Abstract

We describe three simple pupil function filters that, in conjunction with a confocal optical system, result in a transfer function that is constant for all spatial frequencies up to the cutoff. We confirm our predictions experimentally by considering a straight-edge object. Edge gradients up to 2.36 times as sharp as the unapodized confocal case are obtained.

© 1991 Optical Society of America

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References

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  1. M. Minsky, U.S. patent3,013,467 (December19, 1961).
  2. T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).
  3. M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, Opt. Acta 31, 923 (1984).
  4. S. J. Hewlett, S. M. Barnett, T. Wilson, J. Mod. Opt. 37, 2017 (1990).
  5. S. J. Hewlett, T. Wilson, “Confocal microscopy with square lenses,”Optik (to be published).
  6. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).

1990

S. J. Hewlett, S. M. Barnett, T. Wilson, J. Mod. Opt. 37, 2017 (1990).

1984

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, Opt. Acta 31, 923 (1984).

Barnett, S. M.

S. J. Hewlett, S. M. Barnett, T. Wilson, J. Mod. Opt. 37, 2017 (1990).

Bertero, M.

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, Opt. Acta 31, 923 (1984).

De Mol, C.

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, Opt. Acta 31, 923 (1984).

Hewlett, S. J.

S. J. Hewlett, S. M. Barnett, T. Wilson, J. Mod. Opt. 37, 2017 (1990).

S. J. Hewlett, T. Wilson, “Confocal microscopy with square lenses,”Optik (to be published).

Minsky, M.

M. Minsky, U.S. patent3,013,467 (December19, 1961).

Pike, E. R.

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, Opt. Acta 31, 923 (1984).

Walker, J. G.

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, Opt. Acta 31, 923 (1984).

Wilson, T.

S. J. Hewlett, S. M. Barnett, T. Wilson, J. Mod. Opt. 37, 2017 (1990).

S. J. Hewlett, T. Wilson, “Confocal microscopy with square lenses,”Optik (to be published).

J. Mod. Opt.

S. J. Hewlett, S. M. Barnett, T. Wilson, J. Mod. Opt. 37, 2017 (1990).

Opt. Acta

M. Bertero, C. De Mol, E. R. Pike, J. G. Walker, Opt. Acta 31, 923 (1984).

Other

S. J. Hewlett, T. Wilson, “Confocal microscopy with square lenses,”Optik (to be published).

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965).

M. Minsky, U.S. patent3,013,467 (December19, 1961).

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

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Figures (6)

Fig. 1
Fig. 1

Geometrical interpretation of the square-shaped pupil plane filters that modify the pupil functions of the imaging lenses.

Fig. 2
Fig. 2

Coherent transfer function in the case of two square lenses [curve (a)] and one square and one double-slit lens [curve (b)].

Fig. 3
Fig. 3

Theoretical edge responses. The solid curve represents the double-slit/square lens case, and the dashed curve represents the circular lens confocal case.

Fig. 4
Fig. 4

Experimental line scans across a cleaved edge of a GaAs semiconductor for (a) the double-slit/square lens case and (b) the circular lens confocal case.

Fig. 5
Fig. 5

Experimental line scan across a cleaved edge of a GaAs semiconductor for the double-point/circular lens case.

Fig. 6
Fig. 6

Comparison of the theoretical and experimental edge gradients obtained with various pupil function geometries. The values in parentheses indicate the result as a percentage of the theoretical gradient obtained in the traditional confocal system that employs two circular lenses.

Equations (10)

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I ( t ) = 1 4 | 1 2 π 0 c ( m ˜ , n ˜ = 0 ) sin ( m ˜ t ) m ˜ d m ˜ | 2 ,
c ( m ˜ , n ˜ ) = ( P 1 P 2 ) ( m ˜ , n ˜ ) ,
d I ( t ) d t | t = 0 = 1 π 0 c ( m ˜ , 0 ) d m ˜ ,
P 1 , 2 ( ξ , η ) = { 1 for | ξ | 1 / 2 and | η | 1 / 2 0 otherwise .
P 2 ( ξ , η ) = { δ ( ξ ± 1 / 2 ) for | η | 1 / 2 0 otherwise .
I ( t ) = 1 4 [ 1 2 π Si ( t 2 ) ] 2 ,
P 2 ( ξ , η ) = δ ( ξ ± 1 / 2 ) δ ( η ± 1 / 2 ) ,
c ( m ˜ , n ˜ ) = 1 for | m ˜ | 2 and | n ˜ | 2 .
P 2 ( ξ , η ) = δ ( ξ ± 1 ) δ ( n ) ,
c ( m ˜ , 0 ) = 1 for | m ˜ | 2 ,

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