Abstract

White-light interferometry is a standard optical tool with which to measure profiles of discontinuous structures such as diffractive optical elements. But there is one outstanding technological problem: The interferometers have to be symmetric; i.e., the geometrical path lengths in glass have to be the same for both interferometer arms. If these paths in glass are not equal within the field of view, a dispersion error will occur that is rather complicated to compensate for. The error appears in the measured profile in the form of steps of λ/2 in height. A simulation of interferograms disturbed by dispersion deviations is presented, and an algorithm is introduced that eliminates the steps without changing the actual phase information or averaging neighboring pixels. The results are shown with simulated and real data.

© 2001 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  4. Zygo Corporation, “What is frequency domain analysis,” (Zygo Corp., Middlefield, Conn., 1993).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2001 (1)

2000 (1)

1995 (1)

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

1994 (1)

1993 (1)

P. Sandoz, G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[CrossRef]

1992 (2)

K. B. Farr, N. George, “Beamsplitter cube for white light interferometry,” Opt. Eng. 31, 2191–2196 (1992).
[CrossRef]

Th. Dresel, G. Häusler, H. Venzke, “Three-dimensional sensing of rough surface by coherence radar,” Appl. Opt. 31, 919–925 (1992).
[CrossRef] [PubMed]

1990 (1)

Chamberlain, J.

J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, New York, 1979), pp. 5–11.

Chim, S. S. C.

de Groot, P.

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Deck, L.

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Dresel, Th.

Farr, K. B.

K. B. Farr, N. George, “Beamsplitter cube for white light interferometry,” Opt. Eng. 31, 2191–2196 (1992).
[CrossRef]

George, N.

K. B. Farr, N. George, “Beamsplitter cube for white light interferometry,” Opt. Eng. 31, 2191–2196 (1992).
[CrossRef]

Harasaki, A.

Häusler, G.

Kino, G. S.

Sandoz, P.

P. Sandoz, G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[CrossRef]

Schmidt, J.

Schwider, J.

Tribillon, G.

P. Sandoz, G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[CrossRef]

Venzke, H.

Wyant, J. C.

Zhou, L.

Appl. Opt. (4)

J. Mod. Opt. (2)

P. Sandoz, G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[CrossRef]

P. de Groot, L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Opt. Eng. (1)

K. B. Farr, N. George, “Beamsplitter cube for white light interferometry,” Opt. Eng. 31, 2191–2196 (1992).
[CrossRef]

Opt. Lett. (1)

Other (2)

J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, New York, 1979), pp. 5–11.

Zygo Corporation, “What is frequency domain analysis,” (Zygo Corp., Middlefield, Conn., 1993).

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Figures (8)

Fig. 1
Fig. 1

Schematic of a Linnik interferometer: PZT, piezoelectric transducer; CCD, charge-coupled device.

Fig. 2
Fig. 2

White-light interferogram seen by a single pixel of a CCD camera during a Z scan (simulated).

Fig. 3
Fig. 3

Procedure for evaluation of z 0.

Fig. 4
Fig. 4

Shift of the envelope at four values of c (simulated).

Fig. 5
Fig. 5

Profiles that experience a dispersion error (top, real; bottom, simulated).

Fig. 6
Fig. 6

Result after the results of both algorithms are subtracted from each other (top, real; bottom, simulated).

Fig. 7
Fig. 7

Map generated for the unwrapping algorithm that contains only the values 1, 0, and -1 (top, real; bottom, simulated).

Fig. 8
Fig. 8

Corrected profiles (top, real; bottom, simulated).

Equations (13)

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FTfz-z0=FTfzexp-ikz0,
Φ := kz0.
h=z0/2,
Φ=Φ0+2nπ,  n=0, ±1, ±2, ±3,
h=Φ/2k0.
h=12k0Φ0-2π intΦ0-z0k02π.
Izx, y=I01+V coskzx, y.
IWLzx, y=k1k2 I01+V coskzx, ydk=k2-k1I01+V sinck2-k12π ×zx, ycosk2+k12 zx, y.
IWLzx, y=k1k2 I01+V coskzx, y+k-k0cx, ydk=k2-k1I01+V sinck2-k12π×zx, y+cx, y×cosk2+k12zx, y+cx, y-k0cx, y.
c=2m+1πk0=2m+12 λ0,m=0, ±1, ±2,,
n := intΦ0-z0k02π
d=ck02k1k2γ=2m+1π2k1k2γ,  γ=n1-n2k1-k2,
u := 2 intΦ0-z0k02π-intΦ0-z0k02π+14-intΦ0-z0k02π-14.

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