Abstract

We present two novel optical methods to achieve a significative improvement in the optical-sectioning capacity of confocal scanning microscopes. The techniques, whose real power is the simplicity with which they can be implemented, consist of a suitable combination of symmetrical defocusing with two different manners of apodizing both parts of the confocal architecture. It is shown that the proposed techniques are useful in both the bright-field and the fluorescence modes and for reflection and transmission geometries.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).
  2. I. J. Cox, C. J. R. Sheppard, T. Wilson, “Improvement in resolution by nearly confocal microscopy,” Appl. Opt. 21, 778–781 (1982).
    [CrossRef] [PubMed]
  3. Z. S. Hegedus, “Annular pupil arrays. Application to confocal microscopy,” Opt. Acta 32, 815–826 (1985).
    [CrossRef]
  4. Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
    [CrossRef]
  5. J. G. Walker, E. R. Pike, R. E. Davies, M. R. Young, G. J. Brakenhoff, M. Bertero, “Superresolving scanning optical microscopy using holographic optical processing,” J. Opt. Soc. Am. A 10, 59–64 (1993).
    [CrossRef]
  6. J. Gromalicki, E. R. Pike, J. G. Walker, M. Bertero, P. Boccaci, R. E. Davies, “Superresolving masks for incoherent scanning microscopes,” J. Opt. Soc. Am. A 10, 1074–1077 (1993).
    [CrossRef]
  7. T. Wilson, S. J. Hewlett, “The use of annular pupil plane filters to tune the imaging properties in confocal microscopy,” J. Mod. Opt. 37, 2025–2046 (1990).
    [CrossRef]
  8. R. H. Webb, “Confocal optical microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
    [CrossRef]
  9. C. J. R. Sheppard, M. Gu, “Improvement of axial resolution in confocal microscopy using annular filters,” Opt. Commun. 84, 7–13 (1991).
    [CrossRef]
  10. M. Martínez-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]
  11. S. Hell, E. H. K. Stelzer, “Properties of a 4Pi confocal fluorescence microscope,” J. Opt. Soc. Am. A 9, 2159–2166 (1992).
    [CrossRef]
  12. E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
    [CrossRef]
  13. S. Lindek, C. Cremer, E. H. K. Stelzer, “Confocal theta fluorescence microscopy with annular apertures,” Appl. Opt. 35, 126–130 (1996).
    [CrossRef] [PubMed]
  14. S. Kimura, T. Wilson, “Effect of axial pinhole displacement in confocal microscopes,” Appl. Opt. 32, 2257–2261 (1993).
    [CrossRef] [PubMed]
  15. C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
    [CrossRef]
  16. Ho, Shao, “Axial resolution of confocal microscopes revisited,” Optik (Stuttgart) 88, 147 (1991).
  17. M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, “On-axis diffractional behavior of two-dimensional pupils,” Appl. Opt. 33, 2223–2229 (1994).
    [CrossRef] [PubMed]
  18. J. Ojeda-Castañeda, P. Andrés, M. Martínez-Corral, “Zone plates with cells apodized by Legendre profiles,” Appl. Opt. 29, 1299–1303 (1990).
    [CrossRef] [PubMed]
  19. In Ref. 17 it is shown that, if a 1-D function is expressed in terms of the Legendre polynomials as t(x) = ∑n=0∞anPn(x), its Fourier transform is given by t̃(u) = ∑n=0∞ (-i)nanjn(πu). The function 4ζ2 can be expanded in terms of the Legendre polynomials as 4ζ2 = (1/3)P0(ζ) + (2/3)P2(ζ). Then the squared modulus of its 1-D Fourier transform is given by Eq. (15).

1996 (2)

1995 (1)

M. Martínez-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]

1994 (2)

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
[CrossRef]

M. Martínez-Corral, P. Andrés, J. Ojeda-Castañeda, “On-axis diffractional behavior of two-dimensional pupils,” Appl. Opt. 33, 2223–2229 (1994).
[CrossRef] [PubMed]

1993 (3)

1992 (1)

1991 (2)

C. J. R. Sheppard, M. Gu, “Improvement of axial resolution in confocal microscopy using annular filters,” Opt. Commun. 84, 7–13 (1991).
[CrossRef]

Ho, Shao, “Axial resolution of confocal microscopes revisited,” Optik (Stuttgart) 88, 147 (1991).

1990 (2)

J. Ojeda-Castañeda, P. Andrés, M. Martínez-Corral, “Zone plates with cells apodized by Legendre profiles,” Appl. Opt. 29, 1299–1303 (1990).
[CrossRef] [PubMed]

T. Wilson, S. J. Hewlett, “The use of annular pupil plane filters to tune the imaging properties in confocal microscopy,” J. Mod. Opt. 37, 2025–2046 (1990).
[CrossRef]

1986 (1)

1985 (1)

Z. S. Hegedus, “Annular pupil arrays. Application to confocal microscopy,” Opt. Acta 32, 815–826 (1985).
[CrossRef]

1984 (1)

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

1982 (1)

Andrés, P.

Bertero, M.

Boccaci, P.

Brakenhoff, G. J.

Cox, I. J.

Cremer, C.

Davies, R. E.

Gromalicki, J.

Gu, M.

C. J. R. Sheppard, M. Gu, “Improvement of axial resolution in confocal microscopy using annular filters,” Opt. Commun. 84, 7–13 (1991).
[CrossRef]

Hamilton, D. K.

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

Hegedus, Z. S.

Z. S. Hegedus, V. Sarafis, “Superresolving filters in confocally scanned imaging systems,” J. Opt. Soc. Am. A 3, 1892–1896 (1986).
[CrossRef]

Z. S. Hegedus, “Annular pupil arrays. Application to confocal microscopy,” Opt. Acta 32, 815–826 (1985).
[CrossRef]

Hell, S.

Hewlett, S. J.

T. Wilson, S. J. Hewlett, “The use of annular pupil plane filters to tune the imaging properties in confocal microscopy,” J. Mod. Opt. 37, 2025–2046 (1990).
[CrossRef]

Ho,

Ho, Shao, “Axial resolution of confocal microscopes revisited,” Optik (Stuttgart) 88, 147 (1991).

Kimura, S.

Lindek, S.

S. Lindek, C. Cremer, E. H. K. Stelzer, “Confocal theta fluorescence microscopy with annular apertures,” Appl. Opt. 35, 126–130 (1996).
[CrossRef] [PubMed]

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
[CrossRef]

Martínez-Corral, M.

Ojeda-Castañeda, J.

Pike, E. R.

Saavedra, G.

M. Martínez-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]

Sarafis, V.

Shao,

Ho, Shao, “Axial resolution of confocal microscopes revisited,” Optik (Stuttgart) 88, 147 (1991).

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, “Improvement of axial resolution in confocal microscopy using annular filters,” Opt. Commun. 84, 7–13 (1991).
[CrossRef]

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Improvement in resolution by nearly confocal microscopy,” Appl. Opt. 21, 778–781 (1982).
[CrossRef] [PubMed]

Stelzer, E. H. K.

S. Lindek, C. Cremer, E. H. K. Stelzer, “Confocal theta fluorescence microscopy with annular apertures,” Appl. Opt. 35, 126–130 (1996).
[CrossRef] [PubMed]

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (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]

Walker, J. G.

Webb, R. H.

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

Wilson, T.

Young, M. R.

Appl. Opt. (5)

J. Mod. Opt. (1)

T. Wilson, S. J. Hewlett, “The use of annular pupil plane filters to tune the imaging properties in confocal microscopy,” J. Mod. Opt. 37, 2025–2046 (1990).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Acta (2)

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

Z. S. Hegedus, “Annular pupil arrays. Application to confocal microscopy,” Opt. Acta 32, 815–826 (1985).
[CrossRef]

Opt. Commun. (3)

C. J. R. Sheppard, M. Gu, “Improvement of axial resolution in confocal microscopy using annular filters,” Opt. Commun. 84, 7–13 (1991).
[CrossRef]

M. Martínez-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]

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
[CrossRef]

Optik (Stuttgart) (1)

Ho, Shao, “Axial resolution of confocal microscopes revisited,” Optik (Stuttgart) 88, 147 (1991).

Rep. Prog. Phys. (1)

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

Other (2)

In Ref. 17 it is shown that, if a 1-D function is expressed in terms of the Legendre polynomials as t(x) = ∑n=0∞anPn(x), its Fourier transform is given by t̃(u) = ∑n=0∞ (-i)nanjn(πu). The function 4ζ2 can be expanded in terms of the Legendre polynomials as 4ζ2 = (1/3)P0(ζ) + (2/3)P2(ζ). Then the squared modulus of its 1-D Fourier transform is given by Eq. (15).

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 (12)

Fig. 1
Fig. 1

Schematic layout of a symmetrically defocused transmission-mode CSM. The defocus parameter W 20 D gives a measure of the axial shifting of the focal points.

Fig. 2
Fig. 2

Axial IPSF’s corresponding to the illuminating and the collecting arms of a CSM under symmetrical defocusing of the magnitude of W 20 D = 0.75.

Fig. 3
Fig. 3

Normalized axial IPSF corresponding to some symmetrically defocused CSM’s. The solid curve corresponds to the strictly confocal architecture.

Fig. 4
Fig. 4

Member of the family of axially superresolving pupil filters (∊ = 0.4): (a) ζ-space representation, (b) 1-D representation, and (c) actual 2-D representation.

Fig. 5
Fig. 5

Axial irradiance pattern corresponding to the filter shown in Fig. 4. As a result of the interference process a quite narrow central lobe is obtained. The solid curve corresponds to the axial response of a circular pupil.

Fig. 6
Fig. 6

Normalized axial IPSF corresponding to a suitably apodized, symmetrically defocused confocal device (light solid curve). The parameters of the setup are ∊ = 0.4 and W 20 D = 2/3. The bold solid curve plots the axial response corresponding to a strictly confocal nonapodized setup, whereas the dashed curve corresponds to the nonapodized but symmetrically defocused system (W 20 D = 1).

Fig. 7
Fig. 7

Irradiance images of two point sources separated by the normalized axial distances (a) d = 0.76 and (b) d = 0.54. The dashed curves correspond to the strictly confocal arrangement.

Fig. 8
Fig. 8

Integrated-irradiance function corresponding to the setups under study.

Fig. 9
Fig. 9

Axial-irradiance impulse response corresponding to the filter given by Eq. (13). Note that, as a result of the destructive interference between the waves proceeding from the inner and the outer parts of this filter, zero irradiance is achieved at the focus. In addition, the lateral lobes are quite strong and narrow.

Fig. 10
Fig. 10

Normalized axial IPSF corresponding to a confocal system under destructive-interference apodization and symmetrical defocusing of the magnitude of W 20 D = 4/3. With the solid curve we have also plotted the axial response corresponding to the strictly confocal, nonapodized setup.

Fig. 11
Fig. 11

Irradiance image of two point sources. The points are separated by d = 0.58. The 26% dip according to the Rayleigh criterion is obtained. Therefore 24% axial resolution is achieved [see Fig. 7(a)]. The dashed curve corresponds to the strictly confocal arrangement.

Fig. 12
Fig. 12

I(W 20) function for the same setups that were used for Fig. 10.

Equations (18)

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

I v = 0 ,   W 20 = | h 1 v = 0 ,   W 20 | 2 | h 2 v = 0 ,   W 20 | 2 ,
h 1 v = 0 ,   W 20 = 2   0 1   p 1 ρ exp i 2 π W 20 ρ 2 ρ d ρ
h 2 v = 0 ,   W 20 = 2   0 1   p 2 ρ exp ± i 2 π W 20 ρ 2 ρ d ρ
ζ = ρ 2 - 0.5 ,     q ζ = p ρ .
h 1 v = 0 ,   W 20 = - 0.5 0.5   q 1 ζ exp i 2 π W 20 ζ d ζ ,
h 2 v = 0 ,   W 20 = - 0.5 0.5   q 2 ζ exp ± i 2 π W 20 ζ d ζ .
I v = 0 ,   W 20 = sinc 2 W 20 sinc 2 W 20 = sinc 4 W 20 .
q 1 ζ = q 1 ζ exp i 2 π   W 20 D 2   ζ ,
q 2 ζ = q 2 ζ exp i 2 π   W 20 D 2   ζ .
I v = 0 ,   W 20 = | h 1 v = 0 ,   W 20 | 2 | h 2 v = 0 ,   W 20 | 2 = - 0.5 0.5   q 1 ζ exp i 2 π W 20 + W 20 D 2 ζ 2 × - 0.5 0.5   q 2 ζ exp ± i 2 π W 20 - W 20 D 2 ζ 2 = h 1 v = 0 ,   W 20 + W 20 D 2 2 × h 2 v = 0 ,   W 20 - W 20 D 2 2 .
I v = 0 ,   W 20 = sinc 2 W 20 + W 20 D 2 sinc 2 W 20 - W 20 D 2 .
q ζ = rect ζ + 1 2 1 - + rect ζ - 1 2 1 - ,     0 < < 0.5 .
I int W 20 = 0   I v ,   W 20 v d v .
I W 20 = - 0.5 0.5   q 1 ζ q 2 ζ exp i 2 π 2 W 20 ζ d ζ 2 .
I W 20 = - 0.5 0.5   q 1 ζ q 2 ζ exp i 2 π 2 W 20 ζ d ζ 2 = - 0.5 0.5   q ζ exp i 2 π 2 W 20 ζ d ζ 2 .
q ζ = 2 ζ .
| h v = 0 ,   W 20 | 2 = | j 1 π W 20 | 2 .
I W 20 = 1 3   j 0 2 π W 20 - 2 3   j 2 2 π W 20 2 .

Metrics