Abstract

We demonstrate a simple way of increasing the data acquisition and processing speed in a scanning white-light interferometer for surface topography measurement. The method consists of undersampling interference data and processing the resultant sub-Nyquist interferograms in the frequency domain to create complete three-dimensional images. Experimental results on a 20-μm step height standard show a measurement repeatability of 10 nm.

© 1993 Optical Society of America

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References

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  1. N. Balasubramanian, “Optical system for surface topography measurement,” U.S. Patent4,340,306 (July20, 1982).
  2. M. Davidson, K. Kaufman, I. Mazor, Solid State Technol. 30, 57 (1987).
  3. T. Dresel, G. Haeusler, H. Venzke, Appl. Opt. 31, 919 (1992).
    [CrossRef] [PubMed]
  4. P. C. Montgomery, J.-P. Fillard, Proc. Soc. Photo-Opt. Instrum. Eng. 1755, 12 (1992).
  5. S. S. C. Chim, G. S. Kino, Appl. Opt. 31, 2550 (1992).
    [CrossRef] [PubMed]
  6. P. J. Caber, “Interferometric profiles for rough surfaces,” Appl. Opt. 32, 3438 (1993).
    [CrossRef] [PubMed]
  7. B. L. Danielson, C. Y. Boisrobert, Appl. Opt. 30, 2975 (1991).
    [CrossRef] [PubMed]
  8. A. Kohlhass, C. Froemchen, E. Brinkmeyer, J. Lightwave Technol. 9, 1493 (1991).
    [CrossRef]

1993 (1)

1992 (3)

1991 (2)

A. Kohlhass, C. Froemchen, E. Brinkmeyer, J. Lightwave Technol. 9, 1493 (1991).
[CrossRef]

B. L. Danielson, C. Y. Boisrobert, Appl. Opt. 30, 2975 (1991).
[CrossRef] [PubMed]

1987 (1)

M. Davidson, K. Kaufman, I. Mazor, Solid State Technol. 30, 57 (1987).

Balasubramanian, N.

N. Balasubramanian, “Optical system for surface topography measurement,” U.S. Patent4,340,306 (July20, 1982).

Boisrobert, C. Y.

Brinkmeyer, E.

A. Kohlhass, C. Froemchen, E. Brinkmeyer, J. Lightwave Technol. 9, 1493 (1991).
[CrossRef]

Caber, P. J.

Chim, S. S. C.

Danielson, B. L.

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, Solid State Technol. 30, 57 (1987).

Dresel, T.

Fillard, J.-P.

P. C. Montgomery, J.-P. Fillard, Proc. Soc. Photo-Opt. Instrum. Eng. 1755, 12 (1992).

Froemchen, C.

A. Kohlhass, C. Froemchen, E. Brinkmeyer, J. Lightwave Technol. 9, 1493 (1991).
[CrossRef]

Haeusler, G.

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, Solid State Technol. 30, 57 (1987).

Kino, G. S.

Kohlhass, A.

A. Kohlhass, C. Froemchen, E. Brinkmeyer, J. Lightwave Technol. 9, 1493 (1991).
[CrossRef]

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, Solid State Technol. 30, 57 (1987).

Montgomery, P. C.

P. C. Montgomery, J.-P. Fillard, Proc. Soc. Photo-Opt. Instrum. Eng. 1755, 12 (1992).

Venzke, H.

Appl. Opt. (4)

J. Lightwave Technol. (1)

A. Kohlhass, C. Froemchen, E. Brinkmeyer, J. Lightwave Technol. 9, 1493 (1991).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

P. C. Montgomery, J.-P. Fillard, Proc. Soc. Photo-Opt. Instrum. Eng. 1755, 12 (1992).

Solid State Technol. (1)

M. Davidson, K. Kaufman, I. Mazor, Solid State Technol. 30, 57 (1987).

Other (1)

N. Balasubramanian, “Optical system for surface topography measurement,” U.S. Patent4,340,306 (July20, 1982).

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Figures (4)

Fig. 1
Fig. 1

Scanning white-light interferometer. The PZT translates the object in a direction perpendicular to the optical axis of the objective while intensity images are recorded with the detector array. These images are processed in the spatial frequency domain to generate a three-dimensional representation of the surface topography.

Fig. 2
Fig. 2

Simulated interference data, (a) Dense sampling correctly represents the complete interference pattern, (b) Sub-Nyquist sampling (1 point every 5π/2) results in a severely distorted data set that is still useful for three-dimensional imaging if correctly processed.

Fig. 3
Fig. 3

Fourier transform of the sub-Nyquist data shown in Fig. 2(b). The arrow indicates the mean or peak wave number, which is much smaller than the actual mean wave number of the interference pattern because of undersampling. The phase information in (b) is used to calculate local surface height.

Fig. 4
Fig. 4

Three-dimensional profile of a 20-μm standard step height obtained from sub-Nyquist white-light interferograms. The repeatability of the measurement is 10 nm.

Equations (3)

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I = 1 + cos ( ϕ ) ,
ϕ = k Z .
Z = d ϕ / d k .

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