Abstract

White-light interferometry uses a white-light source with a short coherent length that provides a narrowly localized interferogram that is used to measure three-dimensional surface profiles with possible large step heights without 2π-ambiguity. Combining coherence and phase information improves the vertical resolution. But, inconsistencies between phase and coherence occur at highly curved surfaces such as spherical and tilted surfaces, and these inconsistencies often cause what are termed ghost steps in the measurement result. In this paper, we describe a modified version of white-light interferometry for eliminating these ghost steps and improving the accuracy of white-light interferometry. Our proposed technique is verified by measuring several test samples.

© 2012 Optical Society of America

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References

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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]
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    [CrossRef]

2007 (3)

R. Berger, T. Sure, and W. Osten, “Measurement errors of mirrorlike, tilted objects in white-light interferometry,” Proc. SPIE 6616, 66162E (2007).
[CrossRef]

J. Niehues and P. Lehmann, “Dual-wavelength vertical scanning low-coherence interference microscope,” Proc. SPIE 6616, 661606 (2007).
[CrossRef]

J. Niehues, P. Lehmann, and K. Bobey, “Dual-wavelength vertical scanning low-coherence interferometric microscope,” Appl. Opt. 46, 7141–7148 (2007).
[CrossRef]

2006 (1)

P. Lehmann, “Systematic effects in coherence peak and phase evaluation of signals obtained with a vertical scanning white-light Mirau interferometer,” Proc. SPIE 6188, 618811 (2006).
[CrossRef]

2002 (1)

2000 (2)

1997 (1)

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

1996 (1)

1995 (1)

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

1993 (2)

1992 (1)

1990 (1)

1972 (1)

Berger, R.

R. Berger, T. Sure, and W. Osten, “Measurement errors of mirrorlike, tilted objects in white-light interferometry,” Proc. SPIE 6616, 66162E (2007).
[CrossRef]

Bobey, K.

Caber, P. J.

Chim, S. S. C.

de Groot, P.

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
[CrossRef]

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

P. de Groot and L. Deck, “Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms,” Opt. Lett. 18, 1462–1464 (1993).
[CrossRef]

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “High precision surface inspection on the microscale by broadband interferometry,” in Fringe 2001: The 4th International Workshop on Automatic Processing of Fringe Patterns, W. Osten and W. Jüptner, eds. (2001), pp. 47–55.

de Lega, X. C.

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
[CrossRef]

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “High precision surface inspection on the microscale by broadband interferometry,” in Fringe 2001: The 4th International Workshop on Automatic Processing of Fringe Patterns, W. Osten and W. Jüptner, eds. (2001), pp. 47–55.

Deck, L.

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

P. de Groot and L. Deck, “Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms,” Opt. Lett. 18, 1462–1464 (1993).
[CrossRef]

Devillers, R.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Dresel, T.

Floumoy, P. A.

Harasaki, A.

Häusler, G.

Kino, G. S.

Kramer, J.

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
[CrossRef]

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “High precision surface inspection on the microscale by broadband interferometry,” in Fringe 2001: The 4th International Workshop on Automatic Processing of Fringe Patterns, W. Osten and W. Jüptner, eds. (2001), pp. 47–55.

Larkin, K. G.

Lehmann, P.

J. Niehues, P. Lehmann, and K. Bobey, “Dual-wavelength vertical scanning low-coherence interferometric microscope,” Appl. Opt. 46, 7141–7148 (2007).
[CrossRef]

J. Niehues and P. Lehmann, “Dual-wavelength vertical scanning low-coherence interference microscope,” Proc. SPIE 6616, 661606 (2007).
[CrossRef]

P. Lehmann, “Systematic effects in coherence peak and phase evaluation of signals obtained with a vertical scanning white-light Mirau interferometer,” Proc. SPIE 6188, 618811 (2006).
[CrossRef]

McClure, R. W.

Niehues, J.

J. Niehues, P. Lehmann, and K. Bobey, “Dual-wavelength vertical scanning low-coherence interferometric microscope,” Appl. Opt. 46, 7141–7148 (2007).
[CrossRef]

J. Niehues and P. Lehmann, “Dual-wavelength vertical scanning low-coherence interference microscope,” Proc. SPIE 6616, 661606 (2007).
[CrossRef]

Osten, W.

R. Berger, T. Sure, and W. Osten, “Measurement errors of mirrorlike, tilted objects in white-light interferometry,” Proc. SPIE 6616, 66162E (2007).
[CrossRef]

Plata, A.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Sandoz, P.

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Schmit, J.

Sure, T.

R. Berger, T. Sure, and W. Osten, “Measurement errors of mirrorlike, tilted objects in white-light interferometry,” Proc. SPIE 6616, 66162E (2007).
[CrossRef]

Turzhitsky, M.

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “Determination of fringe order in white-light interference microscopy,” Appl. Opt. 41, 4571–4578 (2002).
[CrossRef]

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “High precision surface inspection on the microscale by broadband interferometry,” in Fringe 2001: The 4th International Workshop on Automatic Processing of Fringe Patterns, W. Osten and W. Jüptner, eds. (2001), pp. 47–55.

Venzke, H.

Wyant, J. C.

Wyntjes, G.

Appl. Opt. (8)

J. Mod. Opt. (2)

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

P. Sandoz, R. Devillers, and A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

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

Opt. Lett. (1)

Proc. SPIE (3)

P. Lehmann, “Systematic effects in coherence peak and phase evaluation of signals obtained with a vertical scanning white-light Mirau interferometer,” Proc. SPIE 6188, 618811 (2006).
[CrossRef]

R. Berger, T. Sure, and W. Osten, “Measurement errors of mirrorlike, tilted objects in white-light interferometry,” Proc. SPIE 6616, 66162E (2007).
[CrossRef]

J. Niehues and P. Lehmann, “Dual-wavelength vertical scanning low-coherence interference microscope,” Proc. SPIE 6616, 661606 (2007).
[CrossRef]

Other (1)

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, “High precision surface inspection on the microscale by broadband interferometry,” in Fringe 2001: The 4th International Workshop on Automatic Processing of Fringe Patterns, W. Osten and W. Jüptner, eds. (2001), pp. 47–55.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Interference signals of scanning white-light interferometry during scanning in the step height measurement, (b) a white-light interference fringe pattern for a single pixel, showing the meaning of envelope peak and phase peak and (b) surface profiles of a steel ball obtained by two different peak evaluations.

Fig. 2.
Fig. 2.

Conceptual illustration of a white-light interferogram and its Fourier transform. (a) a white-light interference pattern is composed of multiple-constituent monochromatic interference patterns and (b) results of a Fourier transform of a white-light interferogram.

Fig. 3.
Fig. 3.

A series of signal procedures of a dual-wavelength approach: (a) surface profiles taken with two different wavelengths, which are determined with Eq. (4), (b) difference between two measurement results in part (a), which are determined with Eq. (5) (bottom graph is the magnified region outlined in top graph), (c) phase difference Δδ (red line), (d) determined with Eq. (6), and (e) final measurement result after ghost-step correction.

Fig. 4.
Fig. 4.

Measurement results of a tilted step height. (a) three-dimensional measurement result using the conventional analysis, (b) cross sectional height profile between points A and A, (c) three-dimensional measurement results after application of our ghost step analysis and correction, and (d) cross sectional profile of part (c) between points A and A.

Fig. 5.
Fig. 5.

Another measurement result of a steel ball. (a) three-dimensional measurement result using the conventional analysis, (b) cross sectional height profile between points A and A, (c) three-dimensional measurement results after application of our ghost step analysis and correction, and (d) Cross sectional profile of part (c) between points A and A.

Tables (1)

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Table 1. Fringe Order Determination For Removing Spikes Errors (l=0,±1,±2,)

Equations (6)

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h=L2nG.
h=12n[(ϕ0α)k02k0Int{(ϕ0α)(2k0·h·n)2}].
h=λ04πϕ0+λ02m,m=Int{ϕ04πλ0h2π},ϕ0=ϕ0α.
h1=λ14πϕ1+λ12m1,h2=λ24πϕ2+λ22m2.
Δh=λ12m1λ22m2+Δδ.
Δh=ΔhΔδ=λ12m1λ12m2.

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