Abstract

We present a fiber-optical sensor for distance measurement of smooth and rough surfaces that is based on white-light interferometry; the sensor measures the distance from the sample surface to the sensor head. Because white light is used, the measurement is absolute. The measurement uncertainty depends not on the aperture of the optical system but only on the properties of the rough surface and is commonly ∼1 µm. The measurement range is approximately 1 mm. The sensor includes no mechanical moving parts; mechanical movement is replaced by the spectral decomposition of light at the interferometer output. The absence of mechanical moving parts enables a high measuring rate to be reached.

© 2005 Optical Society of America

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2002

1999

1997

G. Häusler, G. Leuchs, “Physikalische Grenzen der optischen Formerfassung mit Licht,” Phys. Bl. 53, 417–422 (1997).
[CrossRef]

1994

1993

K. Hotate, O. Kamatani, “Optical coherence domain reflectometry by synthesis of coherence function,” J. Lightwave Technol. 11, 1701–1710 (1993).
[CrossRef]

1992

1990

Bail, M.

M. Bail, B. Gebhardt, G. Häusler, M. W. Lindner, P. Pavliček, R. Ringler, “Optical range sensing with spatially modulated coherence,” in Optical Metrology, Z. Füzessy, W. Jüptner, W. Osten, eds.,Vol. 2 of the Proceedings of the International Symposium on Laser Applications in Precision Measurement (Balatonfüred, Hungary, 1996), pp. 27–33.

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]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 2001).

Chim, S. S. C.

de Groot, P.

Dorsch, R. G.

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]

Gebhardt, B.

M. Bail, B. Gebhardt, G. Häusler, M. W. Lindner, P. Pavliček, R. Ringler, “Optical range sensing with spatially modulated coherence,” in Optical Metrology, Z. Füzessy, W. Jüptner, W. Osten, eds.,Vol. 2 of the Proceedings of the International Symposium on Laser Applications in Precision Measurement (Balatonfüred, Hungary, 1996), pp. 27–33.

Haruna, M.

Häusler, G.

G. Häusler, G. Leuchs, “Physikalische Grenzen der optischen Formerfassung mit Licht,” Phys. Bl. 53, 417–422 (1997).
[CrossRef]

R. G. Dorsch, G. Häusler, J. M. Herrmann, “Laser triangulation: fundamental uncertainty in distance measurement,” Appl. Opt. 33, 1306–1314 (1994).
[CrossRef] [PubMed]

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]

G. Häusler, J. M. Herrmann, V. Höfer, M. W. Lindner, P. Pavliček, “A fibre-optical implementation of range sensor, based on spectral radar,” presented at the EOS Topical Meeting on Free Space Micro-Optical Systems, Engelberg, Switzerland, 1–3 April 1996.

M. Bail, B. Gebhardt, G. Häusler, M. W. Lindner, P. Pavliček, R. Ringler, “Optical range sensing with spatially modulated coherence,” in Optical Metrology, Z. Füzessy, W. Jüptner, W. Osten, eds.,Vol. 2 of the Proceedings of the International Symposium on Laser Applications in Precision Measurement (Balatonfüred, Hungary, 1996), pp. 27–33.

Herrmann, J. M.

R. G. Dorsch, G. Häusler, J. M. Herrmann, “Laser triangulation: fundamental uncertainty in distance measurement,” Appl. Opt. 33, 1306–1314 (1994).
[CrossRef] [PubMed]

G. Häusler, J. M. Herrmann, V. Höfer, M. W. Lindner, P. Pavliček, “A fibre-optical implementation of range sensor, based on spectral radar,” presented at the EOS Topical Meeting on Free Space Micro-Optical Systems, Engelberg, Switzerland, 1–3 April 1996.

Höfer, V.

G. Häusler, J. M. Herrmann, V. Höfer, M. W. Lindner, P. Pavliček, “A fibre-optical implementation of range sensor, based on spectral radar,” presented at the EOS Topical Meeting on Free Space Micro-Optical Systems, Engelberg, Switzerland, 1–3 April 1996.

Hotate, K.

K. Hotate, O. Kamatani, “Optical coherence domain reflectometry by synthesis of coherence function,” J. Lightwave Technol. 11, 1701–1710 (1993).
[CrossRef]

Inoue, S.

Kamatani, O.

K. Hotate, O. Kamatani, “Optical coherence domain reflectometry by synthesis of coherence function,” J. Lightwave Technol. 11, 1701–1710 (1993).
[CrossRef]

Kannari, F.

Kato, T.

Kino, G. S.

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]

Lee, B. S.

Lehmann, P.

Leuchs, G.

G. Häusler, G. Leuchs, “Physikalische Grenzen der optischen Formerfassung mit Licht,” Phys. Bl. 53, 417–422 (1997).
[CrossRef]

Lindner, M. W.

G. Häusler, J. M. Herrmann, V. Höfer, M. W. Lindner, P. Pavliček, “A fibre-optical implementation of range sensor, based on spectral radar,” presented at the EOS Topical Meeting on Free Space Micro-Optical Systems, Engelberg, Switzerland, 1–3 April 1996.

M. Bail, B. Gebhardt, G. Häusler, M. W. Lindner, P. Pavliček, R. Ringler, “Optical range sensing with spatially modulated coherence,” in Optical Metrology, Z. Füzessy, W. Jüptner, W. Osten, eds.,Vol. 2 of the Proceedings of the International Symposium on Laser Applications in Precision Measurement (Balatonfüred, Hungary, 1996), pp. 27–33.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Maruyama, M.

Mitsuyama, T.

Ohmi, M.

Oka, K.

Pavlicek, P.

M. Bail, B. Gebhardt, G. Häusler, M. W. Lindner, P. Pavliček, R. Ringler, “Optical range sensing with spatially modulated coherence,” in Optical Metrology, Z. Füzessy, W. Jüptner, W. Osten, eds.,Vol. 2 of the Proceedings of the International Symposium on Laser Applications in Precision Measurement (Balatonfüred, Hungary, 1996), pp. 27–33.

G. Häusler, J. M. Herrmann, V. Höfer, M. W. Lindner, P. Pavliček, “A fibre-optical implementation of range sensor, based on spectral radar,” presented at the EOS Topical Meeting on Free Space Micro-Optical Systems, Engelberg, Switzerland, 1–3 April 1996.

Ringler, R.

M. Bail, B. Gebhardt, G. Häusler, M. W. Lindner, P. Pavliček, R. Ringler, “Optical range sensing with spatially modulated coherence,” in Optical Metrology, Z. Füzessy, W. Jüptner, W. Osten, eds.,Vol. 2 of the Proceedings of the International Symposium on Laser Applications in Precision Measurement (Balatonfüred, Hungary, 1996), pp. 27–33.

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]

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Strand, T. C.

Suzuki, K.

Suzuki, M.

Teramura, Y.

Venzke, H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 2001).

Appl. Opt.

J. Lightwave Technol.

K. Hotate, O. Kamatani, “Optical coherence domain reflectometry by synthesis of coherence function,” J. Lightwave Technol. 11, 1701–1710 (1993).
[CrossRef]

Opt. Lett.

Phys. Bl.

G. Häusler, G. Leuchs, “Physikalische Grenzen der optischen Formerfassung mit Licht,” Phys. Bl. 53, 417–422 (1997).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 2001).

M. Bail, B. Gebhardt, G. Häusler, M. W. Lindner, P. Pavliček, R. Ringler, “Optical range sensing with spatially modulated coherence,” in Optical Metrology, Z. Füzessy, W. Jüptner, W. Osten, eds.,Vol. 2 of the Proceedings of the International Symposium on Laser Applications in Precision Measurement (Balatonfüred, Hungary, 1996), pp. 27–33.

G. Häusler, J. M. Herrmann, V. Höfer, M. W. Lindner, P. Pavliček, “A fibre-optical implementation of range sensor, based on spectral radar,” presented at the EOS Topical Meeting on Free Space Micro-Optical Systems, Engelberg, Switzerland, 1–3 April 1996.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

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 (7)

Fig. 1
Fig. 1

Schematic of the white-light interferometer with dispersion.

Fig. 2
Fig. 2

(a) Phase difference and (b) spectral intensity as functions of wave number.

Fig. 3
Fig. 3

Schematic of the fiber-optic sensor: SLD, superluminescent diode.

Fig. 4
Fig. 4

Evaluation of the interference pattern: (a) interference pattern at the output of the spectrometer, (b) filtered interference pattern (high-pass filter), (c) autoconvolution of the filtered interference pattern.

Fig. 5
Fig. 5

Measured height profile of a spark-eroded surface (Rugotest number N6A).

Fig. 6
Fig. 6

Measured height profile of a spark-eroded surface (Rugotest number N7A).

Fig. 7
Fig. 7

Measured height profile of a finish-turned surface: (a) lateral step, Δx = 5 µm; (b) lateral step Δx = 1 µm.

Equations (12)

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

n ( k ) = n ( k 0 ) + α ( k k 0 ) ,
I k ( k ) = 1 / 2 I k 0 [ 1 + cos ϕ ( k ) ] ,
ϕ ( k ) = 2 k { z d [ n ( k ) 1 ] } = 2 k { z d [ n ( k 0 ) + α ( k k 0 ) 1 ] } ,
k C = z 2 α d [ n ( k 0 ) α k 0 1 ] d 2 α d .
z = [ n ( k 0 ) + 2 α k C α k 0 1 ] d = [ N ( k C ) 1 ] d ,
z 0 = [ n ( k 0 ) + α k 0 1 ] d = [ N ( k 0 ) 1 ] d .
k C k 0 = z z 0 2 α d .
Δ z 2 α d Δ k ,
α f c λ 0 2 4 π D ,
k C k 0 = z z 0 2 ( α f h α f ) L ,
Δ z 2 ( α f h α f ) L Δ k .
s = ( f 1 f 2 ) 2 1.22 λ NA 2 ,

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