978).

Berry, M. V.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Optics50, 13–50 (2007).
[CrossRef]

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt.6(4), 289–300 (2004).
[CrossRef]

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]

Bobroff, N.

N. Bobroff, “Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum.57(6), 1152 –1157(1986).
[CrossRef]

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]

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]

Dorn, R.

S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
[CrossRef]

Eberlerm, M.

S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
[CrossRef]

Fernández-Suárez, M.

M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol.9(12), 929–943 (2008).
[CrossRef] [PubMed]

Glockl, O.

S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
[CrossRef]

Hamilton, W. R.

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. Royal Irish. Acad.1–144 (1833).

Hauge, P. S.

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci.96(1-3), 108–140 (1980).
[CrossRef]

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]

Jacobson, K.

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Annu. Rev. Biophys. Biomol. Struct.26(1), 373–399 (1997).
[CrossRef] [PubMed]

Jeffrey, M. R.

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Optics50, 13–50 (2007).
[CrossRef]

Khapalyuk, A. P.

A. M. Belsky and A. P. Khapalyuk, “Internal conical refraction of limited light-beams in 2-axes crystals,” Opt. Spectrosc.44, 746–751 (1978).

Larson, D. R.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
[CrossRef] [PubMed]

Leuchs, G.

S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
[CrossRef]

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]

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]

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]

Poggendorff, J. C.

J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann.124(11), 461–462 (1839).

Quabis, S.

S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
[CrossRef]

Raman, C. V.

C. V. Raman, “'Conical refraction in biaxial crystals,” Nature107(2702), 747–747 (1921).
[CrossRef]

Saxton, M. J.

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Annu. Rev. Biophys. Biomol. Struct.26(1), 373–399 (1997).
[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]

Thompson, R. E.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
[CrossRef] [PubMed]

Ting, A. Y.

M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol.9(12), 929–943 (2008).
[CrossRef] [PubMed]

Webb, W. W.

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
[CrossRef] [PubMed]

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

M. J. Saxton and K. Jacobson, “Single-particle tracking: applications to membrane dynamics,” Annu. Rev. Biophys. Biomol. Struct.26(1), 373–399 (1997).
[CrossRef] [PubMed]

Appl. Phys. B (1)

S. Quabis, R. Dorn, M. Eberlerm, O. Glockl, and G. Leuchs, “The focus of light: theoretical calculation and experimental tomographic reconstruction,” Appl. Phys. B72(1), 109–113 (2001).
[CrossRef]

Biophys. J. (1)

R. E. Thompson, D. R. Larson, and W. W. Webb, “Precise nanometer localization analysis for individual fluorescent probes,” Biophys. J.82(5), 2775–2783 (2002).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

M. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike,” J. Opt. A, Pure Appl. Opt.6(4), 289–300 (2004).
[CrossRef]

Nat. Rev. Mol. Cell Biol. (1)

M. Fernández-Suárez and A. Y. Ting, “Fluorescent probes for super-resolution imaging in living cells,” Nat. Rev. Mol. Cell Biol.9(12), 929–943 (2008).
[CrossRef] [PubMed]

Nature (1)

C. V. Raman, “'Conical refraction in biaxial crystals,” Nature107(2702), 747–747 (1921).
[CrossRef]

Opt. Spectrosc. (1)

A. M. Belsky and A. P. Khapalyuk, “Internal conical refraction of limited light-beams in 2-axes crystals,” Opt. Spectrosc.44, 746–751 (1978).

Pogg. Ann. (1)

J. C. Poggendorff, “Ueber die konische refraction,” Pogg. Ann.124(11), 461–462 (1839).

Prog. Optics (1)

M. V. Berry and M. R. Jeffrey, “Conical diffraction: Hamilton's diabolical point at the heart of crystal optics,” Prog. Optics50, 13–50 (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

N. Bobroff, “Position measurement with a resolution and noise-limited instrument,” Rev. Sci. Instrum.57(6), 1152 –1157(1986).
[CrossRef]

Science (1)

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]

Surf. Sci. (1)

P. S. Hauge, “Recent developments in instrumentation in ellipsometry,” Surf. Sci.96(1-3), 108–140 (1980).
[CrossRef]

Trans. Cambridge Philos. Soc. (1)

G. B. Airy, “On the diffraction of an object-glass with circular aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).

Trans. Royal Irish. Acad. (1)

W. R. Hamilton, “Third supplement to an essay on the theory of systems of rays,” Trans. Royal Irish. Acad.1–144 (1833).

Other (6)

H. Llyold, “On the phenomena presented by light in its passage along the axes of biaxal crystals,” Phil. Mag. 1,112–120 and 207–210 (1833).

J. B. Pawley, Handbook of Biological Confocal Microscopy, 3rd Ed. (Springer Science + Business Media, LLC, 2006).

G. Y. Sirat, Patent application PCT/FR2011/000555.

B. Boulanger and J. Zyss, Physical Properties of Crystals. Vol. D of International Tables for Crystallography, A. Authier, Ed. (Kluwer, Dordrecht, 1997).

G. Y. Sirat, Patent application US 2009/0168613 A1.

M. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: observations and theory,” Proc. R. Soc. A. 462(2070), 1629–1642 (2006).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

A schematic illustration of the signal generation procedure according to our scheme. An electric field polarization distribution is created inside the illumination beam (a), which is then manipulated by polarimetry techniques to obtain a continuous spatio-temporal modulation of the light incident on the sample (b). The emission signal, uniquely modulated according to the location [R1, θ1] of the particle, is integrated by the detector (c) and Fourier transformed (d), to create a frequency domain label by which I [t, R1, θ1] is identified and the particle’s location is reconstructed.

Fig. 2
Fig. 2

Geometry of conical diffraction for a circularly polarized incident beam. In a thick crystal configuration (Aa), the diffracted beam emerges out of the crystal as a hollow cylinder, forming the two Poggendorff rings at the focal image plane (Ab). In a thin crystal configuration (Ba), the diffracted beam is mostly confined to its original width, forming a unique spatial polarization distribution inside the Airy disk area at the focal image plane (Bb).

Fig. 3
Fig. 3

(a) Schematics of the optical module integrated into the microscope’s illumination light path. (b) An illustration of the PSF intensity profiles incident on the sample at 16 equally spaced instances throughout the first half of the QWP rotation cycle.

Fig. 4
Fig. 4

Location dependency of the frequency domain signals obtained in our system. (a) 2ω amplitude signal, (b) 4ω amplitude signal and (c) 4ω phase signal ranging between [-π,π]. Row A: calculated frequency domain signals based on the system's ρ0 parameter. Coordinates are normalized with respect to the Airy radius. Row B: Scanning measurement preformed on a 250nm diameter silver dot. The dashed black lines denote the Airy disk borderlines. Coordinates are given in microns.

Equations (4)

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

R 0 = l n 2 ( n 2 n 1 )( n 3 n 2 )
E (R,θ)= E F (R)+ E V (R,θ)=[ B 0 (R)×I+ B 1 (R)×( cosθ sinθ sinθ cosθ ) ]|P
B 0 (R)=k d U U a 0 (U)cos(k R 0 U) J 0 (kUR) B 1 (R)=k d U U a 0 (U)sin(k R 0 U) J 1 (kUR)
I(R,θ,t)= 1 2 [ ( S 0 (R,θ)+ S 1 (R,θ) 2 ) S 3 (R,θ)sin2ωt+ S 2 (R,θ) 2 sin4ωt+ S 1 (R,θ) 2 cos4ωt ]

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