Abstract

We present a novel technique for considerably decreasing the sidelobe height of the axial point-spread function of one-photon 4Pi-confocal microscopes. By means of a numerical example, in which the ratio between the excitation and the fluorescence wavelengths was set to ϵ=λexc/λdet=0.8, we show that simply inserting a pair of properly designed two-ring binary masks in the illumination set allows the height of the axial sidelobes to be reduced from 20% to 5% of the height of the central peak. This allows one to receive the full benefit of the strong narrowness of the central lobe provided by the 4Pi-confocal technique.

© 2002 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), Chap. 8.
  2. T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).
  3. S. Hell, E. H. K. Stelzer, “Properties of a 4Pi confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
    [CrossRef]
  4. S. Hell, E. H. K. Stelzer, “Fundamental improvement of resolution with a 4Pi-confocal fluorescence microscope using two-photon excitation,” Opt. Commun. 93, 277–282 (1992).
    [CrossRef]
  5. S. W. Hell, S. Lindek, E. H. K. Stelzer, “Enhancing the axial resolution in far-field light microscopy: two-photon 4Pi confocal fluorescence microscopy,” J. Mod. Opt. 41, 675–681 (1994).
    [CrossRef]
  6. M. Nagorni, S. W. Hell, “Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts,” J. Opt. Soc. Am. A 18, 36–48 (2001).
    [CrossRef]
  7. P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, “Two-photon excitation 4Pi confocal microscope: enhanced resolution for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
    [CrossRef]
  8. M. Schrader, S. W. Hell, H. T. M. van der Voort, “Three-dimensional super-resolution with 4Pi-confocal microscope using image restoration,” J. Appl. Phys. 84, 4033–4042 (1998).
    [CrossRef]
  9. M. Nagorni, S. W. Hell, “Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. II. Power and limitations of nonlinear image restoration,” J. Opt. Soc. Am. A 18, 49–51 (2001).
    [CrossRef]
  10. G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
    [CrossRef]
  11. P. Jacquinot, B. Rozien-Dossier, “Apodization,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3.
  12. G. R. Boyer, “Réalisation d’un filtrage super-résolvant,” Opt. Acta 30, 807–816 (1983).
    [CrossRef]
  13. G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
    [CrossRef]
  14. Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [CrossRef]
  15. S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
    [CrossRef]
  16. M. Martı́nez-Corral, P. Andrés, J. Ojeda-Castañeda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
    [CrossRef]
  17. M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, V. Sarafis, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
    [CrossRef]
  18. M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).
  19. Z. Ding, G. Wang, M. Gu, Z. Wang, Z. Fan, “Superresolution with an apodization film in a confocal setup,” Appl. Opt. 36, 360–363 (1997).
    [CrossRef] [PubMed]
  20. M. Kowalczyk, C. J. Zapata-Rodrı́guez, M. Martı́nez-Corral, “Asymmetric apodization in confocal imaging systems,” Appl. Opt. 37, 8206–8214 (1998).
    [CrossRef]
  21. M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
    [CrossRef]
  22. C. J. R. Sheppard, “Binary optics and confocal imaging,” Opt. Lett. 24, 505–506 (1999).
    [CrossRef]
  23. S. W. Hell, S. Lindek, C. Cremer, E. H. K. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64, 1335–1337 (1994).
    [CrossRef]
  24. The term apodization etymologically comes from the Greek (to remove foot), and involves the suppression, or at least a considerable decrease, of the sidelobes of the PSF.
  25. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
    [CrossRef]
  26. M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, Berlin, 2000).
  27. C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. Am. A 4, 1354–1360 (1987).
    [CrossRef]
  28. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–244 (1964).
    [CrossRef]
  29. S. Grill, E. H. K. Stelzer, “Method to calculate lateral and axial gain factors of optical setups with a large solid angle,” J. Opt. Soc. Am. A 16, 2658–2665 (1999).
    [CrossRef]
  30. C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001).
    [CrossRef]

2001 (3)

2000 (1)

1999 (3)

1998 (3)

M. Kowalczyk, C. J. Zapata-Rodrı́guez, M. Martı́nez-Corral, “Asymmetric apodization in confocal imaging systems,” Appl. Opt. 37, 8206–8214 (1998).
[CrossRef]

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Three-dimensional super-resolution with 4Pi-confocal microscope using image restoration,” J. Appl. Phys. 84, 4033–4042 (1998).
[CrossRef]

1997 (1)

1995 (3)

S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

M. Martı́nez-Corral, P. Andrés, J. Ojeda-Castañeda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, “Two-photon excitation 4Pi confocal microscope: enhanced resolution for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

1994 (2)

S. W. Hell, S. Lindek, C. Cremer, E. H. K. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64, 1335–1337 (1994).
[CrossRef]

S. W. Hell, S. Lindek, E. H. K. Stelzer, “Enhancing the axial resolution in far-field light microscopy: two-photon 4Pi confocal fluorescence microscopy,” J. Mod. Opt. 41, 675–681 (1994).
[CrossRef]

1992 (2)

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

S. Hell, E. H. K. Stelzer, “Properties of a 4Pi confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
[CrossRef]

1987 (1)

1986 (1)

1983 (1)

G. R. Boyer, “Réalisation d’un filtrage super-résolvant,” Opt. Acta 30, 807–816 (1983).
[CrossRef]

1979 (1)

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

1964 (1)

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

1952 (1)

G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[CrossRef]

Andrés, P.

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

M. Martı́nez-Corral, P. Andrés, J. Ojeda-Castañeda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Barends, P.

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

Bewersdorf, J.

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001).
[CrossRef]

Blanca, C. M.

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001).
[CrossRef]

Blom, P.

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), Chap. 8.

Boyer, G. R.

G. R. Boyer, “Réalisation d’un filtrage super-résolvant,” Opt. Acta 30, 807–816 (1983).
[CrossRef]

Brakenhoff, G. J.

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

Cremer, C.

S. W. Hell, S. Lindek, C. Cremer, E. H. K. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64, 1335–1337 (1994).
[CrossRef]

Ding, Z.

Fan, Z.

Grill, S.

Gu, M.

Hänninen, P. E.

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, “Two-photon excitation 4Pi confocal microscope: enhanced resolution for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

Hegedus, Z. S.

Hell, S.

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

S. Hell, E. H. K. Stelzer, “Properties of a 4Pi confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
[CrossRef]

Hell, S. W.

M. Nagorni, S. W. Hell, “Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. I. Comparative study of concepts,” J. Opt. Soc. Am. A 18, 36–48 (2001).
[CrossRef]

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001).
[CrossRef]

M. Nagorni, S. W. Hell, “Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy. II. Power and limitations of nonlinear image restoration,” J. Opt. Soc. Am. A 18, 49–51 (2001).
[CrossRef]

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Three-dimensional super-resolution with 4Pi-confocal microscope using image restoration,” J. Appl. Phys. 84, 4033–4042 (1998).
[CrossRef]

S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, “Two-photon excitation 4Pi confocal microscope: enhanced resolution for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

S. W. Hell, S. Lindek, E. H. K. Stelzer, “Enhancing the axial resolution in far-field light microscopy: two-photon 4Pi confocal fluorescence microscopy,” J. Mod. Opt. 41, 675–681 (1994).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, E. H. K. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64, 1335–1337 (1994).
[CrossRef]

Jacquinot, P.

P. Jacquinot, B. Rozien-Dossier, “Apodization,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3.

Juskaitis, R.

Kowalczyk, M.

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

M. Kowalczyk, C. J. Zapata-Rodrı́guez, M. Martı́nez-Corral, “Asymmetric apodization in confocal imaging systems,” Appl. Opt. 37, 8206–8214 (1998).
[CrossRef]

Kuusisto, A.

S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

Laczik, Z. J.

Lindek, S.

S. W. Hell, S. Lindek, E. H. K. Stelzer, “Enhancing the axial resolution in far-field light microscopy: two-photon 4Pi confocal fluorescence microscopy,” J. Mod. Opt. 41, 675–681 (1994).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, E. H. K. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64, 1335–1337 (1994).
[CrossRef]

Marti´nez-Corral, M.

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

M. Kowalczyk, C. J. Zapata-Rodrı́guez, M. Martı́nez-Corral, “Asymmetric apodization in confocal imaging systems,” Appl. Opt. 37, 8206–8214 (1998).
[CrossRef]

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

M. Martı́nez-Corral, P. Andrés, J. Ojeda-Castañeda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Matthews, H. J.

McCutchen, C. W.

Nagorni, M.

Neil, M. A. A.

Ojeda-Castañeda, J.

M. Martı́nez-Corral, P. Andrés, J. Ojeda-Castañeda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Rozien-Dossier, B.

P. Jacquinot, B. Rozien-Dossier, “Apodization,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3.

Saavedra, G.

M. Martı́nez-Corral, P. Andrés, J. Ojeda-Castañeda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Salo, J.

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, “Two-photon excitation 4Pi confocal microscope: enhanced resolution for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

Sarafis, V.

Schrader, M.

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Three-dimensional super-resolution with 4Pi-confocal microscope using image restoration,” J. Appl. Phys. 84, 4033–4042 (1998).
[CrossRef]

S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, “Binary optics and confocal imaging,” Opt. Lett. 24, 505–506 (1999).
[CrossRef]

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. Am. A 4, 1354–1360 (1987).
[CrossRef]

Soini, E.

S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, “Two-photon excitation 4Pi confocal microscope: enhanced resolution for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

Stelzer, E. H. K.

S. Grill, E. H. K. Stelzer, “Method to calculate lateral and axial gain factors of optical setups with a large solid angle,” J. Opt. Soc. Am. A 16, 2658–2665 (1999).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, E. H. K. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64, 1335–1337 (1994).
[CrossRef]

S. W. Hell, S. Lindek, E. H. K. Stelzer, “Enhancing the axial resolution in far-field light microscopy: two-photon 4Pi confocal fluorescence microscopy,” J. Mod. Opt. 41, 675–681 (1994).
[CrossRef]

S. Hell, E. H. K. Stelzer, “Properties of a 4Pi confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
[CrossRef]

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

Toraldo di Francia, G.

G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[CrossRef]

van der Voort, H. T. M.

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Three-dimensional super-resolution with 4Pi-confocal microscope using image restoration,” J. Appl. Phys. 84, 4033–4042 (1998).
[CrossRef]

Wang, G.

Wang, Z.

Wilson, T.

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), Chap. 8.

Zapata-Rodri´guez, C. J.

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

M. Kowalczyk, C. J. Zapata-Rodrı́guez, M. Martı́nez-Corral, “Asymmetric apodization in confocal imaging systems,” Appl. Opt. 37, 8206–8214 (1998).
[CrossRef]

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

Appl. Opt. (2)

Appl. Phys. Lett. (3)

C. M. Blanca, J. Bewersdorf, S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001).
[CrossRef]

P. E. Hänninen, S. W. Hell, J. Salo, E. Soini, “Two-photon excitation 4Pi confocal microscope: enhanced resolution for biological research,” Appl. Phys. Lett. 66, 1698–1700 (1995).
[CrossRef]

S. W. Hell, S. Lindek, C. Cremer, E. H. K. Stelzer, “Measurement of the 4Pi-confocal point spread function proves 75 nm axial resolution,” Appl. Phys. Lett. 64, 1335–1337 (1994).
[CrossRef]

J. Appl. Phys. (1)

M. Schrader, S. W. Hell, H. T. M. van der Voort, “Three-dimensional super-resolution with 4Pi-confocal microscope using image restoration,” J. Appl. Phys. 84, 4033–4042 (1998).
[CrossRef]

J. Microsc. (1)

G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
[CrossRef]

J. Mod. Opt. (1)

S. W. Hell, S. Lindek, E. H. K. Stelzer, “Enhancing the axial resolution in far-field light microscopy: two-photon 4Pi confocal fluorescence microscopy,” J. Mod. Opt. 41, 675–681 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Nuovo Cimento Suppl. (1)

G. Toraldo di Francia, “Supergain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–435 (1952).
[CrossRef]

Opt. Acta (1)

G. R. Boyer, “Réalisation d’un filtrage super-résolvant,” Opt. Acta 30, 807–816 (1983).
[CrossRef]

Opt. Commun. (4)

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

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
[CrossRef]

S. W. Hell, P. E. Hänninen, A. Kuusisto, M. Schrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
[CrossRef]

M. Martı́nez-Corral, P. Andrés, J. Ojeda-Castañeda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
[CrossRef]

Opt. Lett. (2)

Optik (Stuttgart) (1)

M. Martı́nez-Corral, P. Andrés, C. J. Zapata-Rodrı́guez, C. J. R. Sheppard, “Improvement of three-dimensional resolution in confocal scanning microscopy by combination of two pupil filters,” Optik (Stuttgart) 107, 145–148 (1998).

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

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959).
[CrossRef]

Other (5)

M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, Berlin, 2000).

The term apodization etymologically comes from the Greek (to remove foot), and involves the suppression, or at least a considerable decrease, of the sidelobes of the PSF.

P. Jacquinot, B. Rozien-Dossier, “Apodization,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1964), Vol. 3.

M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, UK, 1999), Chap. 8.

T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).

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Figures (8)

Fig. 1
Fig. 1

Numerically evaluated axial intensity PSF for a 4Pi(C)-confocal microscope. The parameters for the calculation were λ exc = 350   nm , ϵ = 0.8 , NA = 1.4

Fig. 2
Fig. 2

Normalized z response to an infinitely thin fluorescent layer for a 4Pi(C)-confocal microscope. The parameters for the calculation are the same as in Fig. 1.

Fig. 3
Fig. 3

Mapped amplitude transmittance, q ( ζ ) , of an axially superresolving two-ring filter. The relation between the parameter ζ and the normalized radial coordinate in the filter plane is r = ( 1 - ζ 2 ) 1 / 2 / sin   α . Then the actual normalized radii for the transparent annuli are r 0 = 0 and r 1 = [ 1 - ( 1 - η l / 2 ) 2 ] 1 / 2 / sin   α (inner annulus) and r 2 = [ 1 - ( cos   α + η l / 2 ) 2 ] 1 / 2 / sin   α and r 3 = 1 (outer annulus). The light efficiency of the filter is given by η = r 3 2 - r 2 2 + r 1 2 - r 0 2 .

Fig. 4
Fig. 4

Binary two-ring pupil filter whose axial projection consists of two equal-width rectangles. The shaded areas correspond to regions of transmittance equal to 1.

Fig. 5
Fig. 5

Schematic geometry of a 4Pi(C) apodized confocal-scanning optical microscope. Relay lenses are used to focus the filters into the back focal plane of the objectives. BS, beam splitter.

Fig. 6
Fig. 6

Relative height of the axial sidelobe versus the light efficiency of the pupil filters.

Fig. 7
Fig. 7

Numerically evaluated transverse PSF for a 4Pi(C)-confocal microscope. For the calculation we considered ϕ = π / 2 in Eq. (2).

Fig. 8
Fig. 8

Axial intensity PSF of the illumination part of a 4Pi(C)-confocal microscope.

Equations (6)

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E ( u ,   v ,   ϕ ) = [ I 0 ( u ,   v ) + I 2 ( u ,   v ) cos   2 ϕ ] i + I 2 ( u ,   v ) sin   2 ϕ j - 2 iI 1 ( u ,   v ) cos   ϕ k .
H ( u ,   v ,   ϕ ) = | E exc ( u ,   v ,   ϕ ) + E exc ( - u ,   v ,   ϕ ) | 2 × | E det ( ϵ u ,   ϵ v ) + E det ( - ϵ u ,   ϵ v ) | 2 ,
h ( u ) = 0 α A ( θ ) exp i cos   θ 4   sin 2   α / 2 u sin   θ d θ ,
ζ = cos   θ , q ( ζ ) = A ( θ ) ,
h ( u ) = cos   α 1 q ( ζ ) exp i ζ 4   sin 2   α / 2 u d ζ .
E ( u ,   v = 0 ) = I 0 ( u ,   v = 0 ) = 0 α ( 1 + cos   θ ) A ( θ ) × exp i cos   θ 4   sin 2   α / 2 u sin   θ   d θ = cos   α 1 ( 1 + ζ ) q ( ζ ) exp i ζ 4   sin 2   α / 2 u d ζ .

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