Abstract

A description is given of a confocal scanning microscope in which a two-mode optical fiber is used both to launch the light into the microscope and to detect the image signal. There is a discussion of the variety of imaging modes that result from variation of the combination of fiber modes used to launch and to detect the signal. The form of the three-dimensional transfer function is considered in all the cases, and the effect of the finite size of the fiber core is included.

© 1993 Optical Society of America

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References

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  1. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).
  2. T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).
  3. S. Kimura, T. Wilson, “Confocal scanning optical microscope using single mode fibre for signal detection,” Appl. Opt. 30, 2143–2150 (1991).
    [CrossRef] [PubMed]
  4. R. Juskaitis, F. Reinholz, T. Wilson, “Fibre-optic based confocal scanning microscopy with semiconductor laser excitation and detection,” Electron. Lett. 28, 986–987 (1992).
    [CrossRef]
  5. R. Juskaitis, T. Wilson, “Differential confocal scanning microscope with a two-mode optical fibre,” Appl. Opt. 31, 898–902 (1992).
    [CrossRef] [PubMed]
  6. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  7. B. R. Frieden, “Optical transfer of the three-dimensional object,”J. Opt. Soc. Am. 57, 56–66 (1967).
    [CrossRef]
  8. N. Striebl, “Fundamental restrictions for 3-D light distributions,” Optik (Stuttgart) 66, 341–354 (1984).
  9. N. Striebl, “Depth transfer by an imaging system,” Opt. Acta 31, 1233–1244 (1984).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).
  11. A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985).
  12. T. Wilson, F. Reinholz, “Confocal microscopy via reciprocal optical fibre detection,” Micron Microsc. Acta 23, 429–435 (1992).
    [CrossRef]
  13. R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. 92, 315–325 (1992).
    [CrossRef]
  14. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
    [CrossRef]
  15. M. Gu, X. Gan, C. J. R. Sheppard, “Three dimensional coherent transfer functions in fibre optic confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
    [CrossRef]
  16. C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. (Oxford) 165, 377–390 (1992).
    [CrossRef]
  17. R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. (to be published).

1992 (5)

T. Wilson, F. Reinholz, “Confocal microscopy via reciprocal optical fibre detection,” Micron Microsc. Acta 23, 429–435 (1992).
[CrossRef]

R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. 92, 315–325 (1992).
[CrossRef]

R. Juskaitis, F. Reinholz, T. Wilson, “Fibre-optic based confocal scanning microscopy with semiconductor laser excitation and detection,” Electron. Lett. 28, 986–987 (1992).
[CrossRef]

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. (Oxford) 165, 377–390 (1992).
[CrossRef]

R. Juskaitis, T. Wilson, “Differential confocal scanning microscope with a two-mode optical fibre,” Appl. Opt. 31, 898–902 (1992).
[CrossRef] [PubMed]

1991 (2)

1984 (2)

N. Striebl, “Fundamental restrictions for 3-D light distributions,” Optik (Stuttgart) 66, 341–354 (1984).

N. Striebl, “Depth transfer by an imaging system,” Opt. Acta 31, 1233–1244 (1984).
[CrossRef]

1967 (1)

1953 (1)

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Frieden, B. R.

Gan, X.

Gu, M.

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. (Oxford) 165, 377–390 (1992).
[CrossRef]

M. Gu, X. Gan, C. J. R. Sheppard, “Three dimensional coherent transfer functions in fibre optic confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[CrossRef]

Juskaitis, R.

R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. 92, 315–325 (1992).
[CrossRef]

R. Juskaitis, F. Reinholz, T. Wilson, “Fibre-optic based confocal scanning microscopy with semiconductor laser excitation and detection,” Electron. Lett. 28, 986–987 (1992).
[CrossRef]

R. Juskaitis, T. Wilson, “Differential confocal scanning microscope with a two-mode optical fibre,” Appl. Opt. 31, 898–902 (1992).
[CrossRef] [PubMed]

R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. (to be published).

Kimura, S.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Reinholz, F.

T. Wilson, F. Reinholz, “Confocal microscopy via reciprocal optical fibre detection,” Micron Microsc. Acta 23, 429–435 (1992).
[CrossRef]

R. Juskaitis, F. Reinholz, T. Wilson, “Fibre-optic based confocal scanning microscopy with semiconductor laser excitation and detection,” Electron. Lett. 28, 986–987 (1992).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. (Oxford) 165, 377–390 (1992).
[CrossRef]

M. Gu, X. Gan, C. J. R. Sheppard, “Three dimensional coherent transfer functions in fibre optic confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

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

Striebl, N.

N. Striebl, “Fundamental restrictions for 3-D light distributions,” Optik (Stuttgart) 66, 341–354 (1984).

N. Striebl, “Depth transfer by an imaging system,” Opt. Acta 31, 1233–1244 (1984).
[CrossRef]

Wilson, T.

R. Juskaitis, T. Wilson, “Differential confocal scanning microscope with a two-mode optical fibre,” Appl. Opt. 31, 898–902 (1992).
[CrossRef] [PubMed]

R. Juskaitis, F. Reinholz, T. Wilson, “Fibre-optic based confocal scanning microscopy with semiconductor laser excitation and detection,” Electron. Lett. 28, 986–987 (1992).
[CrossRef]

T. Wilson, F. Reinholz, “Confocal microscopy via reciprocal optical fibre detection,” Micron Microsc. Acta 23, 429–435 (1992).
[CrossRef]

R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. 92, 315–325 (1992).
[CrossRef]

S. Kimura, T. Wilson, “Confocal scanning optical microscope using single mode fibre for signal detection,” Appl. Opt. 30, 2143–2150 (1991).
[CrossRef] [PubMed]

R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. (to be published).

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

Yariv, A.

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985).

Appl. Opt. (2)

Electron. Lett. (1)

R. Juskaitis, F. Reinholz, T. Wilson, “Fibre-optic based confocal scanning microscopy with semiconductor laser excitation and detection,” Electron. Lett. 28, 986–987 (1992).
[CrossRef]

J. Microsc. (Oxford) (1)

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. (Oxford) 165, 377–390 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Micron Microsc. Acta (1)

T. Wilson, F. Reinholz, “Confocal microscopy via reciprocal optical fibre detection,” Micron Microsc. Acta 23, 429–435 (1992).
[CrossRef]

Opt. Acta (1)

N. Striebl, “Depth transfer by an imaging system,” Opt. Acta 31, 1233–1244 (1984).
[CrossRef]

Opt. Commun. (1)

R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. 92, 315–325 (1992).
[CrossRef]

Optik (Stuttgart) (1)

N. Striebl, “Fundamental restrictions for 3-D light distributions,” Optik (Stuttgart) 66, 341–354 (1984).

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

H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217, 408–432 (1953).
[CrossRef]

Other (6)

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

T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1975).

A. Yariv, Optical Electronics (Holt, Rinehart & Winston, New York, 1985).

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

R. Juskaitis, T. Wilson, “Imaging in reciprocal fibre-optic based confocal scanning microscopes,” Opt. Commun. (to be published).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of a confocal microscope that employs optical fibers both to launch light into the microscope and to detect the image signals. Although the launching and detecting fibers are shown here as being separate, some advantage may result if the same fiber is used in a reciprocal arrangement.

Fig. 2
Fig. 2

Region of integration required for calculation of the three-dimensional transfer function. If s2/4 ≤ r ≤ 1 − s(1 − s/2), then the integral must be performed around circles such as A. If 1 − s(1 − s/2) ≤ r ≤ 1, then circles such as B must be considered, and here the θ variable is restricted to certain values.

Fig. 3
Fig. 3

Transfer function for a reflection-mode confocal microscope shown (a) as an isometric plot and (b) as a contour plot. Note that the effect of the fiber is merely to multiply those curves by exp(−αr/2).

Fig. 4
Fig. 4

Depth discrimination property as measured by the variation in detected signal as a perfect reflector is scanned through focus for a variety of values of α. The solid curve corresponds to α = 0, the dashed curve corresponds to α = 5, and the dotted-dashed curves correspond to α = 15.

Fig. 5
Fig. 5

Contour plot of the function c1(m, 0, r). The dashed contours represent negative values.

Fig. 6
Fig. 6

Contour plots of the three-dimensional transfer functions (a) g(m, 0, r) and (b) g(0, n, r). Note that the dashed contours represent negative values. Again the effect of the fiber is merely to multiply these curves by exp(−αr/2).

Fig. 7
Fig. 7

Isometric plots of the transfer function c(0, n, r) for the cases (a) α = 0, (b) α = 5, and (c) α = 10.

Fig. 8
Fig. 8

Two-dimensional transfer functions in the m (dotted–dashed curve) and n (dashed curve) directions. The traditional confocal transfer function is shown as the solid curve.

Fig. 9
Fig. 9

Line-spread function of the true confocal microscope (dashed curve) is compared with the fiber system for α = 0 (solid curve) and α = 15 (dotted–dashed curve).

Fig. 10
Fig. 10

Depth discrimination property is measured by the variation in detected signal as a perfect reflector is scanned through focus. The dashed curve corresponds to the traditional confocal case, whereas the solid curve represents the fiber case with α = 0. The effects of finite values of α are shown as the dotted–dashed curve (α = 5) and the dotted–dotted–dashed curve (α = 15).

Fig. 11
Fig. 11

Differential axial responses when both modes are excited. The phase shift between the modes is zero (dashed curve) and π/2 (solid curve).

Fig. 12
Fig. 12

Effect of finite values of α on the differential axial response. (a) Corresponds to a zero phase shift between the modes, and (b) corresponds to a π/2 phase shift. In all the cases the curves were normalized such that the response in (a) was always unity. The solid curves correspond to α = 0, the dotted–dashed curve corresponds to α = 5, and the dashed curves correspond to α = 15. In (a) the α = 5 curve did not differ significantly from the α = 0 curve.

Equations (57)

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S = a 10 exp ( - j β 1 l ) e 1 + a 20 exp ( - j β 2 l ) e 2 ,
a 1 = ( h eff h 1 eff ) τ ,
h eff ~ h S ,             h 1 eff ~ h e 1 ,
a 2 = ( h eff h 2 eff ) τ ,
h 2 eff ~ h e 2 .
h ( u , t , w ) = - P ( ξ , η ) exp [ j u 2 ( ξ 2 + η 2 ) ] × exp [ - j ( t ξ + w η ) ] d ξ d η ,
u = ( 8 π / λ ) z sin 2 ( ϕ / 2 ) ,
( t , w ) = ( x , y ) ( 2 π / λ ) sin ϕ .
h eff ~ h S = a 10 h 1 exp ( - j β 1 l ) + a 20 h 1 t exp ( - j B 2 l ) ,
h 1 eff = h 1 ,
h 2 eff = h 1 t ,
h 1 = h ( u + j α / 2 , t , w ) .
α 1 = a 10 ( h 1 2 τ ) exp ( - j β 1 l ) + a 20 ( a h 1 t τ ) exp ( - j β 2 l )
a 2 = a 10 ( h 1 h 1 t τ ) exp ( - j β 1 l ) + a 20 [ ( h 1 t ) 2 τ ] exp ( - j β 2 l ) .
U = a 1 exp ( - j β 1 l ) e 1 + a 2 exp ( - j β 2 l ) e 2 .
I sum = a 1 2 + a 2 2
I diff = 2 Re [ a 1 a 2 * exp ( j δ ) ]
I = h 1 2 τ 2 ,
T ( m , n , r ) = - τ ( t , w , u ) × exp [ - j ( m t + n w + r u ) ] d t d w d u ,
I ( t s , w s , u s ) = | - c ( m , n , r ) T ( m , n , r ) × exp [ j ( m t s + n w s + r u s ) ] d m d n d r | 2 ,
c ( m , n , r ) = - h 1 2 ( t , w , u ) × exp [ - j ( m t + n w + r u ) ] d t d w d u ,
c 2 ( m , n , u ) = - h 1 2 ( t , w , u ) exp [ - j ( m t + n w ) ] d t d w ,
c ( m , n , r ) = - c 2 ( m , n , u ) exp ( - j r u ) d u .
c 2 ( m , n , u ) = - P 1 ( ξ 1 η ) P 1 [ - ( ξ + m ) - ( η + n ) ] d ξ d η ,
P 1 ( ξ , η ) = P ( ξ , η ) exp [ j 1 2 ( u + j α 2 ) ( ξ 2 + η 2 ) ]
c 2 ( m , n , u ) = S exp { j ( u + j α 2 ) [ ( ξ + m 2 ) 2 + ( η + n 2 ) 2 + m 2 + n 2 4 ] } d ξ d η ,
c 2 ( s , u ) = S exp [ j ( u + j α 2 ) ( ρ 2 + s 2 4 ) ] ρ d ρ d ϕ ,
c ( m , n , r ) = c ( s , r ) = exp ( - α r 2 ) S δ ( r - ρ 2 - s 2 4 ) d ρ d ϕ = exp ( - α r 2 ) f ( s , r ) ,
f ( s , r ) = { 1 s 2 / 4 r 1 - s ( 1 - s / 2 ) 2 γ / π 1 - s ( 1 - s / 2 ) r 1 0 otherwise ,
γ = sin - 1 [ 1 - r s ( r - s 2 / 4 ) 1 / 2 ] .
I ( u ) = | 0 1 c ( 0 , 0 , r ) exp ( j r u ) d r | 2 .
c ( 0 , 0 , r ) = exp ( - α r / 2 )             0 < r < 1 ,
I ( u ) = | sinc [ 1 2 ( u + j α 2 ) ] | 2 ,
I = | h 1 h 1 t τ | 2 ,
I ~ | h 1 2 t τ | 2 = | h 1 2 τ t | 2 = | t ( h 1 2 τ ) | 2 ,
c 1 ( m , n , r ) ~ ( j m / 2 ) c ( m , n , r ) ,
I ~ Re [ ( h 1 * 2 τ * ) ( h 1 h 1 t τ ) exp ( j δ ) ] .
I ( t s , w s , u s ) = - C ( m , n , r ; m , n , r ) T ( m , n , r ) × T * ( m , n , r ) exp { j [ ( m - m ) t s + ( n - n ) w s + ( r - r ) u s ] } d m d n d r d m d n d r .
C ( m , n , r ; m , n , r ) = j m c ( m , n , r ) c ( m , n , r ) ,
I ~ Re [ τ τ t exp ( j δ ) ] .
τ = a exp ( j ϕ ) ,
I ~ Re [ ( a 2 t - 2 j a 2 ϕ t ) exp ( j δ ) ] ;
I = | ( h 1 t ) 2 τ | 2 ,
c ( m , n , r ) = exp ( - α r / 2 ) g ( m , n , r ) ,
g ( m , 0 , r ) = { r - 3 m 2 / 4 m 2 / 4 r 1 - m ( 1 - m / 2 ) ( r / π ) [ 2 γ - sin ( 2 γ ) ] - ( m 2 / 4 π ) [ 6 γ - sin ( 2 γ ) ] 1 - m ( 1 - m / 2 ) r 1 ,
g ( 0 , n , r ) = { r - n 2 / 4 n 2 / 4 r 1 - n ( 1 - n / 2 ) ( 1 / π ) ( r - n 2 / 4 ) [ 2 γ + sin ( 2 γ ) ] 1 - n ( 1 - n / 2 ) r 1 ,
c ( m ; 0 ) = 2 π [ cos - 1 ( m 2 ) - m 6 ( 13 - 5 m 2 2 ) ( 1 - m 2 4 ) 1 / 2 ] ,
c ( n ; 0 ) = 2 π [ cos - 1 ( n 2 ) - n 6 ( 5 - n 2 2 ) ( 1 - n 2 4 ) 1 / 2 ] ,
c ( m ; 0 ) = 2 π [ cos - 1 ( m 2 ) - ( 1 - m 2 4 ) 1 / 2 ] .
I ( u ) = exp ( - α / 4 ) q 2 | exp ( j q 2 ) - sinc ( q 2 ) | 2 ,
C ( m , n , r ; m , n , r ) j m c ( m , n , r ) g ( m , n , r )
I ~ Re { ( h 1 * 2 τ * ) [ ( h 1 t ) 2 τ ] exp ( j δ ) } ,
c ( 0 , n , r , 0 , n , r ) = f ( n , r ) g ( 0 , n , r ) ,
I ( u ) ~ 2 Re { exp ( j δ ) - c ( 0 , 0 , r ; 0 , 0 , r ) × exp [ j ( r - r ) u ] d r d r } .
F ( u ) = - f ( 0 , r ) exp ( j r u ) d r = exp ( j u 2 ) V ( u ) ,
G ( u ) = 0 1 r exp ( - j r u ) d r = j F * u .
I ( u ) = Re [ ( V 2 + j V 2 u ) exp ( j δ ) ] .

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