Abstract

The on-axis intensity response of a confocal scanning optical microscope was measured for an objective of numerical aperture 0.9. The data compare favorably with theoretical calculations obtained by numerical integration of the standard theory, provided that lens aberrations are taken into account. The invariance of the shape of the central lobe to surface roughness and tilt is also demonstrated.

© 1986 Optical Society of America

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References

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  1. C. J. R. Sheppard, in Imaging Modes of Scanning Optical Microscopy, E. A. Ash, ed. (Academic, New York, 1980).
  2. K. Liang, G. S. Kino, B. T. Khuri-Yakub, IEEE Trans. Sonics Ultrason. SU-32, 213 (1985).
    [CrossRef]
  3. C. J. R. Sheppard, T. Wilson, Appl. Phys. Lett. 38, 858 (1981).
    [CrossRef]
  4. T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).
  5. B. Richards, E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  6. I. J. Cox, D. K. Hamilton, C. J. R. Sheppard, Appl. Phys. Lett. 41, 604 (1981).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

1985 (1)

K. Liang, G. S. Kino, B. T. Khuri-Yakub, IEEE Trans. Sonics Ultrason. SU-32, 213 (1985).
[CrossRef]

1981 (2)

C. J. R. Sheppard, T. Wilson, Appl. Phys. Lett. 38, 858 (1981).
[CrossRef]

I. J. Cox, D. K. Hamilton, C. J. R. Sheppard, Appl. Phys. Lett. 41, 604 (1981).
[CrossRef]

1959 (1)

B. Richards, E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

Cox, I. J.

I. J. Cox, D. K. Hamilton, C. J. R. Sheppard, Appl. Phys. Lett. 41, 604 (1981).
[CrossRef]

Hamilton, D. K.

I. J. Cox, D. K. Hamilton, C. J. R. Sheppard, Appl. Phys. Lett. 41, 604 (1981).
[CrossRef]

Khuri-Yakub, B. T.

K. Liang, G. S. Kino, B. T. Khuri-Yakub, IEEE Trans. Sonics Ultrason. SU-32, 213 (1985).
[CrossRef]

Kino, G. S.

K. Liang, G. S. Kino, B. T. Khuri-Yakub, IEEE Trans. Sonics Ultrason. SU-32, 213 (1985).
[CrossRef]

Liang, K.

K. Liang, G. S. Kino, B. T. Khuri-Yakub, IEEE Trans. Sonics Ultrason. SU-32, 213 (1985).
[CrossRef]

Richards, B.

B. Richards, E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard, T. Wilson, Appl. Phys. Lett. 38, 858 (1981).
[CrossRef]

I. J. Cox, D. K. Hamilton, C. J. R. Sheppard, Appl. Phys. Lett. 41, 604 (1981).
[CrossRef]

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

C. J. R. Sheppard, in Imaging Modes of Scanning Optical Microscopy, E. A. Ash, ed. (Academic, New York, 1980).

Wilson, T.

C. J. R. Sheppard, T. Wilson, Appl. Phys. Lett. 38, 858 (1981).
[CrossRef]

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

Wolf, E.

B. Richards, E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

Appl. Phys. Lett. (2)

C. J. R. Sheppard, T. Wilson, Appl. Phys. Lett. 38, 858 (1981).
[CrossRef]

I. J. Cox, D. K. Hamilton, C. J. R. Sheppard, Appl. Phys. Lett. 41, 604 (1981).
[CrossRef]

IEEE Trans. Sonics Ultrason. (1)

K. Liang, G. S. Kino, B. T. Khuri-Yakub, IEEE Trans. Sonics Ultrason. SU-32, 213 (1985).
[CrossRef]

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

B. Richards, E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Other (3)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

C. J. R. Sheppard, in Imaging Modes of Scanning Optical Microscopy, E. A. Ash, ed. (Academic, New York, 1980).

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

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of apparatus. H.V., high-voltage power supply to drive scanning stage; D/A, digital-to-analog converter; A/D, analog-to-digital converter.

Fig. 2
Fig. 2

|V(z)|2 curve for objective of N.A. 0.9. Experimental data, dotted curve. Theoretical calculations, solid and dashed curves.

Fig. 3
Fig. 3

V(z) curve for a rough substrate tilted at an angle of 5° (solid curve). Reflections from a mirror, dashed curve.

Equations (5)

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E ( θ , z ) = 0 θ 0 ( 1 + cos θ ) sin θ ( cos θ ) 1 / 2 exp ( i k z cos θ ) P ( θ ) d θ .
V ( z ) = 0 θ 0 ( 1 + cos θ ) sin θ ( cos θ ) 1 / 2 × exp ( - 2 i k z cos θ ) P ( θ ) R ( θ ) d θ .
V ( z ) = | sin k z ( 1 - cos θ 0 ) k z ( 1 - cos θ 0 ) | .
( Δ z ) 3 d B = 0.45 λ 1 - cos θ 0 .
P ( θ ) = exp ( A sin 2 θ ) exp ( - j B sin 4 θ ) ( θ < θ 0 ) , P ( θ ) = 0 ( θ > θ 0 ) ,

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