Abstract

The resolution of a fluorescent confocal scanning optical microscope (CSOM) is superior to that of a conventional fluorescent optical microscope. To attain this superiority, the fluorescent CSOM uses a pinhole in front of the detector. Thus, the resolution of the CSOM is dependent on the pinhole radius. Three-dimensional optical transfer functions are calculated for the various radii to elucidate this dependence. The results show that a CSOM with a radius smaller than ~1 optical unit has a bandwidth comparable with that of an infinitely small radius.

© 1990 Optical Society of America

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References

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  1. C. J. R. Sheppard, A. Choudhury, “Image Formation in the Scanning Microscope,” Opt. Acta 24, 1051–1073 (1977).
    [CrossRef]
  2. T. Wilson, A. R. Carlini, “Size of the Detector in Confocal Imaging Systems,” Opt. Lett. 12, 227–229 (1987).
    [CrossRef] [PubMed]
  3. T. Wilson, A. R. Carlini, “Three-Dimensional Imaging in Confocal Imaging Systems with Finite Sized Detectors,” J. Microsc. 149, 51–66 (1988).
    [CrossRef]
  4. I. J. Cox, C. J. R. Sheppard, T. Wilson, “Super-Resolution by Confocal Fluorescent Microscopy,” Optik 60, 391–396 (1982).
  5. K. Carlsson, N. Åslund, “Confocal Imaging for 3-D Digital Microscopy,” Appl. Opt. 26, 3232–3238 (1987).
    [CrossRef] [PubMed]
  6. W. B. Amos, J. G. White, M. Fordham, “Use of Confocal Imaging in the Study of Biological Structures,” Appl. Opt. 26, 3239–3243 (1987).
    [CrossRef] [PubMed]
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    [PubMed]
  8. O. Nakamura, S. Kawata, S. Minami, “Three-Dimensional Imaging Characteristics of Confocal Laser-Scanning Microscope,” Oyo Butsuri 57, 784–791 (1988), in Japanese.
  9. C. J. R. Sheppard, “The Spatial Frequency Cut-Off in Three-Dimensional Imaging,” Optik 72, 131–133 (1986).
  10. C. J. R. Sheppard, “The Spatial Frequency Cut-Off in Three-Dimensional Imaging II,” Optik 74, 128–129 (1986).
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    [CrossRef]
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    [CrossRef]
  15. M. Y. Chiu, H. H. Barrett, R. G. Simpson, C. Chou, J. W. Arendt, G. R. Gindi, “Three-Dimensional Radiographic Imaging with a Restricted View Angle,” J. Opt. Soc. Am. 69, 1323–1333 (1979).
    [CrossRef]
  16. N. Streibl, “Fundamental Restrictions for 3-D Light Distributions,” Optik 66, 341–354 (1984).
  17. B. R. Frieden, “Optical Transfer of the Three-Dimensional Object,” J. Opt. Soc. Am. 57, 56–66 (1967).
    [CrossRef]

1989 (1)

1988 (3)

T. Wilson, A. R. Carlini, “Three-Dimensional Imaging in Confocal Imaging Systems with Finite Sized Detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

G. J. Brakenhoff, H. T. M. van der Voort, E. A. van Spronsen, N. Nanninga, “3-Dimensional Imaging of Biological Structures by High Resolution Confocal Scanning Laser Microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

O. Nakamura, S. Kawata, S. Minami, “Three-Dimensional Imaging Characteristics of Confocal Laser-Scanning Microscope,” Oyo Butsuri 57, 784–791 (1988), in Japanese.

1987 (3)

1986 (2)

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).

1984 (2)

I. J. Cox, “Scanning Optical Fluorescence Microscopy,” J. Microsc. 133, 149–154 (1984).
[CrossRef] [PubMed]

N. Streibl, “Fundamental Restrictions for 3-D Light Distributions,” Optik 66, 341–354 (1984).

1982 (1)

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Super-Resolution by Confocal Fluorescent Microscopy,” Optik 60, 391–396 (1982).

1979 (1)

1977 (1)

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

1969 (1)

1967 (1)

1955 (1)

H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Amos, W. B.

Arendt, J. W.

Åslund, N.

Barrett, H. H.

Brakenhoff, G. J.

G. J. Brakenhoff, H. T. M. van der Voort, E. A. van Spronsen, N. Nanninga, “3-Dimensional Imaging of Biological Structures by High Resolution Confocal Scanning Laser Microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

Carlini, A. R.

T. Wilson, A. R. Carlini, “Three-Dimensional Imaging in Confocal Imaging Systems with Finite Sized Detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

T. Wilson, A. R. Carlini, “Size of the Detector in Confocal Imaging Systems,” Opt. Lett. 12, 227–229 (1987).
[CrossRef] [PubMed]

Carlsson, K.

Chiu, M. Y.

Chou, C.

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, “Scanning Optical Fluorescence Microscopy,” J. Microsc. 133, 149–154 (1984).
[CrossRef] [PubMed]

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Super-Resolution by Confocal Fluorescent Microscopy,” Optik 60, 391–396 (1982).

Fordham, M.

Frieden, B. R.

Gindi, G. R.

Hopkins, H. H.

H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Kawata, S.

O. Nakamura, S. Kawata, S. Minami, “Three-Dimensional Imaging Characteristics of Confocal Laser-Scanning Microscope,” Oyo Butsuri 57, 784–791 (1988), in Japanese.

Kimura, S.

Minami, S.

O. Nakamura, S. Kawata, S. Minami, “Three-Dimensional Imaging Characteristics of Confocal Laser-Scanning Microscope,” Oyo Butsuri 57, 784–791 (1988), in Japanese.

Munakata, C.

Nakamura, O.

O. Nakamura, S. Kawata, S. Minami, “Three-Dimensional Imaging Characteristics of Confocal Laser-Scanning Microscope,” Oyo Butsuri 57, 784–791 (1988), in Japanese.

Nanninga, N.

G. J. Brakenhoff, H. T. M. van der Voort, E. A. van Spronsen, N. Nanninga, “3-Dimensional Imaging of Biological Structures by High Resolution Confocal Scanning Laser Microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

Sheppard, C. J. R.

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).

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Super-Resolution by Confocal Fluorescent Microscopy,” Optik 60, 391–396 (1982).

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

Simpson, R. G.

Stokseth, P. A.

Streibl, N.

N. Streibl, “Fundamental Restrictions for 3-D Light Distributions,” Optik 66, 341–354 (1984).

van der Voort, H. T. M.

G. J. Brakenhoff, H. T. M. van der Voort, E. A. van Spronsen, N. Nanninga, “3-Dimensional Imaging of Biological Structures by High Resolution Confocal Scanning Laser Microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

van Spronsen, E. A.

G. J. Brakenhoff, H. T. M. van der Voort, E. A. van Spronsen, N. Nanninga, “3-Dimensional Imaging of Biological Structures by High Resolution Confocal Scanning Laser Microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

White, J. G.

Wilson, T.

T. Wilson, A. R. Carlini, “Three-Dimensional Imaging in Confocal Imaging Systems with Finite Sized Detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

T. Wilson, A. R. Carlini, “Size of the Detector in Confocal Imaging Systems,” Opt. Lett. 12, 227–229 (1987).
[CrossRef] [PubMed]

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Super-Resolution by Confocal Fluorescent Microscopy,” Optik 60, 391–396 (1982).

Appl. Opt. (2)

J. Microsc. (2)

T. Wilson, A. R. Carlini, “Three-Dimensional Imaging in Confocal Imaging Systems with Finite Sized Detectors,” J. Microsc. 149, 51–66 (1988).
[CrossRef]

I. J. Cox, “Scanning Optical Fluorescence Microscopy,” J. Microsc. 133, 149–154 (1984).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

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 (4)

N. Streibl, “Fundamental Restrictions for 3-D Light Distributions,” Optik 66, 341–354 (1984).

I. J. Cox, C. J. R. Sheppard, T. Wilson, “Super-Resolution by Confocal Fluorescent Microscopy,” Optik 60, 391–396 (1982).

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).

Oyo Butsuri (1)

O. Nakamura, S. Kawata, S. Minami, “Three-Dimensional Imaging Characteristics of Confocal Laser-Scanning Microscope,” Oyo Butsuri 57, 784–791 (1988), in Japanese.

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Scanning Microsc. (1)

G. J. Brakenhoff, H. T. M. van der Voort, E. A. van Spronsen, N. Nanninga, “3-Dimensional Imaging of Biological Structures by High Resolution Confocal Scanning Laser Microscopy,” Scanning Microsc. 2, 33–40 (1988).
[PubMed]

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Figures (5)

Fig. 1
Fig. 1

Basic arrangement of a fluorescent CSOM.

Fig. 2
Fig. 2

Three-dimensional views of the normalized 3-D OTF for a fluorescent CSOM. The altitude represents the OTF value and vr denotes the pinhole radius.

Fig. 3
Fig. 3

Normalized 3-D OTFs on the w-axis for various pinhole radii.

Fig. 4
Fig. 4

Halfwidth at half-maximum (HWHM) of the 3-D OTF on the w-axis and variation of the normalized power through the pinhole as a function of the pinhole radius.

Fig. 5
Fig. 5

Normalized 3-D OTFs on the s-axis for the various pinhole radii.

Equations (19)

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v x = 2 π λ x sin α , v y = 2 π λ y sin α , u = 2 π λ z sin 2 α ,
I f ( v x , v y , u ; v x s , v y s , u s ) = h ( v x , v y , u ) 2 o ( v x - v x s , v y - v y s , u - u s ) ,
I ( v x D , v y D , u D ; v y s , u s ) = 1 ( 2 π ) 3 / 2 - h ( v x , v y , u ) 2 × h ( v x D - v x , v y D - v y , u D - u ) 2 × o ( v x - v x s , v y - v y s , u - u s ) d v x d v y d u .
D ( v x D , v y D ) = { 1 if v x D 2 + v y D 2 _ v r , 0 if v x D 2 + v y D 2 > v r ,
P ( v x s , v y s , u s ) = - I ( v x D , v y D , 0 ; v x s , v y s , u s ) × D ( v x D , v y D ) d v x D d v y D .
p c ( v x , v y , u ) = 1 2 π - h ( v x , v y , u ) 2 × h ( v x D - v x , v y D - v y - u ) 2 D ( v x D , v y D ) d v x D d v y D .
s = λ sin α f x , t = λ sin α f y , w = λ sin 2 α f z ,
Ω ( s , t , w ) = Ω 0 ( s , t , w ) Ω 0 ( 0 , 0 , 0 ) ,
Ω 0 ( s , t , w ) = 1 2 π - H ( s , t , u ) exp ( - i u w ) d u .
H ( s , t , u ) = 1 2 π - p c ( v x , v y , u ) exp [ - i ( v x s + v y t ) ] d v x d v y .
H ( s , t , u ) = { F 2 [ h ( v x , v y , u ) 2 ] F 2 [ D ( v x , v y ) ] } F 2 [ h ( v x , v y , u ) 2 ] ,
T ( s , t ; u ) = F 2 [ h ( v x , v y , u ) 2 ] .
T ( s , 0 ; u ) = { g 1 ( s ) { J 1 [ u g 2 ( s ) ] u g 2 ( s ) } , if 0 < s < 2 , 0 , if 2 _ s ,
g 1 ( s ) = 2 ( 1 - 0.69 s + 0.0076 s 2 + 0.043 s 3 ) , g 2 ( s ) = s - 0.5 s 2 ,
T ( s , t ; u ) = T ( s 2 + t 2 , O ; u ) .
F 2 [ D ( v x , v y ) ] = v r s 2 + t 2 J 1 ( v r s 2 + t 2 ) .
Ω ( s , 0 , 0 ) = 1 Ω 0 ( 0 , 0 , 0 ) - H ( s , 0 , u ) d u .
P ( v x s , v y s , 0 ) = C 1 H ( 0 , 0 , 0 ) ,
Ω 0 ( s , t , w ) = { F 3 [ | h ( v x β , v y β , u β ) | 2 ] F 3 [ D ( v x β , v y β ) δ ( u β ) ] } F 3 [ h ( v x , v y , u ) 2 ] ,

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