Abstract

We propose an approach to obtain a diffraction-limited spherical focal spot in 4Pi microscopy. By combining the dipole antenna radiation pattern and the Richards–Wolf vectorial diffraction method, an input field at a pupil plane of aplanatic objective lenses for generating a spherical spot can be found analytically by solving the inverse problem. The required field at the pupil plane is found to be a radial polarization with spatial amplitude modulation. With spatial phase modulation, two identical spherical spots with diffraction-limited size and variable distance along the optical axis can also be obtained.

© 2009 Optical Society of America

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References

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  1. S. Weiss, Science 283, 1676 (1999).
    [CrossRef] [PubMed]
  2. A. Ashikin and J. Z. Dziedzic, Science 235, 1517 (1987).
    [CrossRef]
  3. S. Hell and E. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
    [CrossRef]
  4. M. C. Lang, T. Staudt, J. Engelhardt, and S. Hell, New J. Phys. 10, 043041 (2008).
    [CrossRef]
  5. N. Bokor and N. Davidson, Opt. Lett. 29, 1968 (2004).
    [CrossRef] [PubMed]
  6. E. Wolf, Proc. R. Soc. London Ser. A 253, 349 (1959).
    [CrossRef]
  7. B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
    [CrossRef]
  8. M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, New York, 1999).
  9. K. S. Youngworth and T. G. Brown, Opt. Express 7, 77 (2000).
    [CrossRef] [PubMed]

2008 (1)

M. C. Lang, T. Staudt, J. Engelhardt, and S. Hell, New J. Phys. 10, 043041 (2008).
[CrossRef]

2004 (1)

2000 (1)

1999 (1)

S. Weiss, Science 283, 1676 (1999).
[CrossRef] [PubMed]

1992 (1)

1987 (1)

A. Ashikin and J. Z. Dziedzic, Science 235, 1517 (1987).
[CrossRef]

1959 (2)

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]

Ashikin, A.

A. Ashikin and J. Z. Dziedzic, Science 235, 1517 (1987).
[CrossRef]

Bokor, N.

Brown, T. G.

Davidson, N.

Dziedzic, J. Z.

A. Ashikin and J. Z. Dziedzic, Science 235, 1517 (1987).
[CrossRef]

Engelhardt, J.

M. C. Lang, T. Staudt, J. Engelhardt, and S. Hell, New J. Phys. 10, 043041 (2008).
[CrossRef]

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, New York, 1999).

Hell, S.

M. C. Lang, T. Staudt, J. Engelhardt, and S. Hell, New J. Phys. 10, 043041 (2008).
[CrossRef]

S. Hell and E. Stelzer, J. Opt. Soc. Am. A 9, 2159 (1992).
[CrossRef]

Lang, M. C.

M. C. Lang, T. Staudt, J. Engelhardt, and S. Hell, New J. Phys. 10, 043041 (2008).
[CrossRef]

Richards, B.

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

Staudt, T.

M. C. Lang, T. Staudt, J. Engelhardt, and S. Hell, New J. Phys. 10, 043041 (2008).
[CrossRef]

Stelzer, E.

Weiss, S.

S. Weiss, Science 283, 1676 (1999).
[CrossRef] [PubMed]

Wolf, E.

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

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

Youngworth, K. S.

J. Opt. Soc. Am. A (1)

New J. Phys. (1)

M. C. Lang, T. Staudt, J. Engelhardt, and S. Hell, New J. Phys. 10, 043041 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. R. Soc. London Ser. A (1)

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

Proc. R. Soc. London, Ser. A (1)

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

Science (2)

S. Weiss, Science 283, 1676 (1999).
[CrossRef] [PubMed]

A. Ashikin and J. Z. Dziedzic, Science 235, 1517 (1987).
[CrossRef]

Other (1)

M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, New York, 1999).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the proposed method. A dipole antenna situated at the foci of two high-NA objective lenses is aligned along the optical axis. The radiation field is collected and collimated by the 4Pi focusing system, and the input field at the pupil planes for creating spherical focal spot is found.

Fig. 2
Fig. 2

Generation of a spherical spot with the use of L = 4 λ dipole antenna: (a) input field at the pupil plane for producing a spherical spot, (b) calculated electric energy density | E | 2 distribution in the vicinity of focal point, (c) linescans of corresponding axial and transversal energy density distributions.

Fig. 3
Fig. 3

Creating a spherical spot with the use of L = 6 λ dipole antenna to shift the maximum sidelobes: (a) calculated electric energy density | E | 2 distribution in the vicinity of focal point, (b) linescans of corresponding axial and transversal energy density distributions.

Fig. 4
Fig. 4

Generation of two diffraction-limited spherical spots with the use of an L = 3.5 λ dipole antenna: (a) input field at the pupil plane for producing two spherical spots, (b) calculated electric energy density | E | 2 distribution in the vicinity of the focal point, (c) linescans of corresponding axial and transversal energy density distributions; E ( r ) and E + ( r ) are transversal linescans for the two spherical spots respectively overlaid on the axial linescan.

Equations (4)

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R ( θ ) = C [ cos ( k L 2 cos θ ) cos ( k L 2 ) ] sin θ a θ ,
E i ( r ) = R ( θ ) cos θ ,
E z ( r p , ψ , z p ) = j A 0 θ max sin 2 θ P ( θ ) R ( θ ) J 0 ( k r sin θ ) e j k z cos θ d θ ,
E r ( r p , ψ , z p ) = A 0 θ max sin θ cos θ P ( θ ) R ( θ ) J 1 ( k r sin θ ) e j k z cos θ d θ .

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