Abstract

The effects of the refractive-index mismatch in confocal laser scanning microscopy were extensively studied. The axial aberration induced in the case of fluorescent microspheres was measured. The data were used to take into account the mismatch-induced aberrations and to consider object-size influence. Then we focused on the effect of refractive-index mismatch on the effective system’s point-spread function under different mismatch conditions and on depth of focusing. We experimentally verified that the peak of the point-spread function intensity profile decreases and the point-spread function itself progressively broadens as a function of the combined effect of the refractive-index mismatch and of the penetration depth, leading to a worsening of the system’s overall performances. We also performed these same measurements by embedding subresolution beads in an oocyte’s cytoplasm, which can be considered a turbid medium. We found evidence consistent with the previously developed theoretical model; in particular we found a strong dependence of the intensity peak on the focusing depth.

© 2002 Optical Society of America

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References

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  1. D. M. Shotton, “Confocal scanning optical microscopy and its applications for biological specimens,” J. Cell. Sci. 94, 175–206 (1989).
  2. A. Diaspro, ed. Confocal and Two-Photon Microscopy: Foundations, Applications, and Advances (Wiley-Liss, New York, 2001).
  3. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
    [CrossRef]
  4. M. Minsky, “Microscopy apparatus,” U.S. patent3,013,467 (19December1961).
  5. C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
    [CrossRef]
  6. T. Wilson, C. J. R. Sheppard, Theory and Practice in Scanning Optical Microscopy (Academic, London, 1984).
  7. J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41–48 (1987).
    [CrossRef] [PubMed]
  8. G. J. Brakenhoff, P. Blom, P. Barends, “Confocal scanning light microscopy with high aperture immersion lenses,” J. Microsc. 117, 219–232 (1979).
    [CrossRef]
  9. B. Bianco, A. Diaspro, “Analysis of the three dimensional cell imaging obtained with optical microscopy techniques based on defocusing,” Cell Biophys. 15, 189–200 (1989).
    [CrossRef] [PubMed]
  10. C. J. R. Sheppard, “Axial resolution of confocal fluorescence microscopy,” J. Microsc. 154, 237–242 (1989).
    [CrossRef]
  11. T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143–156 (1989).
    [CrossRef]
  12. A. Diaspro, M. Sartore, C. Nicolini, “Three-dimensional representation of biostructures imaged with an optical microscope. I. Digital optical sectioning.” Image Vision Comput. 8, 130–134 (1990).
    [CrossRef]
  13. K. Carlsson, “The influence of specimen refractive index, detector signal integration, and non-uniform scan speed on the imaging properties in confocal microscopy,” J. Microsc. 163, 167–178 (1991).
    [CrossRef]
  14. T. D. Visser, J. L. Oud, G. J. Brakenhoff, “Refractive index and axial distance measurements in 3-D microscopy,” Optik 90, 17–19 (1992).
  15. S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
    [CrossRef]
  16. C. J. R. Sheppard, P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 18, 366–374 (1997).
    [CrossRef]
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, U.K., 1999).
    [CrossRef]
  18. X. Gan, M. Gu, “Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media,” Opt. Lett. 24, 741–743 (1999).
    [CrossRef]
  19. D. S. Wan, M. Rajadhyasksha, R. H. Webb, “Analysis of spherical aberration of a water immersion objective: Application to specimens with refractive indices 1.33–1.40,” J. Microsc. 197, 274–284 (2000).
    [CrossRef] [PubMed]
  20. I. J. Cox, C. J. R. Sheppard, “Digital image processing of confocal images,” Image Vision Comput. 1, 52–56 (1983).
    [CrossRef]
  21. G. T. M. Van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
    [CrossRef]
  22. A. Diaspro, S. Annunziata, M. Robello, “Single-pinhole confocal imaging of sub-resolution sparse objects using experimental point spread function and image restoration,” Microsc. Res. Tech. 51, 400–405 (2000).
  23. P. Torok, P. Varga, “Electromagnetic diffraction of light through a stratified medium,” Appl. Opt. 36, 2305–2312 (1997).
    [CrossRef]
  24. A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
    [CrossRef]
  25. C. J. R. Sheppard, “Confocal imaging through weakly aberrating media,” Appl. Opt. 39, 6366–6368 (2000).
    [CrossRef]

2000 (3)

A. Diaspro, S. Annunziata, M. Robello, “Single-pinhole confocal imaging of sub-resolution sparse objects using experimental point spread function and image restoration,” Microsc. Res. Tech. 51, 400–405 (2000).

D. S. Wan, M. Rajadhyasksha, R. H. Webb, “Analysis of spherical aberration of a water immersion objective: Application to specimens with refractive indices 1.33–1.40,” J. Microsc. 197, 274–284 (2000).
[CrossRef] [PubMed]

C. J. R. Sheppard, “Confocal imaging through weakly aberrating media,” Appl. Opt. 39, 6366–6368 (2000).
[CrossRef]

1999 (2)

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
[CrossRef]

X. Gan, M. Gu, “Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media,” Opt. Lett. 24, 741–743 (1999).
[CrossRef]

1997 (2)

P. Torok, P. Varga, “Electromagnetic diffraction of light through a stratified medium,” Appl. Opt. 36, 2305–2312 (1997).
[CrossRef]

C. J. R. Sheppard, P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 18, 366–374 (1997).
[CrossRef]

1996 (1)

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

1995 (1)

G. T. M. Van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

1993 (1)

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

1992 (1)

T. D. Visser, J. L. Oud, G. J. Brakenhoff, “Refractive index and axial distance measurements in 3-D microscopy,” Optik 90, 17–19 (1992).

1991 (1)

K. Carlsson, “The influence of specimen refractive index, detector signal integration, and non-uniform scan speed on the imaging properties in confocal microscopy,” J. Microsc. 163, 167–178 (1991).
[CrossRef]

1990 (1)

A. Diaspro, M. Sartore, C. Nicolini, “Three-dimensional representation of biostructures imaged with an optical microscope. I. Digital optical sectioning.” Image Vision Comput. 8, 130–134 (1990).
[CrossRef]

1989 (4)

D. M. Shotton, “Confocal scanning optical microscopy and its applications for biological specimens,” J. Cell. Sci. 94, 175–206 (1989).

B. Bianco, A. Diaspro, “Analysis of the three dimensional cell imaging obtained with optical microscopy techniques based on defocusing,” Cell Biophys. 15, 189–200 (1989).
[CrossRef] [PubMed]

C. J. R. Sheppard, “Axial resolution of confocal fluorescence microscopy,” J. Microsc. 154, 237–242 (1989).
[CrossRef]

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143–156 (1989).
[CrossRef]

1987 (1)

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41–48 (1987).
[CrossRef] [PubMed]

1983 (1)

I. J. Cox, C. J. R. Sheppard, “Digital image processing of confocal images,” Image Vision Comput. 1, 52–56 (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]

1977 (1)

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

Amos, W. B.

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41–48 (1987).
[CrossRef] [PubMed]

Annunziata, S.

A. Diaspro, S. Annunziata, M. Robello, “Single-pinhole confocal imaging of sub-resolution sparse objects using experimental point spread function and image restoration,” Microsc. Res. Tech. 51, 400–405 (2000).

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
[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]

Bianco, B.

B. Bianco, A. Diaspro, “Analysis of the three dimensional cell imaging obtained with optical microscopy techniques based on defocusing,” Cell Biophys. 15, 189–200 (1989).
[CrossRef] [PubMed]

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 (Pergamon, Oxford, U.K., 1999).
[CrossRef]

Brakenhoff, G. J.

T. D. Visser, J. L. Oud, G. J. Brakenhoff, “Refractive index and axial distance measurements in 3-D microscopy,” Optik 90, 17–19 (1992).

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

Carlsson, K.

K. Carlsson, “The influence of specimen refractive index, detector signal integration, and non-uniform scan speed on the imaging properties in confocal microscopy,” J. Microsc. 163, 167–178 (1991).
[CrossRef]

Choudhury, A.

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

Cox, I. J.

I. J. Cox, C. J. R. Sheppard, “Digital image processing of confocal images,” Image Vision Comput. 1, 52–56 (1983).
[CrossRef]

Cremer, C.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Diaspro, A.

A. Diaspro, S. Annunziata, M. Robello, “Single-pinhole confocal imaging of sub-resolution sparse objects using experimental point spread function and image restoration,” Microsc. Res. Tech. 51, 400–405 (2000).

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
[CrossRef]

A. Diaspro, M. Sartore, C. Nicolini, “Three-dimensional representation of biostructures imaged with an optical microscope. I. Digital optical sectioning.” Image Vision Comput. 8, 130–134 (1990).
[CrossRef]

B. Bianco, A. Diaspro, “Analysis of the three dimensional cell imaging obtained with optical microscopy techniques based on defocusing,” Cell Biophys. 15, 189–200 (1989).
[CrossRef] [PubMed]

Fordham, M.

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41–48 (1987).
[CrossRef] [PubMed]

Gan, X.

Gu, M.

Hell, S.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Minsky, M.

M. Minsky, “Microscopy apparatus,” U.S. patent3,013,467 (19December1961).

Nicolini, C.

A. Diaspro, M. Sartore, C. Nicolini, “Three-dimensional representation of biostructures imaged with an optical microscope. I. Digital optical sectioning.” Image Vision Comput. 8, 130–134 (1990).
[CrossRef]

Oud, J. L.

T. D. Visser, J. L. Oud, G. J. Brakenhoff, “Refractive index and axial distance measurements in 3-D microscopy,” Optik 90, 17–19 (1992).

Raimondo, M.

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
[CrossRef]

Rajadhyasksha, M.

D. S. Wan, M. Rajadhyasksha, R. H. Webb, “Analysis of spherical aberration of a water immersion objective: Application to specimens with refractive indices 1.33–1.40,” J. Microsc. 197, 274–284 (2000).
[CrossRef] [PubMed]

Ramoino, P.

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
[CrossRef]

Reiner, G.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Robello, M.

A. Diaspro, S. Annunziata, M. Robello, “Single-pinhole confocal imaging of sub-resolution sparse objects using experimental point spread function and image restoration,” Microsc. Res. Tech. 51, 400–405 (2000).

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
[CrossRef]

Sartore, M.

A. Diaspro, M. Sartore, C. Nicolini, “Three-dimensional representation of biostructures imaged with an optical microscope. I. Digital optical sectioning.” Image Vision Comput. 8, 130–134 (1990).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, “Confocal imaging through weakly aberrating media,” Appl. Opt. 39, 6366–6368 (2000).
[CrossRef]

C. J. R. Sheppard, P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 18, 366–374 (1997).
[CrossRef]

C. J. R. Sheppard, “Axial resolution of confocal fluorescence microscopy,” J. Microsc. 154, 237–242 (1989).
[CrossRef]

I. J. Cox, C. J. R. Sheppard, “Digital image processing of confocal images,” Image Vision Comput. 1, 52–56 (1983).
[CrossRef]

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

T. Wilson, C. J. R. Sheppard, Theory and Practice in Scanning Optical Microscopy (Academic, London, 1984).

Shotton, D. M.

D. M. Shotton, “Confocal scanning optical microscopy and its applications for biological specimens,” J. Cell. Sci. 94, 175–206 (1989).

Stelzer, E. H. K.

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

Strasters, K. C.

G. T. M. Van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

Torok, P.

C. J. R. Sheppard, P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 18, 366–374 (1997).
[CrossRef]

P. Torok, P. Varga, “Electromagnetic diffraction of light through a stratified medium,” Appl. Opt. 36, 2305–2312 (1997).
[CrossRef]

Van der Voort, G. T. M.

G. T. M. Van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

Varga, P.

Visser, T. D.

T. D. Visser, J. L. Oud, G. J. Brakenhoff, “Refractive index and axial distance measurements in 3-D microscopy,” Optik 90, 17–19 (1992).

Wan, D. S.

D. S. Wan, M. Rajadhyasksha, R. H. Webb, “Analysis of spherical aberration of a water immersion objective: Application to specimens with refractive indices 1.33–1.40,” J. Microsc. 197, 274–284 (2000).
[CrossRef] [PubMed]

Webb, R. H.

D. S. Wan, M. Rajadhyasksha, R. H. Webb, “Analysis of spherical aberration of a water immersion objective: Application to specimens with refractive indices 1.33–1.40,” J. Microsc. 197, 274–284 (2000).
[CrossRef] [PubMed]

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

White, J. G.

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41–48 (1987).
[CrossRef] [PubMed]

Wilson, T.

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143–156 (1989).
[CrossRef]

T. Wilson, C. J. R. Sheppard, Theory and Practice in Scanning Optical Microscopy (Academic, London, 1984).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, U.K., 1999).
[CrossRef]

Appl. Opt. (2)

Cell Biophys. (1)

B. Bianco, A. Diaspro, “Analysis of the three dimensional cell imaging obtained with optical microscopy techniques based on defocusing,” Cell Biophys. 15, 189–200 (1989).
[CrossRef] [PubMed]

IEEE Eng. Med. Biol. Mag. (1)

A. Diaspro, S. Annunziata, M. Raimondo, P. Ramoino, M. Robello “Single pinhole confocal laser scanning microscope operating as 3D image formation device in the study of biostructures,” IEEE Eng. Med. Biol. Mag. 18(14), 106–110 (1999).
[CrossRef]

Image Vision Comput. (2)

A. Diaspro, M. Sartore, C. Nicolini, “Three-dimensional representation of biostructures imaged with an optical microscope. I. Digital optical sectioning.” Image Vision Comput. 8, 130–134 (1990).
[CrossRef]

I. J. Cox, C. J. R. Sheppard, “Digital image processing of confocal images,” Image Vision Comput. 1, 52–56 (1983).
[CrossRef]

J. Cell Biol. (1)

J. G. White, W. B. Amos, M. Fordham, “An evaluation of confocal versus conventional imaging of biological structures by fluorescence light microscopy,” J. Cell Biol. 105, 41–48 (1987).
[CrossRef] [PubMed]

J. Cell. Sci. (1)

D. M. Shotton, “Confocal scanning optical microscopy and its applications for biological specimens,” J. Cell. Sci. 94, 175–206 (1989).

J. Microsc. (8)

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

G. T. M. Van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

S. Hell, G. Reiner, C. Cremer, E. H. K. Stelzer, “Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index,” J. Microsc. 169, 391–405 (1993).
[CrossRef]

C. J. R. Sheppard, P. Torok, “Effects of specimen refractive index on confocal imaging,” J. Microsc. 18, 366–374 (1997).
[CrossRef]

K. Carlsson, “The influence of specimen refractive index, detector signal integration, and non-uniform scan speed on the imaging properties in confocal microscopy,” J. Microsc. 163, 167–178 (1991).
[CrossRef]

C. J. R. Sheppard, “Axial resolution of confocal fluorescence microscopy,” J. Microsc. 154, 237–242 (1989).
[CrossRef]

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143–156 (1989).
[CrossRef]

D. S. Wan, M. Rajadhyasksha, R. H. Webb, “Analysis of spherical aberration of a water immersion objective: Application to specimens with refractive indices 1.33–1.40,” J. Microsc. 197, 274–284 (2000).
[CrossRef] [PubMed]

Microsc. Res. Tech. (1)

A. Diaspro, S. Annunziata, M. Robello, “Single-pinhole confocal imaging of sub-resolution sparse objects using experimental point spread function and image restoration,” Microsc. Res. Tech. 51, 400–405 (2000).

Opt. Acta (1)

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

Opt. Lett. (1)

Optik (1)

T. D. Visser, J. L. Oud, G. J. Brakenhoff, “Refractive index and axial distance measurements in 3-D microscopy,” Optik 90, 17–19 (1992).

Rep. Prog. Phys. (1)

R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

Other (4)

M. Minsky, “Microscopy apparatus,” U.S. patent3,013,467 (19December1961).

A. Diaspro, ed. Confocal and Two-Photon Microscopy: Foundations, Applications, and Advances (Wiley-Liss, New York, 2001).

T. Wilson, C. J. R. Sheppard, Theory and Practice in Scanning Optical Microscopy (Academic, London, 1984).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, U.K., 1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for evaluating the focusing depth of the subresolution beads. The PSF’s depth in the mounting medium was evaluated by defocusing with respect to a sample of 2.76-µm-diameter microspheres. This value was then been corrected by use of the experimental scaling factor to account for the refractive-index mismatch.

Fig. 2
Fig. 2

Experimental conditions typically encountered when one is focusing inside a medium whose refractive index does not match that of the objective. A convergent light wave traveling through a medium with refractive index n1 (objective-immersion medium) is focused by the objective into a second medium (sample-immersion medium with refractive index n2). The marginal rays make an angle θ1 with the normal to the interface and an angle θ2 after refraction. In this plot we consider the case n1 > n2.

Fig. 3
Fig. 3

Side view (xz plane) of the 2.76-µm fluorescent microspheres embedded in different media with known refractive indices. The spheres immersed in oil appear to be “more” spherical than the others.

Fig. 4
Fig. 4

Graph of the average scaling factor for different mismatch conditions for 22-µm-diameter versus 3-µm-diameter microspheres (square) and versus 15-µm diameter microspheres (circles). Each point on the graph is the average over 20 microspheres. The data were fitted according to a linear relationship, y = ax + b, in order to point out the dependence of the scaling factor on the object size. The best-fit parameters are a = 1.36 and b = 0.35 with a 99% correlation (for squares) and a = 0.94 and b = -0.07 with a 98% correlation (for circles).

Fig. 5
Fig. 5

Plot of the lateral FWHM (open circles) and axial FWHM (filled circles) versus focusing depth for the oil-immersed PSF (triangles), glycerol-immersed PSF (circles), and air-immersed PSF (squares). Each point given on the graph is the average over 30–40 PSFs at the corresponding focusing depth.

Tables (2)

Tables Icon

Table 1 Lateral and Axial FWHMs as Functions of the Focusing Depth and the Immersion Medium’s Refractive Indexa

Tables Icon

Table 2 Percentage of Variation of the PSF Intensity Peak in Different Mismatch Conditions as a Function of the Focusing Deptha

Equations (2)

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

Δf=n2n11-n1n2 sin θ121/2cos θ1Δz.
I0-I1I0=tg2α0-tg2α1tg2α0,

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