Abstract

For a confocal fluorescent microscope with a finite-sized circular detector, the three-dimensional optical transfer function (OTF) for a thick object has been developed without the use of Stockseth’s approximation. The results show that the OTF has negative values when the radius of the detector exceeds certain magnitudes. The two-dimensional OTF derived from the three-dimensional OTF is also given.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).
  2. C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik 74, 128–129 (1986).
  3. S. Kimura, C. Munakata, “Calculation of three-dimensional transfer function for a confocal scanning fluorescent microscope,” J. Opt. Soc. Am. A 6, 1015–1019 (1989).
    [CrossRef]
  4. S. Kimura, C. Munakata, “Three-dimensional optical transfer function for the fluorescent scanning optical microscope with a slit,” Appl. Opt. 29, 1004–1007 (1990).
    [CrossRef] [PubMed]
  5. S. Kimura, C. Munakata, “Dependence of 3-D optical transfer functions on the pinhole radius in a fluorescent confocal optical microscope,” Appl. Opt. 29, 3007–3011 (1990).
    [CrossRef] [PubMed]
  6. O. Nakamura, S. Kawata, “Three-dimensional transfer-function analysis of the tomographic capability of a confocal fluorescence microscope,” J. Opt. Soc. Am. A 7, 522–529 (1990).
    [CrossRef] [PubMed]
  7. S. Kawata, R. Arimoto, O. Nakamura, “Three-dimensional optical-transfer-function analysis for a laser-scan fluorescence microscope with an extended detector,” J. Opt. Soc. Am. A 8, 171–175 (1991).
    [CrossRef]
  8. P. A. Stockseth, “Properties of a defocused optical system,”J. Opt. Soc. Am. 59, 1314–1321 (1969).
    [CrossRef]
  9. C. J. R. Sheppard, M. Gu, “Approximation to the three-dimensional optical transfer function,” J. Opt. Soc. Am. A 8, 692–694 (1991).
    [CrossRef]
  10. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Microscopy (Academic, London, 1984).
  11. B. R. Frieden, “Optical transfer of the three-dimensional object,”J. Opt. Soc. Am. 57, 56–66 (1967).
    [CrossRef]
  12. X. Gan, M. Gu, C. J. R. Sheppard, “Fluorescent image formation in the fibre optical confocal scanning microscope,” J. Mod. Opt. (to be published).

1991

1990

1989

1986

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik 74, 128–129 (1986).

1969

1967

Arimoto, R.

Frieden, B. R.

Gan, X.

X. Gan, M. Gu, C. J. R. Sheppard, “Fluorescent image formation in the fibre optical confocal scanning microscope,” J. Mod. Opt. (to be published).

Gu, M.

C. J. R. Sheppard, M. Gu, “Approximation to the three-dimensional optical transfer function,” J. Opt. Soc. Am. A 8, 692–694 (1991).
[CrossRef]

X. Gan, M. Gu, C. J. R. Sheppard, “Fluorescent image formation in the fibre optical confocal scanning microscope,” J. Mod. Opt. (to be published).

Kawata, S.

Kimura, S.

Munakata, C.

Nakamura, O.

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, “Approximation to the three-dimensional optical transfer function,” J. Opt. Soc. Am. A 8, 692–694 (1991).
[CrossRef]

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik 74, 128–129 (1986).

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

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

X. Gan, M. Gu, C. J. R. Sheppard, “Fluorescent image formation in the fibre optical confocal scanning microscope,” J. Mod. Opt. (to be published).

Stockseth, P. A.

Wilson, T.

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

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Optik

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik 74, 128–129 (1986).

Other

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

X. Gan, M. Gu, C. J. R. Sheppard, “Fluorescent image formation in the fibre optical confocal scanning microscope,” J. Mod. Opt. (to be published).

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 (4)

Fig. 1
Fig. 1

Comparison of the axial variation of the normalized 3-D OTF at l = 0 given by Eq. (6) (solid curve) with that given by Kimura and Munakata5 (dotted–dashed curve).

Fig. 2
Fig. 2

Normalized 3-D OTF for different radii vd of the detector: (a) transverse variation C(l) at s = 0, (b) axial variation C(s) at l = 0.

Fig. 3
Fig. 3

Unnormalized 3-D OTF for different radii vd of the detector: (a) transverse variation C(l) at s = 0, (b) axial variation C(s) at l = 0.

Fig. 4
Fig. 4

Normalized in-focus (2-D) OTF for different radii of the detector. The dashed curve represents the 2-D OTF when vd → ∞.

Equations (9)

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

h e ( v , u ) = h ( v , u ) 2 [ h ( v , u ) 2 2 D ( v ) ] ,
C ( l , s ) = F 3 { h ( v , u ) 2 [ h ( v , u ) 2 2 D ( v ) ] } ,
C ( l , s ) = F 3 [ h ( v , u ) 2 ] 3 { F 3 [ h ( v , u ) 2 ] F 2 [ D ( v ) ] } ,
F 3 [ h ( v , u ) 2 ] = 1 l Re { [ 1 - ( s l + l 2 ) 2 ] 1 / 2 } ,
F 2 [ D ( v ) ] = v d [ J 1 ( l v d ) / l ] ,
C ( l , s ) = v d v 1 l 1 2 Re { [ l 1 2 - ( | s - s 2 | + l 1 2 2 ) 2 ] 1 / 2 } 1 l 2 2 × Re { [ l 2 2 - ( | s + s 2 | + l 2 2 2 ) 2 ] 1 / 2 } J 1 ( l 2 v d ) l 2 d m d n d s ,
l 1 = [ ( m - l / 2 ) 2 + n 2 ] 1 / 2 ,
l 2 = [ ( m + l / 2 ) 2 + n 2 ] 1 / 2 ,
C 2 ( l ) = - 1 1 C ( l , s ) d s .

Metrics