Abstract

White-light interferometry is a well-established method for measuring the height profiles of samples with rough as well as with smooth surfaces. Because white-light interferometry uses broadband light sources, the problem of dispersion arises. Because the optical paths in the two interferometer arms cannot be balanced for all wavelengths, the white-light correlogram is distorted, which interferes with its evaluation. We investigate the influence of setup parameters on the shape of the correlogram. Calculated values are compared with experimental results.

© 2004 Optical Society of America

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References

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2002 (1)

2001 (2)

1998 (1)

1996 (1)

1994 (2)

P. Hariharan, K. G. Larkin, M. Roy, “The geometric phase: interferometric observation with white light,” J. Mod. Opt. 41, 663–667 (1994).
[CrossRef]

J. F. Biegen, “Determination of the phase change on reflection from two-beam interference,” Opt. Lett. 19, 1690–1692 (1994).
[CrossRef] [PubMed]

1992 (3)

1991 (1)

1990 (1)

Biegen, J. F.

Bohn, G.

G. Häusler, P. Ettl, M. Schenk, G. Bohn, I. Laszlo, “Limits of optical range sensors and how to exploit them,” in International Trends in Optics and Photonics ICO IV, T. Asakura, ed., Vol. 74 of Springer Series in Optical Sciences( Springer Verlag, Berlin, 1999), pp. 328–342.
[CrossRef]

Boisrobert, C. Y.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Chim, S. S. C.

Colonna de Lega, X.

Danielson, B. L.

de Groot, P.

Dresel, T.

Ettl, P.

G. Häusler, P. Ettl, M. Schenk, G. Bohn, I. Laszlo, “Limits of optical range sensors and how to exploit them,” in International Trends in Optics and Photonics ICO IV, T. Asakura, ed., Vol. 74 of Springer Series in Optical Sciences( Springer Verlag, Berlin, 1999), pp. 328–342.
[CrossRef]

Ge, Z.

Gradsteyn, I. S.

I. S. Gradsteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

Hariharan, P.

P. Hariharan, K. G. Larkin, M. Roy, “The geometric phase: interferometric observation with white light,” J. Mod. Opt. 41, 663–667 (1994).
[CrossRef]

Haruna, M.

Hashimoto, M.

Häusler, G.

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

G. Häusler, P. Ettl, M. Schenk, G. Bohn, I. Laszlo, “Limits of optical range sensors and how to exploit them,” in International Trends in Optics and Photonics ICO IV, T. Asakura, ed., Vol. 74 of Springer Series in Optical Sciences( Springer Verlag, Berlin, 1999), pp. 328–342.
[CrossRef]

Kino, G. S.

Kobayashi, F.

Koch, A.

R. Ulrich, A. Koch, “Faseroptischer Antastsensor für rauhe Oberflächen,” F & M 100, 521–524 (1992).

Kramer, J.

Larkin, K. G.

K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).
[CrossRef]

P. Hariharan, K. G. Larkin, M. Roy, “The geometric phase: interferometric observation with white light,” J. Mod. Opt. 41, 663–667 (1994).
[CrossRef]

Laszlo, I.

G. Häusler, P. Ettl, M. Schenk, G. Bohn, I. Laszlo, “Limits of optical range sensors and how to exploit them,” in International Trends in Optics and Photonics ICO IV, T. Asakura, ed., Vol. 74 of Springer Series in Optical Sciences( Springer Verlag, Berlin, 1999), pp. 328–342.
[CrossRef]

Maruyama, H.

Matsuda, S.

Mitsuyama, T.

Ohmi, M.

Pförtner, A.

Roy, M.

P. Hariharan, K. G. Larkin, M. Roy, “The geometric phase: interferometric observation with white light,” J. Mod. Opt. 41, 663–667 (1994).
[CrossRef]

Ryzhik, I. M.

I. S. Gradsteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

Schenk, M.

G. Häusler, P. Ettl, M. Schenk, G. Bohn, I. Laszlo, “Limits of optical range sensors and how to exploit them,” in International Trends in Optics and Photonics ICO IV, T. Asakura, ed., Vol. 74 of Springer Series in Optical Sciences( Springer Verlag, Berlin, 1999), pp. 328–342.
[CrossRef]

Schwider, J.

Tajiri, H.

Takeda, M.

Turzhitsky, M.

Ulrich, R.

R. Ulrich, A. Koch, “Faseroptischer Antastsensor für rauhe Oberflächen,” F & M 100, 521–524 (1992).

Venzke, H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Appl. Opt. (6)

F & M (1)

R. Ulrich, A. Koch, “Faseroptischer Antastsensor für rauhe Oberflächen,” F & M 100, 521–524 (1992).

J. Mod. Opt. (1)

P. Hariharan, K. G. Larkin, M. Roy, “The geometric phase: interferometric observation with white light,” J. Mod. Opt. 41, 663–667 (1994).
[CrossRef]

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

Opt. Lett. (3)

Other (4)

M. Bass, ed., Handbook of Optics (McGraw-Hill, New York, 1995).

I. S. Gradsteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

G. Häusler, P. Ettl, M. Schenk, G. Bohn, I. Laszlo, “Limits of optical range sensors and how to exploit them,” in International Trends in Optics and Photonics ICO IV, T. Asakura, ed., Vol. 74 of Springer Series in Optical Sciences( Springer Verlag, Berlin, 1999), pp. 328–342.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic of the white-light interferometer.

Fig. 2
Fig. 2

Spectrum of a LED measured by a spectrometer (a) in wavelength units and (b) in wave-number units (solid curve). The dashed curve is a Gaussian curve.

Fig. 3
Fig. 3

Experimental schematic of the balanced white-light interferometer with a glass plate in the reference arm.

Fig. 4
Fig. 4

Correlogram I(z) measured with the LED (λ0 = 866 nm; FWHM, 40 nm): (a) without dispersion, (b) with dispersion (10-mm-thick plate of BK7).

Fig. 5
Fig. 5

Correlogram I(z) measured with an incandescent lamp (a) without dispersion, (b) with dispersion (0.4-mm-thick plate of BK7 glass).

Tables (3)

Tables Icon

Table 1 Dispersion Parameters α for Fused Silica and BK7a

Tables Icon

Table 2 Calculated Values and Measured Results for the Correlogram of the LEDa

Tables Icon

Table 3 Calculated Values and Measured Results for the Correlogram of the Incandescent Lampa

Equations (13)

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Sk=12πΔkexp-k-k02Δk2,
nk=nk0+αk-k0,
Iz=0 Sk1+cos2kz-dnk-1+Δφdk,
Iz=I01+1+η2-1/4 exp-11+η2z-slc2×cosη1+η2z-slc2+2k0z-s+Φ0+Δφ,
η=8αdΔk2
s=dnk0+αk0-1=dNk0-1
lc=2Δk-1
Φ0=2αdk02-½ arctan η=2k0dNk0-nk0-½ arctan η
Iz=I01+exp-z/lc2cos2k0z+Δφ.
CC=1+η21/4.
w/w=1+η2.
pp1-η1+η2pπw2z-s.
η=2αd1/w2.

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