Abstract

Elliptical mirror based imaging systems permit aperture angles greater than π/2 to be realized. It is therefore possible to collect part or all of both the forward and backward diffractive fields emitted from single molecules. In this paper we derive rigorous formulae for the image intensity when the single molecule is modeled as a dipole emitter. It is found in theory that the point spread function can be 2.44 times narrower at full-width-half-maximum in the axial direction when using an elliptical mirror with the maximum aperture angle of 2π/3 as compared with a parabolic mirror system with the aperture angle of π/2 whereas the side lobe level is increased by only 0.21% when the dipole is oriented along Z axis.

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References

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  1. S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol.21(11), 1347–1355 (2003).
    [CrossRef] [PubMed]
  2. B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express16(6), 4154–4162 (2008).
    [CrossRef] [PubMed]
  3. J. B. Pawley, Handbook of Biological Confocal Microscopy (Plenum Press, 2006).
  4. R. Oldenbourg, H. Terada, R. Tiberio, and S. Inoué, “Image sharpness and contrast transfer in coherent confocal microscopy,” J. Microsc.172(1), 31–39 (1993).
    [CrossRef] [PubMed]
  5. R. Binet, J. Colineau, and J. C. Lehureau, “Short-range synthetic aperture imaging at 633 nm by digital holography,” Appl. Opt.41(23), 4775–4782 (2002).
    [CrossRef] [PubMed]
  6. S. M. Beck, J. R. Buck, W. F. Buell, R. P. Dickinson, D. A. Kozlowski, N. J. Marechal, and T. J. Wright, “Synthetic-aperture imaging laser radar: laboratory demonstration and signal processing,” Appl. Opt.44(35), 7621–7629 (2005).
    [CrossRef] [PubMed]
  7. N. Lue, W. Choi, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” Opt. Express16(20), 16240–16246 (2008).
    [CrossRef] [PubMed]
  8. S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun.93(5-6), 277–282 (1992).
    [CrossRef]
  9. M. Schrader and S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc.183(2), 110–115 (1996).
    [CrossRef]
  10. A. Drechsler, M. A. Lieb, C. Debus, A. J. Meixner, and G. Tarrach, “Confocal microscopy with a high numerical aperture parabolic mirror,” Opt. Express9(12), 637–644 (2001).
    [CrossRef] [PubMed]
  11. D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
    [CrossRef]
  12. S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science283(5408), 1676–1683 (1999).
    [CrossRef] [PubMed]
  13. T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
    [CrossRef] [PubMed]
  14. H. P. Lu, L. Xun, and X. S. Xie, “Single-molecule enzymatic dynamics,” Science282(5395), 1877–1882 (1998).
    [CrossRef] [PubMed]
  15. D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
    [CrossRef]
  16. L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
    [CrossRef] [PubMed]
  17. M. A. Lieb and A. J. Meixner, “A high numerical aperture parabolic mirror as imaging device for confocal microscopy,” Opt. Express8(7), 458–474 (2001).
    [CrossRef] [PubMed]
  18. J. D. Jackson, Classical Electrodynamics, Wiley, 1992.
  19. J. Liu, J. Tan, T. Wilson, and C. Zhong, “Rigorous theory on elliptical mirror focusing for point scanning microscopy,” Opt. Express20(6), 6175–6184 (2012).
    [CrossRef] [PubMed]
  20. C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging5(4), 205–218 (1997).
    [CrossRef]
  21. T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun.141(5-6), 298–313 (1997).
    [CrossRef]
  22. J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett.33(7), 681–683 (2008).
    [CrossRef] [PubMed]

2012 (1)

2009 (1)

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

2008 (3)

2005 (1)

2003 (1)

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol.21(11), 1347–1355 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (2)

2000 (1)

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
[CrossRef] [PubMed]

1999 (1)

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science283(5408), 1676–1683 (1999).
[CrossRef] [PubMed]

1998 (1)

H. P. Lu, L. Xun, and X. S. Xie, “Single-molecule enzymatic dynamics,” Science282(5395), 1877–1882 (1998).
[CrossRef] [PubMed]

1997 (3)

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging5(4), 205–218 (1997).
[CrossRef]

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun.141(5-6), 298–313 (1997).
[CrossRef]

1996 (2)

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
[CrossRef] [PubMed]

M. Schrader and S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc.183(2), 110–115 (1996).
[CrossRef]

1993 (1)

R. Oldenbourg, H. Terada, R. Tiberio, and S. Inoué, “Image sharpness and contrast transfer in coherent confocal microscopy,” J. Microsc.172(1), 31–39 (1993).
[CrossRef] [PubMed]

1992 (1)

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun.93(5-6), 277–282 (1992).
[CrossRef]

Badizadegan, K.

Barbara, P. F.

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

Beck, S. M.

Binet, R.

Bout, D. A. V.

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

Brabec, C. J.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Braun, K.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Buck, J. R.

Buell, W. F.

Chemla, S.

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
[CrossRef] [PubMed]

Choi, W.

Colineau, J.

Dasari, R. R.

Debus, C.

Dickinson, R. P.

Drechsler, A.

Egelhaaf, H. J.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Enderle, T.

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
[CrossRef] [PubMed]

Feld, M. S.

Fleischer, M.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Fleury, L.

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
[CrossRef] [PubMed]

Ha, T.

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
[CrossRef] [PubMed]

Harke, B.

Hecht, B.

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
[CrossRef] [PubMed]

Hell, S.

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun.93(5-6), 277–282 (1992).
[CrossRef]

Hell, S. W.

B. Harke, J. Keller, C. K. Ullal, V. Westphal, A. Schönle, and S. W. Hell, “Resolution scaling in STED microscopy,” Opt. Express16(6), 4154–4162 (2008).
[CrossRef] [PubMed]

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol.21(11), 1347–1355 (2003).
[CrossRef] [PubMed]

M. Schrader and S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc.183(2), 110–115 (1996).
[CrossRef]

Hennemann, L.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Higdon, P.

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun.141(5-6), 298–313 (1997).
[CrossRef]

Hintz, H.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Hu, D.

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

Hu, D. K.

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

Inoué, S.

R. Oldenbourg, H. Terada, R. Tiberio, and S. Inoué, “Image sharpness and contrast transfer in coherent confocal microscopy,” J. Microsc.172(1), 31–39 (1993).
[CrossRef] [PubMed]

Juškaitis, R.

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun.141(5-6), 298–313 (1997).
[CrossRef]

Keller, J.

Kern, D. P.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Kozlowski, D. A.

Lehureau, J. C.

Lieb, M. A.

Liu, J.

Lu, H. P.

H. P. Lu, L. Xun, and X. S. Xie, “Single-molecule enzymatic dynamics,” Science282(5395), 1877–1882 (1998).
[CrossRef] [PubMed]

Lue, N.

Marechal, N. J.

Meixner, A. J.

Oldenbourg, R.

R. Oldenbourg, H. Terada, R. Tiberio, and S. Inoué, “Image sharpness and contrast transfer in coherent confocal microscopy,” J. Microsc.172(1), 31–39 (1993).
[CrossRef] [PubMed]

Popescu, G.

Schönle, A.

Schrader, M.

M. Schrader and S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc.183(2), 110–115 (1996).
[CrossRef]

Segura, J. M.

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
[CrossRef] [PubMed]

Selvin, R.

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging5(4), 205–218 (1997).
[CrossRef]

Stadler, J.

Stanciu, C.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

J. Stadler, C. Stanciu, C. Stupperich, and A. J. Meixner, “Tighter focusing with a parabolic mirror,” Opt. Lett.33(7), 681–683 (2008).
[CrossRef] [PubMed]

Stelzer, E. H. K.

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun.93(5-6), 277–282 (1992).
[CrossRef]

Stupperich, C.

Swager, T. M.

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

Tan, J.

Tarrach, G.

Terada, H.

R. Oldenbourg, H. Terada, R. Tiberio, and S. Inoué, “Image sharpness and contrast transfer in coherent confocal microscopy,” J. Microsc.172(1), 31–39 (1993).
[CrossRef] [PubMed]

Tiberio, R.

R. Oldenbourg, H. Terada, R. Tiberio, and S. Inoué, “Image sharpness and contrast transfer in coherent confocal microscopy,” J. Microsc.172(1), 31–39 (1993).
[CrossRef] [PubMed]

Török, P.

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging5(4), 205–218 (1997).
[CrossRef]

Ullal, C. K.

Wang, X.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Weiss, S.

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science283(5408), 1676–1683 (1999).
[CrossRef] [PubMed]

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
[CrossRef] [PubMed]

Westphal, V.

Wild, U. P.

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
[CrossRef] [PubMed]

Wilson, T.

J. Liu, J. Tan, T. Wilson, and C. Zhong, “Rigorous theory on elliptical mirror focusing for point scanning microscopy,” Opt. Express20(6), 6175–6184 (2012).
[CrossRef] [PubMed]

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun.141(5-6), 298–313 (1997).
[CrossRef]

Wright, T. J.

Xie, X. S.

H. P. Lu, L. Xun, and X. S. Xie, “Single-molecule enzymatic dynamics,” Science282(5395), 1877–1882 (1998).
[CrossRef] [PubMed]

Xun, L.

H. P. Lu, L. Xun, and X. S. Xie, “Single-molecule enzymatic dynamics,” Science282(5395), 1877–1882 (1998).
[CrossRef] [PubMed]

Yip, W. T.

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

Zhang, D.

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Zhong, C.

Zumofen, G.

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
[CrossRef] [PubMed]

Appl. Opt. (2)

Bioimaging (1)

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging5(4), 205–218 (1997).
[CrossRef]

J. Microsc. (2)

R. Oldenbourg, H. Terada, R. Tiberio, and S. Inoué, “Image sharpness and contrast transfer in coherent confocal microscopy,” J. Microsc.172(1), 31–39 (1993).
[CrossRef] [PubMed]

M. Schrader and S. W. Hell, “4Pi-confocal images with axial superresolution,” J. Microsc.183(2), 110–115 (1996).
[CrossRef]

J. Raman Spectrosc. (1)

D. Zhang, X. Wang, K. Braun, H. J. Egelhaaf, M. Fleischer, L. Hennemann, H. Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, “Parabolic mirror-assisted tip-enhanced spectroscopic imaging for non-transparent materials,” J. Raman Spectrosc.40(10), 1371–1376 (2009).
[CrossRef]

Nat. Biotechnol. (1)

S. W. Hell, “Toward fluorescence nanoscopy,” Nat. Biotechnol.21(11), 1347–1355 (2003).
[CrossRef] [PubMed]

Opt. Commun. (2)

S. Hell and E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun.93(5-6), 277–282 (1992).
[CrossRef]

T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarization microscopes,” Opt. Commun.141(5-6), 298–313 (1997).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

L. Fleury, J. M. Segura, G. Zumofen, B. Hecht, and U. P. Wild, “Nonclassical photon statistics in single-molecule fluorescence at room temperature,” Phys. Rev. Lett.84(6), 1148–1151 (2000).
[CrossRef] [PubMed]

T. Ha, T. Enderle, S. Chemla, R. Selvin, and S. Weiss, “Single molecule dynamics studied by polarization modulation,” Phys. Rev. Lett.77(19), 3979–3982 (1996).
[CrossRef] [PubMed]

Science (3)

H. P. Lu, L. Xun, and X. S. Xie, “Single-molecule enzymatic dynamics,” Science282(5395), 1877–1882 (1998).
[CrossRef] [PubMed]

D. A. V. Bout, W. T. Yip, D. Hu, D. K. Hu, T. M. Swager, and P. F. Barbara, “Discrete intensity jumps and intramolecular electronic energy transfer in the spectroscopy of single conjugated polymer molecules,” Science277(5329), 1074–1077 (1997).
[CrossRef]

S. Weiss, “Fluorescence spectroscopy of single biomolecules,” Science283(5408), 1676–1683 (1999).
[CrossRef] [PubMed]

Other (2)

J. D. Jackson, Classical Electrodynamics, Wiley, 1992.

J. B. Pawley, Handbook of Biological Confocal Microscopy (Plenum Press, 2006).

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Figures (5)

Fig. 1
Fig. 1

Geometrical imaging of dipole emitter located at F1. Sm represents the surface of the elliptical mirror whereas the two wavefront surfaces SF1 and SF2 correspond to inbound and outbound spherical waves with centers at F1 and F2 The corresponding focal lengths are a-c and a + c, respectively; α is the gathering aperture angle of a dipole emitter at F1, θ is the imaging aperture angle at point F2 The maximum values of α and θ are αmax and θmax, respectively; The elliptical mirror is defined as (x2 + y2)/b2 + (z-c)2/a2 = 1, where a and b are denoted the long and short axes of the elliptical mirror, respectively. c = |OF1| = |OF2| = (a2-b2)1/2. ϕ is the angle between meridional plane ZON and axis X.

Fig. 2
Fig. 2

Distribution of |Efe|2 in case of dipole polarization originating in direction X, p = i. (a), (b) and (c) show curves for positive co-ordinate values only because of symmetry. The above normalization is fulfilled by dividing the peak value of the 3D point spread function. The transverse coordinates are in unit of λ.

Fig. 3
Fig. 3

Distribution of |Efe|2 in case of dipole orientation in the Z direction, p = k. The transverse coordinates are in wavelength, and the PSF are drawn in full size to exhibit details of side lobes. The transverse coordinates are in unit of λ.

Fig. 4
Fig. 4

Simulated distributions of cubic root of |Efe|2 in X-Y focal plane of PMBI and EMBI with transverse defocused dipole emitter at rm = λ(cos30°, sin30°, 0). The transverse coordinates are in unit of λ.

Fig. 5
Fig. 5

Simulated distributions of cubic root of |Efe|2 in X-Y focal plane of PMBI and EMBI with longitudinal defocused dipole emitter at rm = (0, 0, λ). The transverse coordinates are in unit of λ.

Equations (10)

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

E de = k 2 ( s 0 ×p)× s 0 1 r exp[i(krwt)],
s 0 =sinαcosϕi+sinαsinϕj+cosαk,
g 0 =cosαcosϕi-cosαsinϕj+sinαk,
s 1 =sinθcosϕi-sinθsinϕj-cosθk,
g 1 =cosθcosϕi+cosθsinϕj-sinθk.
e 1 =β g 1 +γ( g 1 × s 1 ).
β= e 1 · g 1 = E de · g 0 ,
γ= e 1 ·( g 1 × s 1 )= E de ·( g 0 × s 0 ).
{ E fe = i k 3 16 π 3 ε 0 a+c ac 0 θ max 0 2π l( θ ){ [(p· g 0 ) g 1 [p·( g 0 × s 0 )]( g 1 × s 1 )] }× exp[ik( r p s 1 n m r m s 0 )]sinθdθdϕ l( θ )= ac a+c sinα sinθ dα dθ
r p = r p sin θ p cos ϕ p i+ r p sin θ p sin ϕ p j+ r p cos θ p k.

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