Abstract

The effects of defocus and primary spherical aberration on the images of a straight edge in a confocal microscope are investigated. When the aberrations are small, the sharpness of the edge image may be enhanced. But the images are degraded if the aberrations become strong in the system. In the latter case, one can improve the quality of the edge images, particularly the sharpness, by slightly reducing the aperture size of the objective and the collection lenses. This result is qualitatively verified by experimental results.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. J. R. Sheppard, “Scanningoptical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosset, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.
  2. J. T. Lindow, S. D. Bennet, I. R. Smith, “Scanned laser imaging for integrated circuit metrology,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 81–87 (1985).
  3. T. Zapf, R. W. Wijnaendts-van-Resandt, “Confocal laser microscope for submicron structure measurement,” Microelectron. Eng. 5, 573–580 (1986).
    [CrossRef]
  4. S. Mechels, M. Young, “Scanning confocal microscope for precise measurement of optical fibre diameter,” in Scanning Microscopy Instrumentation, G. S. Kino, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1556, 164–170 (1991).
  5. C. J. R. Sheppard, M. Gu, “Edge-setting criterion in confocal microscopy,” Appl. Opt. 31, 4575–4577 (1992).
    [CrossRef] [PubMed]
  6. C. J. R. Sheppard, J. M. Heaton, “Confocal images of straight edges and surface steps,” Optik 68, 371–380 (1984).
  7. C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30, 3563–3568 (1991).
    [CrossRef] [PubMed]
  8. C. J. R. Sheppard, T. Wilson, “Effect of spherical aberration on the imaging properties of scanning optical microscopes,” Appl. Opt. 18, 1058–1063 (1979).
    [CrossRef] [PubMed]
  9. M. Gu, C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on three-dimensional coherent transfer functions in confocal microscopes,” Appl. Opt. 31, 2541–2549 (1992).
    [CrossRef] [PubMed]
  10. C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
    [CrossRef]
  11. M. Gu, C. J. R. Sheppard, H. Zhou, “Optimization of axial resolution in confocal imaging using annular pupils,” Optik 93, 87–90 (1993).
  12. C. J. R. Sheppard, “Confocal interference microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, London, 1990), pp. 389–411.

1993 (1)

M. Gu, C. J. R. Sheppard, H. Zhou, “Optimization of axial resolution in confocal imaging using annular pupils,” Optik 93, 87–90 (1993).

1992 (2)

1991 (1)

1986 (1)

T. Zapf, R. W. Wijnaendts-van-Resandt, “Confocal laser microscope for submicron structure measurement,” Microelectron. Eng. 5, 573–580 (1986).
[CrossRef]

1984 (2)

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

C. J. R. Sheppard, J. M. Heaton, “Confocal images of straight edges and surface steps,” Optik 68, 371–380 (1984).

1979 (1)

Bennet, S. D.

J. T. Lindow, S. D. Bennet, I. R. Smith, “Scanned laser imaging for integrated circuit metrology,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 81–87 (1985).

Gu, M.

Hamilton, D. K.

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

Heaton, J. M.

C. J. R. Sheppard, J. M. Heaton, “Confocal images of straight edges and surface steps,” Optik 68, 371–380 (1984).

Lindow, J. T.

J. T. Lindow, S. D. Bennet, I. R. Smith, “Scanned laser imaging for integrated circuit metrology,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 81–87 (1985).

Mechels, S.

S. Mechels, M. Young, “Scanning confocal microscope for precise measurement of optical fibre diameter,” in Scanning Microscopy Instrumentation, G. S. Kino, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1556, 164–170 (1991).

Sheppard, C. J. R.

M. Gu, C. J. R. Sheppard, H. Zhou, “Optimization of axial resolution in confocal imaging using annular pupils,” Optik 93, 87–90 (1993).

C. J. R. Sheppard, M. Gu, “Edge-setting criterion in confocal microscopy,” Appl. Opt. 31, 4575–4577 (1992).
[CrossRef] [PubMed]

M. Gu, C. J. R. Sheppard, “Effects of defocus and primary spherical aberration on three-dimensional coherent transfer functions in confocal microscopes,” Appl. Opt. 31, 2541–2549 (1992).
[CrossRef] [PubMed]

C. J. R. Sheppard, M. Gu, “Aberration compensation in confocal microscopy,” Appl. Opt. 30, 3563–3568 (1991).
[CrossRef] [PubMed]

C. J. R. Sheppard, J. M. Heaton, “Confocal images of straight edges and surface steps,” Optik 68, 371–380 (1984).

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Effect of spherical aberration on the imaging properties of scanning optical microscopes,” Appl. Opt. 18, 1058–1063 (1979).
[CrossRef] [PubMed]

C. J. R. Sheppard, “Scanningoptical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosset, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.

C. J. R. Sheppard, “Confocal interference microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, London, 1990), pp. 389–411.

Smith, I. R.

J. T. Lindow, S. D. Bennet, I. R. Smith, “Scanned laser imaging for integrated circuit metrology,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 81–87 (1985).

Wijnaendts-van-Resandt, R. W.

T. Zapf, R. W. Wijnaendts-van-Resandt, “Confocal laser microscope for submicron structure measurement,” Microelectron. Eng. 5, 573–580 (1986).
[CrossRef]

Wilson, T.

Young, M.

S. Mechels, M. Young, “Scanning confocal microscope for precise measurement of optical fibre diameter,” in Scanning Microscopy Instrumentation, G. S. Kino, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1556, 164–170 (1991).

Zapf, T.

T. Zapf, R. W. Wijnaendts-van-Resandt, “Confocal laser microscope for submicron structure measurement,” Microelectron. Eng. 5, 573–580 (1986).
[CrossRef]

Zhou, H.

M. Gu, C. J. R. Sheppard, H. Zhou, “Optimization of axial resolution in confocal imaging using annular pupils,” Optik 93, 87–90 (1993).

Appl. Opt. (4)

Microelectron. Eng. (1)

T. Zapf, R. W. Wijnaendts-van-Resandt, “Confocal laser microscope for submicron structure measurement,” Microelectron. Eng. 5, 573–580 (1986).
[CrossRef]

Opt. Acta (1)

C. J. R. Sheppard, D. K. Hamilton, “Edge enhancement by defocusing of confocal images,” Opt. Acta 31, 723–727 (1984).
[CrossRef]

Optik (2)

M. Gu, C. J. R. Sheppard, H. Zhou, “Optimization of axial resolution in confocal imaging using annular pupils,” Optik 93, 87–90 (1993).

C. J. R. Sheppard, J. M. Heaton, “Confocal images of straight edges and surface steps,” Optik 68, 371–380 (1984).

Other (4)

C. J. R. Sheppard, “Confocal interference microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, London, 1990), pp. 389–411.

S. Mechels, M. Young, “Scanning confocal microscope for precise measurement of optical fibre diameter,” in Scanning Microscopy Instrumentation, G. S. Kino, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1556, 164–170 (1991).

C. J. R. Sheppard, “Scanningoptical microscopy,” in Advances in Optical and Electron Microscopy, R. Barer, V. E. Cosset, eds. (Academic, London, 1987), Vol. 10, pp. 1–98.

J. T. Lindow, S. D. Bennet, I. R. Smith, “Scanned laser imaging for integrated circuit metrology,” in Micron and Submicron Integrated Circuit Metrology, K. M. Monahan, ed., Proc. Soc. Photo-Opt. Instrum. Eng.565, 81–87 (1985).

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

2-D CTF when kW 040 = 2 for different values of kW 020: (a) real part, (b) imaginary part.

Fig. 2
Fig. 2

Images of a straight edge when W 040 = 0 for different values of W 020 (in units of wavelength).

Fig. 3
Fig. 3

Gradient of the image intensity at the edge as a function of W 020 (in units of wavelength) when W 040 = 0.

Fig. 4
Fig. 4

Images of a straight edge when W 020 = 0 for different values of W 040 (in units of wavelength).

Fig. 5
Fig. 5

Gradient of the image intensity at the edge as a function of W 040 (in units of wavelength) when W 020 = 0.

Fig. 6
Fig. 6

Images of a straight edge when W 040 = 0.25 for different values of W 020 (in units of wavelength).

Fig. 7
Fig. 7

Gradient of the image intensity at the edge as a function of W 020 (in units of wavelength) when W 040 = 0.25.

Fig. 8
Fig. 8

Images of a straight edge when W 020 = 0.25 for different values of W 040 (in units of wavelength).

Fig. 9
Fig. 9

Gradient of the image intensity at the edge as a function of W 040 (in units of wavelength) when W 020 = 0.25.

Fig. 10
Fig. 10

Images of a straight edge for different values of η when W 020 = 0 and W 040 = 0.5 (in units of wavelength). The dotted curve represents the image of an edge for an aberration-free system at η = 1.

Fig. 11
Fig. 11

Images of a straight edge for different values of η when W 020 = 0.25 and W 040 = 0.3 (in units of wavelength). The dotted curve represents the image of an edge for an aberration-free system at η = 1.

Fig. 12
Fig. 12

Measured edge responses of a silicon wafer in a reflection-mode confocal microscope: a, objective with full aperture (r 0 = 3 mm); b, objective with reduced aperture (r 0 = 2.5 mm).

Equations (8)

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

I ( v x , v y ) = | c ( m , n ) T ( m , n ) exp [ i ( v x m + v y n ) ] d m d n | 2 ,
I ( v x ) = | 1 2 + 1 π 0 c ( m , n = 0 ) m sin ( v x m ) d m | 2 ,
I ( v x = 0 ) = 1 π 0 Re [ c ( m , n = 0 ) ] d m ,
P ( ρ ) = exp ( i k W ) , ρ < η , = 0 , ρ > η ,
W = W 020 ρ 2 + W 040 ρ 4 ,
c ( l ) = P ( l ) 2 P ( l ) .
c ( l ) = C r exp ( i 2 k W 020 l 2 4 ) 0 π/ 2 0 ρ 0 exp { i 2 k W 020 ρ 2 + i k W 040 [ 2 ρ 4 + l 4 8 + ρ r 2 l 2 ( 1 + 2 cos 2 θ ) ] } ρ d ρ d θ,
ρ 0 = l | cos θ | 2 + [ η 2 ( l 2 sin 2 θ ) / 4 ] 1 / 2 ,

Metrics