Abstract

The scalar theory of image formation for a strongly spherical object in reflection confocal optical microscopy is considered. The image contrast is derived from the far-field scattering amplitude. Experimentally obtained images of the sphere are seen to be in good agreement with the theoretical prediction.

© 1996 Optical Society of America

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References

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  1. N. Streibl, J. Opt. Soc. Am. A 2, 121 (1985).
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  2. N. Petford, J. A. Miller, A. H. Rankin, J. Microsc. 178, 37 (1995).
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    [CrossRef]
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  8. L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon, Oxford, 1959), Chap. 17.
  9. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995) p. 114.
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  11. P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck, Optik 98, 45 (1994).

1995

N. Petford, J. A. Miller, A. H. Rankin, J. Microsc. 178, 37 (1995).
[CrossRef]

1994

1993

C. J. R. Sheppard, T. J. Connoly, M. Gu, J. Mod. Opt. 40, 2407 (1993).
[CrossRef]

1985

N. Streibl, J. Opt. Soc. Am. A 2, 121 (1985).
[CrossRef]

M. G. Somekh, H. L. Bertoni, G. A. Briggs, N. J. Burton, Proc. R. Soc. London Ser. A 401, 29 (1985).
[CrossRef]

1982

D. K. Hamilton, T. Wilson, Appl. Phys. B 27, 211 (1982).
[CrossRef]

Bertoni, H. L.

M. G. Somekh, H. L. Bertoni, G. A. Briggs, N. J. Burton, Proc. R. Soc. London Ser. A 401, 29 (1985).
[CrossRef]

Boseck, S.

P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck, Optik 98, 45 (1994).

Briggs, G. A.

M. G. Somekh, H. L. Bertoni, G. A. Briggs, N. J. Burton, Proc. R. Soc. London Ser. A 401, 29 (1985).
[CrossRef]

Burton, N. J.

M. G. Somekh, H. L. Bertoni, G. A. Briggs, N. J. Burton, Proc. R. Soc. London Ser. A 401, 29 (1985).
[CrossRef]

Conchello, J.-A.

Connoly, T. J.

C. J. R. Sheppard, T. J. Connoly, M. Gu, J. Mod. Opt. 40, 2407 (1993).
[CrossRef]

Gu, M.

C. J. R. Sheppard, T. J. Connoly, M. Gu, J. Mod. Opt. 40, 2407 (1993).
[CrossRef]

Hamilton, D. K.

D. K. Hamilton, T. Wilson, Appl. Phys. B 27, 211 (1982).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1995).

Knüttel, A.

Kolosov, O.

P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck, Optik 98, 45 (1994).

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon, Oxford, 1959), Chap. 17.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon, Oxford, 1959), Chap. 17.

Lobkis, O.

P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck, Optik 98, 45 (1994).

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995) p. 114.

McNally, J. G.

Miller, J. A.

N. Petford, J. A. Miller, A. H. Rankin, J. Microsc. 178, 37 (1995).
[CrossRef]

Petford, N.

N. Petford, J. A. Miller, A. H. Rankin, J. Microsc. 178, 37 (1995).
[CrossRef]

Preza, C.

Rankin, A. H.

N. Petford, J. A. Miller, A. H. Rankin, J. Microsc. 178, 37 (1995).
[CrossRef]

Schmitt, J. M.

Sheppard, C. J. R.

C. J. R. Sheppard, T. J. Connoly, M. Gu, J. Mod. Opt. 40, 2407 (1993).
[CrossRef]

Somekh, M. G.

M. G. Somekh, H. L. Bertoni, G. A. Briggs, N. J. Burton, Proc. R. Soc. London Ser. A 401, 29 (1985).
[CrossRef]

Streibl, N.

Thomas, L. J.

Weise, W.

P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck, Optik 98, 45 (1994).

Wilson, T.

D. K. Hamilton, T. Wilson, Appl. Phys. B 27, 211 (1982).
[CrossRef]

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995) p. 114.

Yaslowsky, M.

Zinin, P.

P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck, Optik 98, 45 (1994).

Appl. Phys. B

D. K. Hamilton, T. Wilson, Appl. Phys. B 27, 211 (1982).
[CrossRef]

J. Microsc.

N. Petford, J. A. Miller, A. H. Rankin, J. Microsc. 178, 37 (1995).
[CrossRef]

J. Mod. Opt.

C. J. R. Sheppard, T. J. Connoly, M. Gu, J. Mod. Opt. 40, 2407 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Optik

P. Zinin, W. Weise, O. Lobkis, O. Kolosov, S. Boseck, Optik 98, 45 (1994).

Proc. R. Soc. London Ser. A

M. G. Somekh, H. L. Bertoni, G. A. Briggs, N. J. Burton, Proc. R. Soc. London Ser. A 401, 29 (1985).
[CrossRef]

Other

L. D. Landau, E. M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon, Oxford, 1959), Chap. 17.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995) p. 114.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1995).

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Figures (2)

Fig. 1
Fig. 1

Calculated vertical (left) and lateral (right) scans through a perfectly reflecting sphere.

Fig. 2
Fig. 2

Experimental vertical (left) and lateral (right) scans through a glass sphere.

Equations (10)

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U ( X , Y , Z ) = - - P 2 ( k x , k y ) P 1 ( k x , k y ) × S ( k x , k y , k x k y ) exp { i [ X ( k x i - k x ) + Y ( k y - k y ) ] } × exp [ i Z ( k z - k z ) ] d k x d k y d k x d k y ,
Ψ S ( k k r ) = f ( k k , k k ) exp ( i k r ) r             as  k r .
Ψ S ( k k r ) = - 2 π i k z S ( k x , k y , k x , k y ) exp ( i k r ) r             as  k r .
S ( k x , k y , k x , k y ) = i 2 π k z f ( k k , k k ) .
U ( X , Y , Z ) = - - P ( - k x , - k y ) P ( k x , k y ) × exp { i [ X ( k x - k x ) + Y ( k y - k y ) ] } × exp [ i Z ( k z - k z ) ] f ( k k , k k ) d k x d k y d k x d k y .
f ( k k , k k ) = 1 i k n = 0 ( 2 n + 1 ) A n P n ( cos γ k ) ,
P n ( cos γ k ) = 4 π 2 n + 1 m = - n n Y n , m * ( k k ) Y n , m ( k k ) .
J m ( k R sin θ k ) = ( ± i ) - m 2 π × 0 2 π exp [ ± i ( k R sin θ k cos ϕ k + m ϕ k ) ] d ϕ k ,
U ( R , Z ) = n = 0 m = - n n ( - 1 ) n A n I n m 2 ( R , Z ) ,
I n m ( R , Z ) = ( - i ) m 0 α P ( θ ) exp ( i k Z cos θ ) J m ( k R sin θ ) × P n m ¯ ( cos θ ) sin θ d θ ,

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