Abstract

The confocal-detection principle is open especially for use in medical applications. For inspection systems applications for technical objects in reflection confocal setups are of growing importance. For such applications the confocal measurements need to have a very short measuring time. A fast detection system is needed and to satisfy this requirement only a small number of height levels are measured and a fast-evaluation algorithm is used. Drawbacks of the reduction of height levels are a greater influence of noise and additional systematic errors on the measured heights. Study the effects of the reduction are calculated, different evaluation algorithms are analyzed, and the optimization of the parameters is discussed.

© 2002 Optical Society of America

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References

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  1. T. Wilson (ed.) Confocal Microscopy (Academic, San Diego, Calif., 1990).
  2. T. R. Korle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems, (Academic, San Diego, Calif., 1996).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. J. F. Aguilar, E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42, 1785–1794 (1995).
    [CrossRef]

2001 (2)

2000 (1)

H. J. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

1999 (1)

M. Ishihara, H. Sasaki, “High-speed surface measurement using a nonscanning multiple-beam confocal microscope,” Opt. Eng. 38, 1035–1040 (1999).
[CrossRef]

1995 (1)

J. F. Aguilar, E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42, 1785–1794 (1995).
[CrossRef]

1994 (1)

1989 (1)

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. (Oxford) 154, 243–256 (1989).
[CrossRef]

1987 (1)

Aguilar, J. F.

J. F. Aguilar, E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42, 1785–1794 (1995).
[CrossRef]

Carlini, A. R.

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. (Oxford) 154, 243–256 (1989).
[CrossRef]

T. Wilson, A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12, 227–229 (1987).
[CrossRef] [PubMed]

Conchello, J.-A.

Fleischer, M.

Hansen, E. W.

Hell, S. W.

Ishihara, M.

M. Ishihara, H. Sasaki, “High-speed surface measurement using a nonscanning multiple-beam confocal microscope,” Opt. Eng. 38, 1035–1040 (1999).
[CrossRef]

Kim, J. J.

Kino, G. S.

T. R. Korle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems, (Academic, San Diego, Calif., 1996).

Korle, T. R.

T. R. Korle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems, (Academic, San Diego, Calif., 1996).

Mendez, E. R.

J. F. Aguilar, E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42, 1785–1794 (1995).
[CrossRef]

Nagorni, M.

Sasaki, H.

M. Ishihara, H. Sasaki, “High-speed surface measurement using a nonscanning multiple-beam confocal microscope,” Opt. Eng. 38, 1035–1040 (1999).
[CrossRef]

Steudle, D.

H. J. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

Tiziani, H. J.

M. Fleischer, R. Windecker, H. J. Tiziani, “Theoretical limits of scanning white-light interferometry signal evaluation algorithms,” Appl. Opt. 40, 2815–2820 (2001).
[CrossRef]

H. J. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

Wegner, M.

H. J. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

Wilson, T.

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. (Oxford) 154, 243–256 (1989).
[CrossRef]

T. Wilson, A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12, 227–229 (1987).
[CrossRef] [PubMed]

Windecker, R.

Appl. Opt. (2)

J. Microsc. (Oxford) (1)

T. Wilson, A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” J. Microsc. (Oxford) 154, 243–256 (1989).
[CrossRef]

J. Mod. Opt. (1)

J. F. Aguilar, E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42, 1785–1794 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

M. Ishihara, H. Sasaki, “High-speed surface measurement using a nonscanning multiple-beam confocal microscope,” Opt. Eng. 38, 1035–1040 (1999).
[CrossRef]

H. J. Tiziani, M. Wegner, D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng. 39, 32–39 (2000).
[CrossRef]

Opt. Lett. (1)

Other (2)

T. Wilson (ed.) Confocal Microscopy (Academic, San Diego, Calif., 1990).

T. R. Korle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems, (Academic, San Diego, Calif., 1996).

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Figures (12)

Fig. 1
Fig. 1

(a) Fit of a parabola p(z) to f(z) = sinc2. The z axis is normalized to FWHM/2. (b) First derivative of the curves in (a).

Fig. 2
Fig. 2

Deviations from noise in a theoretical confocal signal. Evaluation by a least squares parabola fit and a center of gravity calculation.

Fig. 3
Fig. 3

Dependence of the factor k to (a) the used signal area, (b) the number of points within the FWHM.

Fig. 4
Fig. 4

Dependence of the factor m to (a) the used signal area, (b) the number of points within the FWHM.

Fig. 5
Fig. 5

Systematic error made when (a) using the center of gravity algorithm, (b) using the corrected center of gravity algorithm if the distribution of points is shifted to the symmetric distribution by an offset.

Fig. 6
Fig. 6

Maximum deviations from the linear part of the systematic error.

Fig. 7
Fig. 7

Noise in the evaluated topography of an inclined plane for different step sizes compared with the theoretical minimum.

Fig. 8
Fig. 8

Correction factor for (a) even, (b) uneven number of points in dependence of the step size.

Fig. 9
Fig. 9

LUT for parameters calculated like color values.

Fig. 10
Fig. 10

LUT for parameters optimized for confocal signals.

Fig. 11
Fig. 11

Deviation from an inclined plane when using (a) the center of gravity algorithm, (b) the corrected center of gravity algorithm, (c) the optimized LUT for height determination.

Fig. 12
Fig. 12

Comparison of the deviations of a measured inclined surface evaluated with the center of gravity and the optimized LUT.

Equations (10)

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

Iz  sinc2az,
C= zIz Iz.
σC2=k2zσz2+m2IσI2,
k=jCzj21/2=1i Izi2×jIzj+zj-CIzj21/2,
m=jCIj21/2=1i Ii2jzj-C21/2,
k=1isinc2zi-hj2coszjsinczj+sinc2zj-h21/2,
m=1isinc2zi-hj zj21/2.
Δzc=Nj I2zj-zc1/2,
a=x1x1+x2+x3, b=x3x1+x2+x3,
a=x2-x1x2+x3-x1x3>x1x2-x3x2+x1-x3x3x1, b=x2-x32x2-x1-x3.

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