Abstract

The images of strong phase edges are calculated for conventional and confocal microscopes operating in the bright-field, dark-field, Zernike, and interference contrast modes by a method which has considerable computational advantages. It is found that in general the confocal images are superior possessing higher contrast than the conventional ones, and the equivalence with the direct view microscope is discussed.

© 1981 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. H. Hopkins, Proc. Phys. Soc. 66, 331 (1953).
    [CrossRef]
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975).
  3. M. E. Barnett, J. Microsc. Oxford 102, 1 (1974).
    [CrossRef]
  4. W. T. Welford, J. Microsc. Oxford 96, 105 (1972).
    [CrossRef]
  5. T. Wilson, Appl. Phys. 22, 119 (1980).
    [CrossRef]
  6. C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
    [CrossRef]
  7. C. J. R. Sheppard, T. Wilson, Optik 55, 331 (1979).
  8. C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
    [CrossRef]
  9. T. Wilson, J. N. Gannaway, Optik, 54, 201 (1979).
  10. M. Abromowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972).
  11. H. Wolter, Ann. Phys. 6, 33 (1950).
    [CrossRef]
  12. T. Wilson, C. J. R. Sheppard, Optik, in press (1981).
  13. K. G. Birch, Opt. Acta 15, 113 (1968).
  14. See, e.g., J. James, Light Microscopic Techniques in Biology and Medicine (Martinas Nijhoff Medical Division, Amsterdam, 1976).
    [CrossRef]
  15. C. J. R. Sheppard, T. Wilson, Philos. Trans. R. Soc. London 295, 513 (1980).
    [CrossRef]
  16. T. Wilson, C. J. R. Sheppard, J. Opt. Soc. Am. 69, 1443 (1979).
  17. M. D. Egger, M. Petrán, Science 157, 305 (1967).
    [CrossRef] [PubMed]
  18. C. J. R. Sheppard, T. Wilson, J. Microsc. Oxford (1981) in press.

1980 (2)

T. Wilson, Appl. Phys. 22, 119 (1980).
[CrossRef]

C. J. R. Sheppard, T. Wilson, Philos. Trans. R. Soc. London 295, 513 (1980).
[CrossRef]

1979 (3)

T. Wilson, C. J. R. Sheppard, J. Opt. Soc. Am. 69, 1443 (1979).

C. J. R. Sheppard, T. Wilson, Optik 55, 331 (1979).

T. Wilson, J. N. Gannaway, Optik, 54, 201 (1979).

1978 (1)

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

1977 (1)

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

1974 (1)

M. E. Barnett, J. Microsc. Oxford 102, 1 (1974).
[CrossRef]

1972 (1)

W. T. Welford, J. Microsc. Oxford 96, 105 (1972).
[CrossRef]

1968 (1)

K. G. Birch, Opt. Acta 15, 113 (1968).

1967 (1)

M. D. Egger, M. Petrán, Science 157, 305 (1967).
[CrossRef] [PubMed]

1953 (1)

H. H. Hopkins, Proc. Phys. Soc. 66, 331 (1953).
[CrossRef]

1950 (1)

H. Wolter, Ann. Phys. 6, 33 (1950).
[CrossRef]

Barnett, M. E.

M. E. Barnett, J. Microsc. Oxford 102, 1 (1974).
[CrossRef]

Birch, K. G.

K. G. Birch, Opt. Acta 15, 113 (1968).

Born, M.

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

Choudhury, A.

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

Egger, M. D.

M. D. Egger, M. Petrán, Science 157, 305 (1967).
[CrossRef] [PubMed]

Gannaway, J. N.

T. Wilson, J. N. Gannaway, Optik, 54, 201 (1979).

Hopkins, H. H.

H. H. Hopkins, Proc. Phys. Soc. 66, 331 (1953).
[CrossRef]

James, J.

See, e.g., J. James, Light Microscopic Techniques in Biology and Medicine (Martinas Nijhoff Medical Division, Amsterdam, 1976).
[CrossRef]

Petrán, M.

M. D. Egger, M. Petrán, Science 157, 305 (1967).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard, T. Wilson, Philos. Trans. R. Soc. London 295, 513 (1980).
[CrossRef]

C. J. R. Sheppard, T. Wilson, Optik 55, 331 (1979).

T. Wilson, C. J. R. Sheppard, J. Opt. Soc. Am. 69, 1443 (1979).

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

T. Wilson, C. J. R. Sheppard, Optik, in press (1981).

C. J. R. Sheppard, T. Wilson, J. Microsc. Oxford (1981) in press.

Welford, W. T.

W. T. Welford, J. Microsc. Oxford 96, 105 (1972).
[CrossRef]

Wilson, T.

T. Wilson, Appl. Phys. 22, 119 (1980).
[CrossRef]

C. J. R. Sheppard, T. Wilson, Philos. Trans. R. Soc. London 295, 513 (1980).
[CrossRef]

T. Wilson, C. J. R. Sheppard, J. Opt. Soc. Am. 69, 1443 (1979).

C. J. R. Sheppard, T. Wilson, Optik 55, 331 (1979).

T. Wilson, J. N. Gannaway, Optik, 54, 201 (1979).

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

T. Wilson, C. J. R. Sheppard, Optik, in press (1981).

C. J. R. Sheppard, T. Wilson, J. Microsc. Oxford (1981) in press.

Wolf, E.

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

Wolter, H.

H. Wolter, Ann. Phys. 6, 33 (1950).
[CrossRef]

Ann. Phys. (1)

H. Wolter, Ann. Phys. 6, 33 (1950).
[CrossRef]

Appl. Phys. (1)

T. Wilson, Appl. Phys. 22, 119 (1980).
[CrossRef]

J. Microsc. Oxford (2)

M. E. Barnett, J. Microsc. Oxford 102, 1 (1974).
[CrossRef]

W. T. Welford, J. Microsc. Oxford 96, 105 (1972).
[CrossRef]

J. Opt. Soc. Am. (1)

T. Wilson, C. J. R. Sheppard, J. Opt. Soc. Am. 69, 1443 (1979).

Opt. Acta (3)

K. G. Birch, Opt. Acta 15, 113 (1968).

C. J. R. Sheppard, A. Choudhury, Opt. Acta 24, 1051 (1977).
[CrossRef]

C. J. R. Sheppard, T. Wilson, Opt. Acta 25, 315 (1978).
[CrossRef]

Optik (2)

T. Wilson, J. N. Gannaway, Optik, 54, 201 (1979).

C. J. R. Sheppard, T. Wilson, Optik 55, 331 (1979).

Philos. Trans. R. Soc. London (1)

C. J. R. Sheppard, T. Wilson, Philos. Trans. R. Soc. London 295, 513 (1980).
[CrossRef]

Proc. Phys. Soc. (1)

H. H. Hopkins, Proc. Phys. Soc. 66, 331 (1953).
[CrossRef]

Science (1)

M. D. Egger, M. Petrán, Science 157, 305 (1967).
[CrossRef] [PubMed]

Other (5)

C. J. R. Sheppard, T. Wilson, J. Microsc. Oxford (1981) in press.

See, e.g., J. James, Light Microscopic Techniques in Biology and Medicine (Martinas Nijhoff Medical Division, Amsterdam, 1976).
[CrossRef]

T. Wilson, C. J. R. Sheppard, Optik, in press (1981).

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

M. Abromowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972).

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

(a) Type I scanning microscope (equivalent to the conventional microscope); (b) confocal scanning microscope.

Fig. 2
Fig. 2

C(m;p) function for a type 1 scanning (or conventional) microscope.

Fig. 3
Fig. 3

Area of summation for type 1 microscopes.

Fig. 4
Fig. 4

Intensity in the image of a phase edge in a type 1 (or conventional) bright-field microscope as a function of normalized distance from the geometrical edge location.

Fig. 5
Fig. 5

Intensity in the image of a phase edge in a confocal bright-field microscope as a function of normalized distance from the geometrical edge location.

Fig. 6
Fig. 6

Intensity in the image of a phase edge in a type 1 (or conventional) dark-field microscope as a function of normalized distance from the geometrical edge location.

Fig. 7
Fig. 7

Intensity in the image of a phase edge in a confocal bright-field microscope as a function of normalized distance from the geometrical edge location.

Fig. 8
Fig. 8

C(m;p) function for the type 1 scanning (or conventional) Zernike phase contrast microscope.

Fig. 9
Fig. 9

Intensity in the image of a phase edge in a type 1 (or conventional) Zernike microscope as a function of normalized distance from the geometrical edge location.

Fig. 10
Fig. 10

Intensity in the image of a phase edge in a confocal Zernike microscope as a function of normalized distance from the geometrical edge location.

Fig. 11
Fig. 11

Scanning interference microscope.

Fig. 12
Fig. 12

Intensity in the image of a phase step from 0 to π/3 in an interference microscope as a function of normalized distance from the geometrical edge location.

Equations (24)

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

T ( m ) = - + t ( x ) exp - 2 π j m x d x ,
I ( x ) = - + C ( m ; p ) T ( m ) T * ( p ) exp 2 π j ( m - p ) x d m d p ,
C ( m ; p ) = - + P 2 ( ξ , η ) 2 P 1 ( ξ - λ d m , η ) P 1 * ( ξ - λ d p , η ) d ξ d η ,
C ( m ; p ) = c ( m ) c * ( p ) ,
c ( m ) = [ P 1 ( λ d m ) P 2 ( λ d m ) ] ,
t ( x ) = exp j ϕ 1 [ ( 1 + exp j Δ ϕ 2 ) - 2 π ( 1 - exp j Δ ϕ ) n = 1 ( - ) n 2 n - 1 cos ( 2 n - 1 ) θ ] ,
I ( x ) = 1 + cos Δ ϕ 2 C ( 0 ; 0 ) - 4 sin Δ ϕ π n = 1 ( - ) n 2 n - 1 Im { C [ ( 2 n - 1 ) α ; 0 ] } cos ( 2 n - 1 ) θ + 4 π 2 ( 1 - cos Δ ϕ ) n = 1 r = 1 ( - ) r + n ( 2 n - 1 ) ( 2 r - 1 ) { C [ ( 2 n - 1 ) α ; ( 2 r - 1 ) θ ] ) cos [ ( 2 n - 1 ) θ - ( 2 r - 1 ) θ ] + C [ ( 2 n - 1 ) α ; - ( 2 r - 1 ) α ] cos [ ( 2 n - 1 ) θ + ( 2 r - 1 ) θ ] } ,
C ( m ; p ) = C ( - m ; - p ) C ( m ; p ) = C * ( p ; m ) } .
I ( x ) = | ( 1 + exp j Δ ϕ 2 ) c ( 0 ) - 2 π ( 1 - exp j Δ ϕ ) × n = 1 ( - ) n ( 2 n - 1 ) c [ ( 2 n - 1 ) α ] cos ( 2 n - 1 ) θ | 2 .
c ( ξ ) = 2 π [ cos - 1 ξ - ξ ( 1 - ξ 2 ) 1 / 2 ] ; ξ < 1 = 0 ξ > 1 } .
I ( x ) = 1 + cos Δ ϕ 2 C ( 0 ; 0 ) - 4 sin Δ ϕ π Im { S 1 } + 4 π 2 ( 1 - cos Δ ϕ ) [ S 2 + S 3 + 2 ( S 4 + S 5 ) ] ,
S 1 = n = 1 ( - ) n ( 2 n - 1 ) c [ ( 2 n - 1 ) α ] cos ( 2 n - 1 ) θ S 2 = n = 1 c [ ( 2 n - 1 ) α ] ( 2 n - 1 ) 2 S 3 = n = 1 c [ 2 ( 2 n - 1 ) α ] ( 2 n - 1 ) 2 cos 2 ( 2 n - 1 ) θ S 4 = n = 1 r = n + 1 ( - ) r + n c [ ( 2 r - 1 ) α ] ( 2 r - 1 ) ( 2 n - 1 ) cos [ ( 2 n - 1 ) θ - ( 2 r - 1 ) θ ] S 5 = n = 1 r = n + 1 ( - ) r + n c [ ( 2 n - 1 ) α + ( 2 r - 1 ) α ] ( 2 r - 1 ) ( 2 n - 1 ) × cos [ ( 2 n - 1 ) θ + ( 2 r - 1 ) θ ] } .
I ( x ) = | ( 1 + exp j Δ ϕ 2 ) c ( 0 ) - [ 2 ( 1 - exp j Δ ϕ ) π ] S 1 | .
v = k x ( N . A . ) ,
I ( x ) = | - + c ( m ) T ( m ) exp 2 π j m x d m | 2 ,
I ( v ) = U 2 sin 2 ( Δ ϕ 2 ) + 1 ,
U = 2 π [ H 1 ( 2 v ) 2 v + 2 v + H 0 ( z ) z d z ] - 2 ,
I ( 0 ) = cos 2 ( Δ ϕ 2 ) ,
c ( ξ ) = 2 π cos - 1 ξ ; = 0 ] ξ < 1 , ξ > 1.
I ( v ) = U D 2 sin 2 Δ ϕ 2 ,
U D = 2 π ( 2 v H 0 ( z ) z d z ) - 1 ,
c ( ξ ) = j ξ = 0 c ( ξ ) = 2 π cos - 1 ξ ξ < 1 , = 0 ξ >
I ( v ) = [ cos ( Δ ϕ 2 ) + U D sin ( Δ ϕ 2 ) ] 2 ,
I ± ( x ) = - C ( m ; p ) T ( m ) T * ( p ) exp 2 π j ( m - p ) x d m d p + w 2 ± 2 Re w * - C ( m ; 0 ) T ( m ) exp 2 π j m x d m ,

Metrics