Abstract

Recently Török and colleagues published in a series of papers a general wave-optical approach to calculating the light-collection efficiency function (CEF) for confocal imaging of dipole emitters [J. Mod. Opt. 45, 1681 (1998); J. Microsc. 194, 127 (1999); Opt. Lett. 25, 1463 (2000)]. In their theory they did not address the possibility that the lifetimes of fluorescing molecules can change significantly near interfaces, which has a direct effect on the CEF. The research of Török and colleagues is extended here to include this effect, which may become important for imaging near surfaces.

© 2003 Optical Society of America

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References

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  1. P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
    [CrossRef]
  2. P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 194, 127 (1999).
    [CrossRef]
  3. P. Török, Opt. Lett. 25, 1463 (2000).
    [CrossRef]
  4. H. Yokota, K. Saito, and T. Yanagida, Phys. Rev. Lett. 80, 4606 (1998).
    [CrossRef]
  5. R. L. Hansen and J. M. Harris, Anal. Chem. 70, 2565 (1998).
    [CrossRef] [PubMed]
  6. P. F. Lenné, E. Etienne, and H. Rignéault, Appl. Phys. Lett. 80, 4106 (2002).
    [CrossRef]
  7. E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
    [CrossRef]
  8. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  9. J. Enderlein, T. Ruckstuhl, and S. Seeger, Appl. Opt. 38, 724 (1999).
    [CrossRef]
  10. J. Enderlein, Opt. Lett. 25, 634 (2000).
    [CrossRef]
  11. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Deutsch, Thun, Frankfurt am Main, Germany, 1984).
  12. J. Enderlein, Chem. Phys. 247, 1 (1999).
    [CrossRef]
  13. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, Appl. Opt. 37, 5271 (1998).
    [CrossRef]

2002

P. F. Lenné, E. Etienne, and H. Rignéault, Appl. Phys. Lett. 80, 4106 (2002).
[CrossRef]

2000

1999

J. Enderlein, T. Ruckstuhl, and S. Seeger, Appl. Opt. 38, 724 (1999).
[CrossRef]

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 194, 127 (1999).
[CrossRef]

J. Enderlein, Chem. Phys. 247, 1 (1999).
[CrossRef]

1998

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, Appl. Opt. 37, 5271 (1998).
[CrossRef]

H. Yokota, K. Saito, and T. Yanagida, Phys. Rev. Lett. 80, 4606 (1998).
[CrossRef]

R. L. Hansen and J. M. Harris, Anal. Chem. 70, 2565 (1998).
[CrossRef] [PubMed]

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

1959

E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Deutsch, Thun, Frankfurt am Main, Germany, 1984).

Djurišic, A. B.

Elazar, J. M.

Enderlein, J.

Etienne, E.

P. F. Lenné, E. Etienne, and H. Rignéault, Appl. Phys. Lett. 80, 4106 (2002).
[CrossRef]

Hansen, R. L.

R. L. Hansen and J. M. Harris, Anal. Chem. 70, 2565 (1998).
[CrossRef] [PubMed]

Harris, J. M.

R. L. Hansen and J. M. Harris, Anal. Chem. 70, 2565 (1998).
[CrossRef] [PubMed]

Higdon, P. D.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 194, 127 (1999).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

Lenné, P. F.

P. F. Lenné, E. Etienne, and H. Rignéault, Appl. Phys. Lett. 80, 4106 (2002).
[CrossRef]

Majewski, M. L.

Rakic, A. D.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Rignéault, H.

P. F. Lenné, E. Etienne, and H. Rignéault, Appl. Phys. Lett. 80, 4106 (2002).
[CrossRef]

Ruckstuhl, T.

Saito, K.

H. Yokota, K. Saito, and T. Yanagida, Phys. Rev. Lett. 80, 4606 (1998).
[CrossRef]

Seeger, S.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Deutsch, Thun, Frankfurt am Main, Germany, 1984).

Török, P.

P. Török, Opt. Lett. 25, 1463 (2000).
[CrossRef]

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 194, 127 (1999).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

Wilson, T.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 194, 127 (1999).
[CrossRef]

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

Wolf, E.

E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Yanagida, T.

H. Yokota, K. Saito, and T. Yanagida, Phys. Rev. Lett. 80, 4606 (1998).
[CrossRef]

Yokota, H.

H. Yokota, K. Saito, and T. Yanagida, Phys. Rev. Lett. 80, 4606 (1998).
[CrossRef]

Anal. Chem.

R. L. Hansen and J. M. Harris, Anal. Chem. 70, 2565 (1998).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

P. F. Lenné, E. Etienne, and H. Rignéault, Appl. Phys. Lett. 80, 4106 (2002).
[CrossRef]

Chem. Phys.

J. Enderlein, Chem. Phys. 247, 1 (1999).
[CrossRef]

J. Microsc.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 194, 127 (1999).
[CrossRef]

J. Mod. Opt.

P. Török, P. D. Higdon, and T. Wilson, J. Mod. Opt. 45, 1681 (1998).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

H. Yokota, K. Saito, and T. Yanagida, Phys. Rev. Lett. 80, 4606 (1998).
[CrossRef]

Proc. R. Soc. London Ser. A

E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
[CrossRef]

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Other

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Deutsch, Thun, Frankfurt am Main, Germany, 1984).

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Figures (2)

Fig. 1
Fig. 1

Geometry of the dipole emission within the sample layer. Shown are only the wave vectors and corresponding transverse unit vectors for a plane wave traveling toward the objective.

Fig. 2
Fig. 2

Axial dependence of the CEF for an isotropically oriented distribution of dipoles in water in front of a gold mirror (left). Imaging is performed from the right by a water-immersion objective (N.A., 1.2; magnification, 60×), and the collected light is detected through a confocal aperture with 100µm diameter. Shown are the results as calculated according to Török and colleagues (crosses) and according to the theory presented in this Letter (solid curve).

Equations (8)

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E=ik032πdqwmepTp+emp+ expiwmzm+Tp-emp- expiwm2d-zm·p+esTs+×expiwmzm+Ts- expiwm2d-zmes·p×expiq·ρ+iwz,
Epη=-nwqnmwm{Tp+ expiwmzm+Tp- exp(iwm2d-zm]},Epη=nwnm{Tp+ expiwmzm-Tp- exp(iwm2d-zm]},Esη=-nwwm{Ts+ expiwmzm+Ts- exp(iwm2d-zm]}.
E=ΩdΩM2n cos ηn cos η1/2epEp+Ep cos ψ+esEs sin ψexpiks·r-iwf,B=nΩdΩM2n cos ηn cos η1/2esEp+Ep cos ψ-epEs sin ψexpiks·r-iwf,
ep=cos ψ cos η,sin ψ cos η,-sin η,s=-cos ψ sin η,-sin ψ sin η,cos η.
s·r=s·R+ρ+z=R-ρ sin η cosψ-ϕ+z cos η,
Ex,yBx,y=0ηmaxdη sin ηn cos ηn cos η1/2×ex,ybx,yexpikz cos η-ikf cos η,
ex=i22 cos ηJ1Ep cos ϕ+cos ηJ0-J2 cos 2ϕ×Ep+J0+J2 cos 2ϕEs,ex=i22 cos ηJ1Ep cos ϕ+cos ηJ0-J2 cos 2ϕ×Ep+J0+J2 cos 2ϕEs,ey=i22 cos ηJ1Ep sin ϕ-cos ηJ2 sin 2ϕEp+J2 sin 2ϕEs,bx=in2-2J1Ep sin ϕ-cos ηJ2×sin 2ϕEs+J2 sin 2ϕEp,by=in22J1Ep cos ϕ+cos η×J0+J2 cos 2ϕEs+J0-J2 cos 2ϕEp.
Cρm,zmc8πStotapertureReE×B*·dA.

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