Abstract

Scanning confocal microscopy is well established and applied frequently in biomedical science and more recently in engineering disciplines. For technical applications a confocal principle based on microlens arrays was developed. The principle permits a high depth resolution on a large field. A theoretical analysis of this principle together with some experimental results are presented.

© 1996 Optical Society of America

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References

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  1. T. Wilson, “Optical aspects of confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, London, 1990), pp. 93–139.
  2. H. Stark, “Theory and measurement of the optical Fourier transform,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982), pp. 2–40.
  3. J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 5, p. 88.
  4. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), Chap. 5, p. 171.
  5. T.R. Corle, C.-H. Chou, G. S. Kino, “Depth response of confocal optical microscopes,” Opt. Lett. 11, 770–772 (1986).
    [CrossRef] [PubMed]
  6. T. Wilson, C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).
  8. T. Wilson, “Depth response of scanning microscopes,” Optik 81, 113–118 (1989).
  9. T. Wilson, A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12, 227–229 (1987).
    [CrossRef] [PubMed]
  10. H.J. Tiziani, H. M. Uhde, “Three-dimensional analysis by a microlens-array confocal arrangement,” Appl. Opt. 33, 567–572 (1994).
    [CrossRef] [PubMed]

1994 (1)

1989 (1)

T. Wilson, “Depth response of scanning microscopes,” Optik 81, 113–118 (1989).

1987 (1)

1986 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Carlini, A. R.

Chou, C.-H.

Corle, T.R.

Goodman, J.W.

J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 5, p. 88.

Kino, G. S.

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), Chap. 5, p. 171.

Sheppard, C.

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

Stark, H.

H. Stark, “Theory and measurement of the optical Fourier transform,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982), pp. 2–40.

Tiziani, H.J.

Uhde, H. M.

Wilson, T.

T. Wilson, “Depth response of scanning microscopes,” Optik 81, 113–118 (1989).

T. Wilson, A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12, 227–229 (1987).
[CrossRef] [PubMed]

T. Wilson, “Optical aspects of confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, London, 1990), pp. 93–139.

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Appl. Opt. (1)

Opt. Lett. (2)

Optik (1)

T. Wilson, “Depth response of scanning microscopes,” Optik 81, 113–118 (1989).

Other (6)

T. Wilson, “Optical aspects of confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, London, 1990), pp. 93–139.

H. Stark, “Theory and measurement of the optical Fourier transform,” in Applications of Optical Fourier Transforms, H. Stark, ed. (Academic, Orlando, Fla., 1982), pp. 2–40.

J.W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 5, p. 88.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), Chap. 5, p. 171.

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

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

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Figures (5)

Fig. 1
Fig. 1

Unfolded sketch of the light path.

Fig. 2
Fig. 2

Arrangement for confocal three-dimensional analysis with a microlens array.

Fig. 3
Fig. 3

Axial response I(z).

Fig. 4
Fig. 4

Topography of a one-cent coin: Field size, 11 mm × 11 mm.

Fig. 5
Fig. 5

Topography of a reflection hologram: field size, 15 mm × 15 mm.

Equations (27)

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a F ( x F , y F ) = 1 i λ f L exp [ i π λ f L ( 1 d f L ) ( x F 2 + y F 2 ) ] × A M ( x M , y M ) × exp [ i 2 π λ f L ( x M x F + y M y F ) ] d x M d y M ,
a F ( x F , y F ) = C ( x F , y F ) FT [ A M ( x M , y M ) ] ,
C ( x F , y F ) = 1 i λ f L exp [ i π λ f L ( 1 d f L ) ( x F 2 + y F 2 ) ]
f x = x F λ f L , f y = y F λ f L ,
| x F | < f L d D L 2 no attenuation of the spectrum , f L d D L 2 < | x F | < f L d D + L 2 partial attenuation of the spectrum , | x F | > f L d D + L 2 total attenuation of the spectrum .
P ( x M , y M ) = circ ( r M h ) exp [ i 2 π λ W ( x M , y M ) ] ,
circ ( r M h ) = { 1 : r M h 0 : r M > h .
P ( x M , y M ) = circ ( r M h ) exp ( i 2 π λ W 0 20 r M 2 ) ,
W 0 20 = h 2 2 f M 2 Δ z ,
exp ( i 2 π λ W 0 20 r M 2 ) .
A 1 ( x M , y M ) = exp ( i 2 π λ 2 0 W 20 r M 2 ) .
A 1 ( x M , y M ) = exp [ i 2 π λ ( 2 0 W 20 r M 2 + 2 0 W 40 r M 4 ) ] ,
A M ( x M , y M ) = rect ( x M L ) × rect ( y M L ) × [ comb ( x M l ) × comb ( y M l ) ] [ rect ( x M 2 h ) × rect ( y M 2 h ) × A 1 ( x M , y M ) ] ,
rect ( x L ) = { 1 : | x | L / 2 0 : | x | > L / 2 , comb ( x l ) = m = δ ( x m l ) ,
a F ( x F , y F ) FT [ circ ( r M h ) exp ( i 2 π λ r M 2 h 2 2 0 W 20 ) ]
W 0 20 = h 2 2 f M 2 Δ z
a F ( x F , y F ) FT [ circ ( r M h ) exp ( 2 i π λ f M 2 Δ z r M 2 ) ] .
a ( w F ) = 0 r M f ( r M ) J 0 ( w F r M ) d r M = H ̂ [ f ( r M ) ] ,
ρ M = r M h , h d ρ M = d r M ,
a F ( w F ) = h 2 0 1 exp ( 2 i π λ h 2 f M 2 Δ z ρ M 2 ) J 0 ( h w F ρ M ) ρ M d ρ M ,
a F ( ω F h ) = h 2 0 1 exp ( 2 i π λ h 2 f M 2 Δ z ρ M 2 ) J 0 ( ω F ρ M ) ρ M d ρ M ,
H ̂ [ circ ( r ) exp ( i u r 2 ) ] = [ U 1 ( 2 u , ω ) + i U 2 ( 2 u , ω ) ] exp ( i u ) 2 u
u = 2 π λ h 2 f m 2 Δ z . U 1 ( 2 u , ω ) = 2 u 0 1 r cos [ u ( 1 r 2 ) ] J 0 ( ω r ) d r , U 2 ( 2 u , ω ) = 2 u 0 1 r sin [ u ( 1 r 2 ) ] J 0 ( ω r ) d r
I ( u , 0 ) 4 u 2 = sin 2 u + ( cos u 1 ) 2 = 2 ( 1 cos u ) .
I ( u , 0 ) = ( sin u 2 u 2 ) 2
FWHM = 0.443 λ / ( 1 cos α ) .
2.44 λ f L / l < d pinhole < 5 / π λ f L / l .

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