Abstract

A new class of axially apodizing continuously transmitting filters is analytically determined and numerically implemented. The longitudinal and lateral properties of the associated point-spread function are displayed both for a single filtered lens and for a combination with a laterally superresolving mask in a confocal configuration. Interesting imaging properties relative to the increase in axial contrast and transverse resolving power for dephasing ring-free pupil filters of moderate losses in luminosity are predicted.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).
  2. M. Kempe, W. Rudolph, “Analysis of confocal microscopy under ultrashort light-pulse illumination,” J. Opt. Soc. Am. 10, 240–245 (1993).
    [CrossRef]
  3. S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
    [CrossRef]
  4. M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short-laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
    [CrossRef]
  5. M. Gu, “Image formation in femtosecond confocal interference microscopy,” Microsc. Microanal. Microstruct. 4, 63–71 (1998).
  6. E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
    [CrossRef]
  7. Min Gu, “Resolution in three-photon fluorescence scanning microscopy,” Opt. Lett. 21, 988–990 (1996).
    [CrossRef] [PubMed]
  8. E. Beaurepaire, L. Moreaux, F. Amblard, J. Mertz, “Combined scanning optical coherence and two-photon-excited fluorescence microscopy,” Opt. Lett. 24, 969–971 (1999).
    [CrossRef]
  9. D. Slepian, “Analytic solution of two apodization problems,” J. Opt. Soc. Am. 55, 1110–1115 (1965).
    [CrossRef]
  10. M. A. A. Neil, R. Juškaitis, 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]
  11. C. J. R. Sheppard, Z. S. Hegedus, “Axial behavior of pupil plane filters,” J. Opt. Soc. Am. A 5, 643–664 (1988).
    [CrossRef]
  12. 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]
  13. M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, 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).
  14. S. Hell, P. Hänninen, A. Kuusisto, M. Shrader, E. Soini, “Annular aperture two-photon excitation microscopy,” Opt. Commun. 117, 20–24 (1995).
    [CrossRef]
  15. G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento 9, 426–438 (1952).
    [CrossRef]
  16. G. R. Boyer, “Pupil filters for moderate superresolution,” Appl. Opt. 15, 3089–3093 (1976).
    [CrossRef] [PubMed]
  17. M. Yzuel, J. C. Escalera, J. Campos, “Polychromatic axial behavior of axial apodizing and hyperresolving filters,” Appl. Opt. 29, 1631–1641 (1990).
    [CrossRef] [PubMed]
  18. M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, M. Kowalczyk, “Three-dimensional superresolution by annular binary filters,” Opt. Commun. 165, 267–278 (1999).
    [CrossRef]
  19. M. Martinez-Corral, P. Andrès, J. Ojeda-Castaneda, G. Saavedra, “Tunable axial superresolution by annular binary filters. Application to confocal microscopy,” Opt. Commun. 119, 491–498 (1995).
    [CrossRef]
  20. C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik (Stuttgart) 99, 32–34 (1995).
  21. M. Gu, T. Tannous, J. R. Sheppard, “Effect of an annular pupil on confocal imaging through highly scattering media,” Opt. Lett. 21, 312–314 (1995).
    [CrossRef]
  22. I. J. Cox, C. J. R. Sheppard, T. Wilson, “Reappraisal of arrays of concentric annuli as superresolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
    [CrossRef]
  23. M. A. A. Neil, T. Wilson, R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (1999).
    [CrossRef]
  24. J. A. Davis, J. C. Escalera, J. Campos, A. Marquez, M. Yzuel, C. Iemmi, “Programmable axial apodizing and hyperresolving amplitude filters with a liquid-crystal spatial light modulator,” Opt. Lett. 24, 628–630 (1999).
    [CrossRef]
  25. G. Boyer, V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik (Stuttgart) 4, 177–179 (2000).
  26. M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).
  27. R. B. Frieden, in Progress in Optics IX, E. Wolf ed. (North-Holland, Amsterdam, 1971).
  28. C. Flammer, Spheroı̈dal Wave Functions (Stanford U. Press, Stanford, Calif.1957).
  29. Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [CrossRef]
  30. G. Boyer, “Réalisation d’un filtrage super-résolvant,” Opt. Acta 30, 807–816 (1983).
    [CrossRef]

2000 (2)

1999 (4)

M. A. A. Neil, T. Wilson, R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (1999).
[CrossRef]

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

J. A. Davis, J. C. Escalera, J. Campos, A. Marquez, M. Yzuel, C. Iemmi, “Programmable axial apodizing and hyperresolving amplitude filters with a liquid-crystal spatial light modulator,” Opt. Lett. 24, 628–630 (1999).
[CrossRef]

E. Beaurepaire, L. Moreaux, F. Amblard, J. Mertz, “Combined scanning optical coherence and two-photon-excited fluorescence microscopy,” Opt. Lett. 24, 969–971 (1999).
[CrossRef]

1998 (2)

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, 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. Gu, “Image formation in femtosecond confocal interference microscopy,” Microsc. Microanal. Microstruct. 4, 63–71 (1998).

1997 (1)

1996 (1)

1995 (5)

M. Gu, T. Tannous, J. R. Sheppard, “Effect of an annular pupil on confocal imaging through highly scattering media,” Opt. Lett. 21, 312–314 (1995).
[CrossRef]

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

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

C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik (Stuttgart) 99, 32–34 (1995).

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short-laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

1994 (2)

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

1993 (1)

M. Kempe, W. Rudolph, “Analysis of confocal microscopy under ultrashort light-pulse illumination,” J. Opt. Soc. Am. 10, 240–245 (1993).
[CrossRef]

1990 (1)

1988 (1)

1986 (1)

1983 (1)

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

1982 (1)

1976 (1)

1965 (1)

1952 (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento 9, 426–438 (1952).
[CrossRef]

Amblard, F.

Andrés, P.

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

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, 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).

Andrès, P.

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

Beaurepaire, E.

Boyer, G.

G. Boyer, V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik (Stuttgart) 4, 177–179 (2000).

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

Boyer, G. R.

Campos, J.

Cox, I. J.

Davis, J. A.

Ding, Z.

Escalera, J. C.

Fan, Z.

Flammer, C.

C. Flammer, Spheroı̈dal Wave Functions (Stanford U. Press, Stanford, Calif.1957).

Frieden, R. B.

R. B. Frieden, in Progress in Optics IX, E. Wolf ed. (North-Holland, Amsterdam, 1971).

Gu, M.

M. Gu, “Image formation in femtosecond confocal interference microscopy,” Microsc. Microanal. Microstruct. 4, 63–71 (1998).

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]

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short-laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

M. Gu, T. Tannous, J. R. Sheppard, “Effect of an annular pupil on confocal imaging through highly scattering media,” Opt. Lett. 21, 312–314 (1995).
[CrossRef]

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

Gu, Min

Hänniken, P. E.

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

Hänninen, P.

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

Hegedus, Z. S.

Hell, S.

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

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Iemmi, C.

Juskaitis, R.

M. A. A. Neil, T. Wilson, R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (1999).
[CrossRef]

Juškaitis, R.

Kempe, M.

M. Kempe, W. Rudolph, “Analysis of confocal microscopy under ultrashort light-pulse illumination,” J. Opt. Soc. Am. 10, 240–245 (1993).
[CrossRef]

Kowalczyk, M.

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

Kuusisto, A.

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

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

Laczik, Z. J.

Lindek, S.

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Marquez, A.

Martinez-Corral, M.

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

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

Mertz, J.

Moreaux, L.

Neil, M. A. A.

M. A. A. Neil, R. Juškaitis, 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]

M. A. A. Neil, T. Wilson, R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (1999).
[CrossRef]

Ojeda-Castaneda, J.

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

Pick, R.

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Ritter, G.

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Rudolph, W.

M. Kempe, W. Rudolph, “Analysis of confocal microscopy under ultrashort light-pulse illumination,” J. Opt. Soc. Am. 10, 240–245 (1993).
[CrossRef]

Saavedra, G.

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

Salmon, N.

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Salo, J.

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

Sarafis, V.

Sheppard, C. J. R.

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, 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, “Leaky annular pupils for improved axial imaging,” Optik (Stuttgart) 99, 32–34 (1995).

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short-laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

C. J. R. Sheppard, Z. S. Hegedus, “Axial behavior of pupil plane filters,” J. Opt. Soc. Am. A 5, 643–664 (1988).
[CrossRef]

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Reappraisal of arrays of concentric annuli as superresolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
[CrossRef]

Sheppard, J. R.

Shrader, M.

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

Slepian, D.

Soini, E.

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

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

Stelzer, E. H. K.

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Stortz, C.

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Stricker, R.

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

Tannous, T.

Ton, J. B.

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

Toraldo di Francia, G.

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento 9, 426–438 (1952).
[CrossRef]

Wang, G.

Wang, Z.

Wilson, T.

M. A. A. Neil, R. Juškaitis, 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]

M. A. A. Neil, T. Wilson, R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (1999).
[CrossRef]

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Reappraisal of arrays of concentric annuli as superresolving filters,” J. Opt. Soc. Am. 72, 1287–1291 (1982).
[CrossRef]

Yzuel, M.

Zapata-Rodriguez, C. J.

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

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, 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. (3)

J. Microsc. (1)

M. A. A. Neil, T. Wilson, R. Juskaitis, “A wavefront generator for complex pupil function synthesis and point spread function engineering,” J. Microsc. 197, 219–223 (1999).
[CrossRef]

J. Mod. Opt. (1)

M. Gu, C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short-laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

Microsc. Microanal. Microstruct. (1)

M. Gu, “Image formation in femtosecond confocal interference microscopy,” Microsc. Microanal. Microstruct. 4, 63–71 (1998).

Nuovo Cimento (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento 9, 426–438 (1952).
[CrossRef]

Opt. Acta (1)

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

Opt. Commun. (5)

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

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

E. H. K. Stelzer, S. Hell, S. Lindek, R. Stricker, R. Pick, C. Stortz, G. Ritter, N. Salmon, “Nonlinear absorption extends confocal fluorescence microscopy into the ultraviolet regime and confines the illumination volume,” Opt. Commun. 104, 223–228 (1994).
[CrossRef]

S. Hell, P. E. Hänniken, J. Salo, A. Kuusisto, E. Soini, T. Wilson, J. B. Ton, “Pulsed and cw confocal microscopy: A comparison of resolution and contrast,” Opt. Commun. 133, 144–152 (1994).
[CrossRef]

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

Opt. Lett. (5)

Optik (Stuttgart) (3)

M. Martinez-Corral, P. Andrés, C. J. Zapata-Rodriguez, 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, “Leaky annular pupils for improved axial imaging,” Optik (Stuttgart) 99, 32–34 (1995).

G. Boyer, V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik (Stuttgart) 4, 177–179 (2000).

Other (4)

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

R. B. Frieden, in Progress in Optics IX, E. Wolf ed. (North-Holland, Amsterdam, 1971).

C. Flammer, Spheroı̈dal Wave Functions (Stanford U. Press, Stanford, Calif.1957).

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Variations of the maximum fractional ratio energy E(u0) versus the length of the segment -u0/2, u0/2.

Fig. 2
Fig. 2

Radial transmittance variations of the axial apodizer for u0=4π, 8π, and 16π diffraction units as a function of the normalized pupil radial variable.

Fig. 3
Fig. 3

Axial log-intensity variations of the corresponding IPSF for same parameters as in Fig. 2.

Fig. 4
Fig. 4

Off-axis log-intensity variations of the corresponding IPSF for same parameters as in Fig. 2.

Fig. 5
Fig. 5

Split diagram of the normalized 3D IPSFs for same parameters of the clear-pupil intensity distribution (left-hand side) and the axially apodized counterpart (right-hand side) for u0=9π. The intensity scale is linear.

Fig. 6
Fig. 6

Out-of-focus imaging properties of a Toraldo-type and axial-apodizer filters (top) in a confocal combination (bottom). The superresolving mask is formed of three in-phase annuli of normalized internal and external radii 0.28–0.33, 0.64–0.67, and 0.91–1.0, respectively, yielding a Strehl ratio of 5.22×10-2. The apodizer has a Strehl ratio of 0.23, with c=8.65π. The relative illumination is 1.21×10-2 at the center of the bright spot.

Fig. 7
Fig. 7

Off-axis and in-focus imaging properties for the same confocal combination as in Fig. 6

Fig. 8
Fig. 8

u-v normalized-intensity diagram of a Toraldo superresolving filter. The dimensions of its concentric annuli are defined in Fig. 6. The intensity scale is linear.

Fig. 9
Fig. 9

u-v normalized-intensity diagram of a confocal Toraldo-free-pupil 3D IPSF. The multifocal aspect is reduced by the multiplicative nature of the IPSF, but remains important. The intensity scale is linear.

Fig. 10
Fig. 10

u-v normalized-intensity diagram of a confocal Toraldo-apodizer 3D IPSF with the same other parameters as for Fig. 9. Note the increase in axial contrast, by comparison with Fig. 9. The intensity scale is linear.

Fig. 11
Fig. 11

u-v normalized-intensity diagram of a confocal free-pupil 3D-IPSF with the same other parameters as for Fig. 9. The intensity scale is linear.

Equations (20)

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

A(u, v)=K(v)01P(ρ)expiu2ρ2J0(vρ)ρdρ.
A(u, v)=12K(v)exp-iu4-1/21/2T(v, x)expiu2xdx.
A(u, 0)exp-iu4-1/21/2T(x)expiu2xdx,
-x0x0ψn(c, x)ψm(c, x)dx=λn(c)δm,n,
-ψn(c, x)ψm(c, x)dx=δm,n,
-x0x0ψn(c, x)exp(iωx)dx=in2πλnx0Ω1/2ψnc,ωx0Ω.
T(x)=n=0,1Manψn(c, x)
E(u0)=-u0/2u0/2|A(u, o)|2du-|A(u, o)|2du,
E(u0)=n=0,1M|an|2λn2(c)n=0,1M|an|2λn(c)=max,
T(x)=a0ψ0(u0/4, x)
E(u0)=λ0(u0/4),
E(u0)1-2(πu0)1/2 exp-u021-38u0+O(u0-2).
E(u0)u02π1-u22144+O(u04).
P(ρ)=ψ0u04, ρ2-12.
φn(x)=j=0dj(n)(c)Pj(x),for|x|1.
j=0dj(n)(c)=1.
I(u, 0)=π2|K(0)|2λ0u0ψ02c,uu0
S(u0)=|A(0, 0)|2|Ac(0, 0)|2.
S(u0)=2πλ0(u0/4)u0.
I(u)=πN2sin(u/4)u/42.

Metrics