Abstract

In modern high-numerical-aperture (NA) optical scanning instruments, such as scanning microscopes, optical data storage systems, or laser trapping technology, the beam emerging from the high-NA objective focuses deeply through an interface between two media of different refractive index. Such a refractive index mismatch introduces an important amount of spherical aberration, which increases dynamically when scanning at increasing depths. This effect strongly degrades the instrument performance. Although in the past few years many different techniques have been reported to reduce the spherical aberration effect, no optimum solution has been found. Here we concentrate on a technique whose main feature is its simplicity. We refer to the use of purely absorbing beam-shaping elements, which with a minimum modification of optical architecture will allow a significant reduction of the spherical aberration effect. Specifically, we will show that an adequately designed reversed-Gaussian aperture permits the production of a focal spot whose form changes very slowly with the spherical aberration.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Tsujiuchi, "Correction of optical images by compensation of aberrations and by spatial frequency filtering," Prog. Oceanogr. 2, 133-180 (1963).
  2. R. Barakat and A. Houston, "Transfer function of an annular aperture in the presence of spherical aberration," J. Opt. Soc. Am. 55, 538-541 (1965).
    [CrossRef]
  3. J. P. Mills and B. J. Thompson, "Effect of aberrations and apodization on the performance of coherent optical systems. I. The amplitude impulse response," J. Opt. Soc. Am. A 3, 694-703 (1986).
    [CrossRef]
  4. J. Ojeda-Castañeda, P. Andrés, and A. Diaz, "Annular apodizers for low sensitivity to defocus and to spherical aberration," Opt. Lett. 11, 487-489 (1986).
    [CrossRef] [PubMed]
  5. J. Ojeda-Castañeda, P. Andrés, and A. Diaz, "Strehl ratio with low sensitivity to spherical aberration," J. Opt. Soc. Am. A 5, 1233-1236 (1988).
    [CrossRef]
  6. J. Ojeda-Castañeda, E. Tepichin, and A. Pons, "Apodization of annular apertures: Strehl ratio," Appl. Opt. 27, 5140-5145 (1988).
    [CrossRef] [PubMed]
  7. S. Mezouari and A. R. Harvey, "Phase pupil functions for reduction of defocus and spherical aberration," Opt. Lett. 28, 771-773 (2003).
    [CrossRef] [PubMed]
  8. J.B.Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, 1995).
  9. S. Stallinga, "Compact description of substrate-related aberrations in high numerical-aperture optical disk readout," Appl. Opt. 44, 849-858 (2005).
    [CrossRef] [PubMed]
  10. A. Rohrbach and E. H. K. Stelzer, "Optical trapping of dielectric particles in arbitrary fields," J. Opt. Soc. Am. A 18, 839-853 (2001).
    [CrossRef]
  11. C. J. R. Sheppard and C. J. Cogswell, "Effects of aberrating layers and the tube length on confocal imaging properties," Optik (Stuttgart) 87, 34-38 (1991).
  12. P. Török, P. Varga, Z. Laczik, and G. R. Booker, "Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation," J. Opt. Soc. Am. A 12, 325-332 (1995).
    [CrossRef]
  13. M. J. Booth, M. A. A. Neil, and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatch media," J. Microsc. 192, 90-98 (1998).
    [CrossRef]
  14. O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part II: Confocal and multiphoton microscopy," Opt. Commun. 235, 1-10 (2004).
    [CrossRef]
  15. T. D. Lister, R. S. Upton, and H. Luo, "Objective lens design for multiple-layer optical data storage," Opt. Eng. 38, 295-301 (1999).
    [CrossRef]
  16. A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constant, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
    [CrossRef] [PubMed]
  17. C. J. R. Sheppard and M. Gu, "Aberration compensation in confocal microscopy," Appl. Opt. 30, 3563-3568 (1991).
    [CrossRef] [PubMed]
  18. P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998).
    [CrossRef]
  19. S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, "Measuring lateral efficiency of optical traps: the effect of tube length," Opt. Commun. 259, 204-211 (2006).
    [CrossRef]
  20. M. Schwertner, M. J. Booth, and T. Wilson, "Simple optimization procedure for objective lens correction collar setting," J. Microsc. 217, 184-187 (2005).
    [CrossRef] [PubMed]
  21. M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
    [CrossRef] [PubMed]
  22. E. Theofanidou, L. Wilson, W. J. Hossak, and J. Artl, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
    [CrossRef]
  23. S. Somalinga, K. Dressbach, M. Hain, S. Stankovic, T. Tschudi, J. Knittel, and H. Richter, "Effective spherical aberration compensation by use of nematic liquid-crystal device," Appl. Opt. 43, 2722-2729 (2004).
    [CrossRef]
  24. M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, "Optimized pupil-plane filters for confocal microscope point-spread function engineering," Opt. Lett. 25, 245-247 (2000).
    [CrossRef]
  25. C. J. R. Sheppard, "Binary optics and confocal imaging," Opt. Lett. 24, 505-506 (1999).
    [CrossRef]
  26. M. Martinez-Corral, M. T. Caballero, E. H. K. Stelzer, and J. Swoger, "Tailoring the axial shape of the point spread function using the Toraldo concept," Opt. Express 10, 98-103 (2002).
    [PubMed]
  27. C. M. Blanca and S. W. Hell, "Axial superresolution with ultrahigh aperture lenses," Opt. Express 10, 893-898 (2002).
    [PubMed]
  28. G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am. A 19, 584-589 (2002).
    [CrossRef]
  29. M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and M. T. Caballero, "Axial gain in resolution in optical sectioning fluorescence microscopy by shaded-ring filters," Opt. Express 11, 1740-1745 (2003).
    [CrossRef] [PubMed]
  30. S. S. Sherif and P. Török, "Pupil plane masks for super-resolution in high-numerical-aperture focusing," J. Mod. Opt. 51, 2007-2019 (2004).
  31. C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, "Quasi-isotropic 3-D resolution in two-photon scanning microscopy," Opt. Express 12, 6168-6174 (2005).
    [CrossRef]
  32. M. Gu, Advanced Optical Imaging Theory (Springer-Verlag, 2000).
  33. C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
    [CrossRef]
  34. P. Török and P. Varga, "Electromagnetic diffraction of light focused through a stratified medium," Appl. Opt. 36, 2305-2312 (1997).
    [CrossRef] [PubMed]
  35. O. Haeberlé, M. Ammar, H. Furukawa, K. Tenjimbayashi, and P. Torok, "Point spread function of optical microscopes imaging through stratified media," Opt. Express 11, 2964-2969 (2003).
    [CrossRef] [PubMed]
  36. J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, "Axially invariant pupil filters," J. Mod. Opt. 47, 57-68 (2000).
  37. D. D. Lowenthal, "Maréchal intensity criteria modified for Gaussian beams," Appl. Opt. 13, 2126-2133 (1974).
    [CrossRef] [PubMed]
  38. M. Martínez-Corral, L. Muñoz-Escriva, M. Kowalczyk, and T. Cichocki, "One-dimensional iterative algorithm for three-dimensional point-spread function engineering," Opt. Lett. 26, 1861-1863 (2001).
    [CrossRef]

2006

S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, "Measuring lateral efficiency of optical traps: the effect of tube length," Opt. Commun. 259, 204-211 (2006).
[CrossRef]

2005

M. Schwertner, M. J. Booth, and T. Wilson, "Simple optimization procedure for objective lens correction collar setting," J. Microsc. 217, 184-187 (2005).
[CrossRef] [PubMed]

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, "Quasi-isotropic 3-D resolution in two-photon scanning microscopy," Opt. Express 12, 6168-6174 (2005).
[CrossRef]

S. Stallinga, "Compact description of substrate-related aberrations in high numerical-aperture optical disk readout," Appl. Opt. 44, 849-858 (2005).
[CrossRef] [PubMed]

2004

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part II: Confocal and multiphoton microscopy," Opt. Commun. 235, 1-10 (2004).
[CrossRef]

S. S. Sherif and P. Török, "Pupil plane masks for super-resolution in high-numerical-aperture focusing," J. Mod. Opt. 51, 2007-2019 (2004).

E. Theofanidou, L. Wilson, W. J. Hossak, and J. Artl, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

S. Somalinga, K. Dressbach, M. Hain, S. Stankovic, T. Tschudi, J. Knittel, and H. Richter, "Effective spherical aberration compensation by use of nematic liquid-crystal device," Appl. Opt. 43, 2722-2729 (2004).
[CrossRef]

2003

2002

2001

2000

1999

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

T. D. Lister, R. S. Upton, and H. Luo, "Objective lens design for multiple-layer optical data storage," Opt. Eng. 38, 295-301 (1999).
[CrossRef]

1998

M. J. Booth, M. A. A. Neil, and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatch media," J. Microsc. 192, 90-98 (1998).
[CrossRef]

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998).
[CrossRef]

1997

C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

P. Török and P. Varga, "Electromagnetic diffraction of light focused through a stratified medium," Appl. Opt. 36, 2305-2312 (1997).
[CrossRef] [PubMed]

1995

1991

C. J. R. Sheppard and M. Gu, "Aberration compensation in confocal microscopy," Appl. Opt. 30, 3563-3568 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard and C. J. Cogswell, "Effects of aberrating layers and the tube length on confocal imaging properties," Optik (Stuttgart) 87, 34-38 (1991).

1988

1986

1974

1965

1963

T. Tsujiuchi, "Correction of optical images by compensation of aberrations and by spatial frequency filtering," Prog. Oceanogr. 2, 133-180 (1963).

Ammar, M.

Andrés, P.

Artl, J.

E. Theofanidou, L. Wilson, W. J. Hossak, and J. Artl, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Barakat, R.

Blanca, C. M.

Booker, G. R.

Booth, M. J.

M. Schwertner, M. J. Booth, and T. Wilson, "Simple optimization procedure for objective lens correction collar setting," J. Microsc. 217, 184-187 (2005).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatch media," J. Microsc. 192, 90-98 (1998).
[CrossRef]

Boyer, G.

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, "Quasi-isotropic 3-D resolution in two-photon scanning microscopy," Opt. Express 12, 6168-6174 (2005).
[CrossRef]

G. Boyer, "New class of axially apodizing filters for confocal scanning microscopy," J. Opt. Soc. Am. A 19, 584-589 (2002).
[CrossRef]

Caballero, M. T.

Campos, J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, "Axially invariant pupil filters," J. Mod. Opt. 47, 57-68 (2000).

Cichocki, T.

Cogswell, C. J.

C. J. R. Sheppard and C. J. Cogswell, "Effects of aberrating layers and the tube length on confocal imaging properties," Optik (Stuttgart) 87, 34-38 (1991).

Diaz, A.

Dressbach, K.

Escalera, J. C.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, "Axially invariant pupil filters," J. Mod. Opt. 47, 57-68 (2000).

Furukawa, H.

Golestanian, R.

S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, "Measuring lateral efficiency of optical traps: the effect of tube length," Opt. Commun. 259, 204-211 (2006).
[CrossRef]

Gu, M.

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998).
[CrossRef]

C. J. R. Sheppard and M. Gu, "Aberration compensation in confocal microscopy," Appl. Opt. 30, 3563-3568 (1991).
[CrossRef] [PubMed]

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

Haeberlé, O.

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part II: Confocal and multiphoton microscopy," Opt. Commun. 235, 1-10 (2004).
[CrossRef]

O. Haeberlé, M. Ammar, H. Furukawa, K. Tenjimbayashi, and P. Torok, "Point spread function of optical microscopes imaging through stratified media," Opt. Express 11, 2964-2969 (2003).
[CrossRef] [PubMed]

Hain, M.

Harvey, A. R.

Hell, S. W.

Hossak, W. J.

E. Theofanidou, L. Wilson, W. J. Hossak, and J. Artl, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Houston, A.

Ibáñez-López, C.

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, "Quasi-isotropic 3-D resolution in two-photon scanning microscopy," Opt. Express 12, 6168-6174 (2005).
[CrossRef]

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and M. T. Caballero, "Axial gain in resolution in optical sectioning fluorescence microscopy by shaded-ring filters," Opt. Express 11, 1740-1745 (2003).
[CrossRef] [PubMed]

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, "Optimized pupil-plane filters for confocal microscope point-spread function engineering," Opt. Lett. 25, 245-247 (2000).
[CrossRef]

Ke, P. C.

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998).
[CrossRef]

Khalesifard, H. R.

S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, "Measuring lateral efficiency of optical traps: the effect of tube length," Opt. Commun. 259, 204-211 (2006).
[CrossRef]

Knittel, J.

Kowalczyk, M.

Laczik, Z.

Laczik, Z. J.

Lister, T. D.

T. D. Lister, R. S. Upton, and H. Luo, "Objective lens design for multiple-layer optical data storage," Opt. Eng. 38, 295-301 (1999).
[CrossRef]

Lowenthal, D. D.

Luo, H.

T. D. Lister, R. S. Upton, and H. Luo, "Objective lens design for multiple-layer optical data storage," Opt. Eng. 38, 295-301 (1999).
[CrossRef]

Martinez-Corral, M.

Martínez-Corral, M.

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, "Quasi-isotropic 3-D resolution in two-photon scanning microscopy," Opt. Express 12, 6168-6174 (2005).
[CrossRef]

M. Martínez-Corral, L. Muñoz-Escriva, M. Kowalczyk, and T. Cichocki, "One-dimensional iterative algorithm for three-dimensional point-spread function engineering," Opt. Lett. 26, 1861-1863 (2001).
[CrossRef]

Mezouari, S.

Mills, J. P.

Muñoz-Escriva, L.

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, "Optimized pupil-plane filters for confocal microscope point-spread function engineering," Opt. Lett. 25, 245-247 (2000).
[CrossRef]

M. J. Booth, M. A. A. Neil, and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatch media," J. Microsc. 192, 90-98 (1998).
[CrossRef]

Ojeda-Castañeda, J.

Pons, A.

Reihani, S. N. S.

S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, "Measuring lateral efficiency of optical traps: the effect of tube length," Opt. Commun. 259, 204-211 (2006).
[CrossRef]

Richter, H.

Rohrbach, A.

Saavedra, G.

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, "Quasi-isotropic 3-D resolution in two-photon scanning microscopy," Opt. Express 12, 6168-6174 (2005).
[CrossRef]

M. Martinez-Corral, C. Ibáñez-López, G. Saavedra, and M. T. Caballero, "Axial gain in resolution in optical sectioning fluorescence microscopy by shaded-ring filters," Opt. Express 11, 1740-1745 (2003).
[CrossRef] [PubMed]

Sarafis, V.

Schwertner, M.

M. Schwertner, M. J. Booth, and T. Wilson, "Simple optimization procedure for objective lens correction collar setting," J. Microsc. 217, 184-187 (2005).
[CrossRef] [PubMed]

Sheppard, C. J. R.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, "Axially invariant pupil filters," J. Mod. Opt. 47, 57-68 (2000).

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

C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

C. J. R. Sheppard and M. Gu, "Aberration compensation in confocal microscopy," Appl. Opt. 30, 3563-3568 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard and C. J. Cogswell, "Effects of aberrating layers and the tube length on confocal imaging properties," Optik (Stuttgart) 87, 34-38 (1991).

Sherif, S. S.

S. S. Sherif and P. Török, "Pupil plane masks for super-resolution in high-numerical-aperture focusing," J. Mod. Opt. 51, 2007-2019 (2004).

Somalinga, S.

Stallinga, S.

Stankovic, S.

Stelzer, E. H. K.

Swoger, J.

Tenjimbayashi, K.

Tepichin, E.

Theofanidou, E.

E. Theofanidou, L. Wilson, W. J. Hossak, and J. Artl, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Thompson, B. J.

Torok, P.

Török, P.

Tschudi, T.

Tsujiuchi, T.

T. Tsujiuchi, "Correction of optical images by compensation of aberrations and by spatial frequency filtering," Prog. Oceanogr. 2, 133-180 (1963).

Upton, R. S.

T. D. Lister, R. S. Upton, and H. Luo, "Objective lens design for multiple-layer optical data storage," Opt. Eng. 38, 295-301 (1999).
[CrossRef]

Varga, P.

Wilson, L.

E. Theofanidou, L. Wilson, W. J. Hossak, and J. Artl, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

Wilson, T.

M. Schwertner, M. J. Booth, and T. Wilson, "Simple optimization procedure for objective lens correction collar setting," J. Microsc. 217, 184-187 (2005).
[CrossRef] [PubMed]

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, "Optimized pupil-plane filters for confocal microscope point-spread function engineering," Opt. Lett. 25, 245-247 (2000).
[CrossRef]

M. J. Booth, M. A. A. Neil, and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatch media," J. Microsc. 192, 90-98 (1998).
[CrossRef]

Yzuel, M. J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, "Axially invariant pupil filters," J. Mod. Opt. 47, 57-68 (2000).

Appl. Opt.

J. Microsc.

C. J. R. Sheppard and P. Török, "Effects of specimen refractive index on confocal imaging," J. Microsc. 185, 366-374 (1997).
[CrossRef]

M. J. Booth, M. A. A. Neil, and T. Wilson, "Aberration correction for confocal imaging in refractive-index-mismatch media," J. Microsc. 192, 90-98 (1998).
[CrossRef]

M. Schwertner, M. J. Booth, and T. Wilson, "Simple optimization procedure for objective lens correction collar setting," J. Microsc. 217, 184-187 (2005).
[CrossRef] [PubMed]

J. Mod. Opt.

P. C. Ke and M. Gu, "Characterization of trapping force in the presence of spherical aberration," J. Mod. Opt. 45, 2159-2168 (1998).
[CrossRef]

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, "Axially invariant pupil filters," J. Mod. Opt. 47, 57-68 (2000).

S. S. Sherif and P. Török, "Pupil plane masks for super-resolution in high-numerical-aperture focusing," J. Mod. Opt. 51, 2007-2019 (2004).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

E. Theofanidou, L. Wilson, W. J. Hossak, and J. Artl, "Spherical aberration correction for optical tweezers," Opt. Commun. 236, 145-150 (2004).
[CrossRef]

S. N. S. Reihani, H. R. Khalesifard, and R. Golestanian, "Measuring lateral efficiency of optical traps: the effect of tube length," Opt. Commun. 259, 204-211 (2006).
[CrossRef]

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part II: Confocal and multiphoton microscopy," Opt. Commun. 235, 1-10 (2004).
[CrossRef]

Opt. Eng.

T. D. Lister, R. S. Upton, and H. Luo, "Objective lens design for multiple-layer optical data storage," Opt. Eng. 38, 295-301 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Optik (Stuttgart)

C. J. R. Sheppard and C. J. Cogswell, "Effects of aberrating layers and the tube length on confocal imaging properties," Optik (Stuttgart) 87, 34-38 (1991).

Proc. Natl. Acad. Sci. U.S.A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, "Adaptive aberration correction in a confocal microscope," Proc. Natl. Acad. Sci. U.S.A. 99, 5788-5792 (2002).
[CrossRef] [PubMed]

Prog. Oceanogr.

T. Tsujiuchi, "Correction of optical images by compensation of aberrations and by spatial frequency filtering," Prog. Oceanogr. 2, 133-180 (1963).

Other

J.B.Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, 1995).

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

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 (6)

Fig. 1
Fig. 1

Scheme of focusing by a high-NA telecentric objective lens.

Fig. 2
Fig. 2

Scheme for the evaluation of phase distortion introduced when a tightly focused light beam passes through a plane surface of refractive index step.

Fig. 3
Fig. 3

Axial intensity profiles corresponding to a low-NA (dotted curves) and a high-NA (solid curves) focusing element with a clear circular aperture as the aperture stop and for increasing values of w 40 . Since to perform the nonlinear mapping of Eqs. (7), the value of α must be known, in our calculations we assumed NA = 0.1 (air) and NA = 1.2 (water).

Fig. 4
Fig. 4

(a) Axial intensity profiles corresponding to a high-NA focusing element with the reversed-Gaussian aperture as the aperture stop and for increasing values of w 40 . In our calculations we considered the case w = 0.65 . (b) Intensity profiles produced by the circular aperture (dashed curve) and the reversed-Gaussian filter (solid curve) for w 40 = 3 λ .

Fig. 5
Fig. 5

Lateral responses corresponding to a high-NA focusing element with the circular (solid curve) or the reversed-Gaussian aperture (dashed curve) as the aperture stop and for increasing values of w 40 .

Fig. 6
Fig. 6

Numerically evaluated images of a typical spoke target for increasing SA.

Equations (15)

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

U ( v , z N ) = 0 α P ( θ ) cos θ J 0 ( k v sin θ sin α ) exp [ i k W ( θ ) ] exp ( i k z N sin 2 ( θ 2 ) sin 2 ( α 2 ) ) sin θ d θ .
v = r sin α , z N = 2 z sin 2 ( α 2 ) ,
P ( θ ) = t ( ρ ) , ρ = sin θ sin α ,
W ( θ ) = n l n l = d ( n cos θ n cos θ ) ,
W ( θ ) = d ( n n ) [ 1 + 2 n n s 2 + 2 ( n + n ) n 2 n 3 s 4 + ] .
U ( v , z N ; w 40 ) = 0 α P ( θ ) cos θ J 0 ( k v sin θ sin α ) exp { i k [ w 40 sin 4 ( θ 2 ) sin 4 ( α 2 ) z N sin 2 ( θ 2 ) sin 2 ( α 2 ) ] } sin θ d θ ,
w 20 = 2 d ( n n ) n n sin 2 ( α 2 ) ,
w 40 = 2 d ( n 2 n 2 ) n 2 n 3 sin 4 ( α 2 ) ,
ζ = sin 2 ( θ 2 ) sin 2 ( a 2 ) 0.5 , q ( ζ ) = P ( θ ) cos θ .
U ( v = 0 , z N ; w 40 ) = 0.5 0.5 q ( ζ ) exp ( i 2 π λ w 40 ζ 2 ) exp [ i 2 π λ ( z N w 40 ) ζ ] d ζ ,
t ( ρ ) = exp [ ( ρ ω ) 2 ] .
P ( θ ) = exp [ ( sin θ ω sin α ) 2 ] .
Q ( ζ ) = exp { 1 [ cos 2 ( α 2 ) 2 ζ sin 2 ( α 2 ) ] 2 ( ω sin α ) 2 } .
Q ¯ ( ζ ) = Q ( ζ ) .
t ¯ ( ρ ) = exp { 1 [ 2 cos 2 ( α 2 ) 1 ρ 2 sin 2 α ] 2 ω 2 sin 2 α } .

Metrics