Abstract

Wavelength scanning profilometry suitable for real-time surface shape measurement is proposed. A phase slope of the interference signal generated by a wavelength scan is measured at an individual image pixel on-line. The parallel outputs of these on-line measurements show a map of surface height in real time. Experiments where a tunable dye laser was used were conducted to simulate the real-time measurements of step objects with specular and diffuse surfaces. The results have shown that a height map is available at any moment during the wavelength scan, and the measurement accuracy of height increases as the scanning proceeds. For a scanning width of 25 nm, the accuracy was as high as 1 µm. Analyses of the measurement accuracy are given.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. A. Massie, “Real-time digital heterodyne interferometry: a system,” Appl. Opt. 19, 154–160 (1980).
    [CrossRef] [PubMed]
  2. J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiré and its applications,” in Fringe ’93, Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. Akademie Verlag, Berlin, 1993), pp. 66–71.
  3. D. M. Meadows, W. O. Johnson, J. B. Allen, “Generation of surface contours by moiré patterns,” Appl. Opt. 9, 942–947 (1970).
    [CrossRef] [PubMed]
  4. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 9, 3977–3982 (1983).
    [CrossRef]
  5. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  6. A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  7. T. Dresel, G. Häuslar, H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
    [CrossRef] [PubMed]
  8. M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
    [CrossRef] [PubMed]
  9. T. Yatagai, “Recent progresses in white light interferometry,” in New Techniques and Analysis in Optical Measurements, M. Kujawińska, K. Patorski, eds., Proc. SPIE.2340, 338–345 (1994).
  10. H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
    [CrossRef] [PubMed]
  11. T. Kobayashi, “Interferometry for measuring distance and displacement using semiconductor lasers,” Kogaku (Jpn. J. Opt.) 17, 279–284 (1988).
  12. M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
    [CrossRef] [PubMed]
  13. L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
    [CrossRef] [PubMed]
  14. 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]
  15. J. C. Marron, K. S. Schroeder, “Three-dimensional lensless imaging using laser frequency diversity,” Appl. Opt. 31, 255–262 (1992).
    [CrossRef] [PubMed]
  16. J. C. Marron, K. S. Schroeder, “Holographic laser radar,” Opt. Lett. 18, 385–387 (1993).
    [CrossRef] [PubMed]
  17. W. G. Driscoll, W. Vaughan, eds., Handbook Optics (McGraw-Hill, New York, 1978), Chap. 2.
  18. N. George, A. Jain, R. D. S. Melville, “Experiments on the space and wavelength dependence of speckle,” Appl. Opt. 7, 157–169 (1975).
  19. J. C. Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88, 305–308 (1992).
    [CrossRef]
  20. L. G. Shirley, P. A. Lo, “Bispectral analysis of the wavelength dependence of speckle: remote sensing of object shape,” J. Opt. Soc. Am. A 11, 1025–1046 (1994).
    [CrossRef]
  21. S. Wada, K. Akagawa, H. Tashiro, “Electronically tuned Ti:sapphire laser,” Opt. Lett. 21, 731–733 (1996).
    [CrossRef] [PubMed]

1996 (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 (3)

1993 (1)

1992 (3)

1991 (1)

1988 (1)

T. Kobayashi, “Interferometry for measuring distance and displacement using semiconductor lasers,” Kogaku (Jpn. J. Opt.) 17, 279–284 (1988).

1986 (1)

1985 (1)

1983 (1)

M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 9, 3977–3982 (1983).
[CrossRef]

1980 (1)

1975 (1)

N. George, A. Jain, R. D. S. Melville, “Experiments on the space and wavelength dependence of speckle,” Appl. Opt. 7, 157–169 (1975).

1973 (1)

1970 (1)

Akagawa, K.

Allen, J. B.

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]

L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
[CrossRef] [PubMed]

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]

L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
[CrossRef] [PubMed]

Dresel, T.

Fercher, A. F.

George, N.

N. George, A. Jain, R. D. S. Melville, “Experiments on the space and wavelength dependence of speckle,” Appl. Opt. 7, 157–169 (1975).

Häuslar, G.

Hu, H. Z.

Iwata, K.

Jain, A.

N. George, A. Jain, R. D. S. Melville, “Experiments on the space and wavelength dependence of speckle,” Appl. Opt. 7, 157–169 (1975).

Johnson, W. O.

Kato, J.

J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiré and its applications,” in Fringe ’93, Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. Akademie Verlag, Berlin, 1993), pp. 66–71.

Kikuta, H.

Kobayashi, T.

T. Kobayashi, “Interferometry for measuring distance and displacement using semiconductor lasers,” Kogaku (Jpn. J. Opt.) 17, 279–284 (1988).

Lo, P. A.

Marron, J. C.

Massie, N. A.

Meadows, D. M.

Melville, R. D. S.

N. George, A. Jain, R. D. S. Melville, “Experiments on the space and wavelength dependence of speckle,” Appl. Opt. 7, 157–169 (1975).

Mutoh, K.

M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 9, 3977–3982 (1983).
[CrossRef]

Nagata, R.

Polhemus, C.

Schroeder, K. S.

Shirley, L. G.

Suematsu, M.

Takeda, M.

Tashiro, H.

Venzke, H.

Vry, U.

Wada, S.

Yamaguchi, I.

J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiré and its applications,” in Fringe ’93, Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. Akademie Verlag, Berlin, 1993), pp. 66–71.

Yamamoto, H.

Yatagai, T.

T. Yatagai, “Recent progresses in white light interferometry,” in New Techniques and Analysis in Optical Measurements, M. Kujawińska, K. Patorski, eds., Proc. SPIE.2340, 338–345 (1994).

Appl. Opt. (12)

M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 9, 3977–3982 (1983).
[CrossRef]

N. George, A. Jain, R. D. S. Melville, “Experiments on the space and wavelength dependence of speckle,” Appl. Opt. 7, 157–169 (1975).

D. M. Meadows, W. O. Johnson, J. B. Allen, “Generation of surface contours by moiré patterns,” Appl. Opt. 9, 942–947 (1970).
[CrossRef] [PubMed]

N. A. Massie, “Real-time digital heterodyne interferometry: a system,” Appl. Opt. 19, 154–160 (1980).
[CrossRef] [PubMed]

A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
[CrossRef] [PubMed]

H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
[CrossRef] [PubMed]

M. Suematsu, M. Takeda, “Wavelength-shift interferometry for distance measurements using the Fourier transform technique for fringe analysis,” Appl. Opt. 30, 4046–4055 (1991).
[CrossRef] [PubMed]

J. C. Marron, K. S. Schroeder, “Three-dimensional lensless imaging using laser frequency diversity,” Appl. Opt. 31, 255–262 (1992).
[CrossRef] [PubMed]

L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
[CrossRef] [PubMed]

M. Takeda, H. Yamamoto, “Fourier-transform speckle profilometry: three-dimensional shape measurements of diffuse objects with large height steps and/or spatially isolated surfaces,” Appl. Opt. 33, 7829–7837 (1994).
[CrossRef] [PubMed]

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

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
[CrossRef] [PubMed]

J. Mod. Opt. (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]

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

Kogaku (Jpn. J. Opt.) (1)

T. Kobayashi, “Interferometry for measuring distance and displacement using semiconductor lasers,” Kogaku (Jpn. J. Opt.) 17, 279–284 (1988).

Opt. Commun. (1)

J. C. Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88, 305–308 (1992).
[CrossRef]

Opt. Lett. (2)

Other (3)

W. G. Driscoll, W. Vaughan, eds., Handbook Optics (McGraw-Hill, New York, 1978), Chap. 2.

T. Yatagai, “Recent progresses in white light interferometry,” in New Techniques and Analysis in Optical Measurements, M. Kujawińska, K. Patorski, eds., Proc. SPIE.2340, 338–345 (1994).

J. Kato, I. Yamaguchi, “Real-time fringe analysis based on electronic moiré and its applications,” in Fringe ’93, Proceedings of the Second International Workshop on Automatic Processing of Fringe Patterns, W. Juptner, W. Osten, eds. Akademie Verlag, Berlin, 1993), pp. 66–71.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Optical setup for wavelength scanning profilometry.

Fig. 2
Fig. 2

Experiment with specular step object: (a) object, (b) interferogram taken at λ = 563.5 nm.

Fig. 3
Fig. 3

Experiment with a specular step object: example of the interference signal on the (a) left and (b) right side of the step.

Fig. 4
Fig. 4

Reconstructed height maps of the specular step object obtained at various wavelength shifts Δλ. The maximum wavelength shift is 25 nm.

Fig. 5
Fig. 5

One-line profile of the height map of the specular step object obtained at the maximum wavelength shift.

Fig. 6
Fig. 6

Standard deviation of the reconstructed surface of the specular object calculated at various wavelength shifts.

Fig. 7
Fig. 7

Experiment with the diffuse step object: (a) object, (b) specklegram taken at λ = 565.9 nm.

Fig. 8
Fig. 8

Experiment with a diffuse step object: example of the interference signal on the (a) left and (b) right side of the step.

Fig. 9
Fig. 9

Reconstructed height maps of the diffuse step object obtained at various wavelength shifts Δλ. The maximum wavelength shift is 25 nm.

Fig. 10
Fig. 10

One-line profile of the height map of the diffuse step object obtained at the maximum wavelength shift.

Fig. 11
Fig. 11

Standard deviation of the reconstructed surface of the diffuse object calculated at various wavelength shifts.

Fig. 12
Fig. 12

Diagram of the principal rays of beams about the wedged half-mirror: C.S., coated surface; B.S., back (rear) surface; R.W., reference wave front; S.W., scattered wave front from the object’s surface; D.A., detector array.

Equations (25)

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

Ik; x, y=I0x, y+Ax, ycosk2hx, y.
ϕk; x, y=k02hx, y+Δk2hx, yϕ0x, y+ΔϕΔk; x, y,  k=k0+Δk,
ΔϕΔk; x, y=2hx, yΔk.
hx, y=12 ΔϕΔk.
hx, y=12 πN-1kN-k1,
kerk=expk/kτk00k>0,
C=2Δk-1 k0k0+Δk Id2kdk1/2Δk-1 k0k0+Δk Ikdk,
Ik; x, y=I0k; x, y+Ak; x, ycosk2hx, y+lk; x, y+θk; x, y+n,
δhh=δϕΔϕ-δkΔk.
δhh2=δϕΔϕ2+δkΔk2,
δh=hδϕΔϕ2+δkΔk21/2.
δϕ2=πδN2+σθ2,
δh=12 πδNΔk2+12 σθΔk2+h δkΔk21/2,
dr=do=wn-11+ψ2n+12n,
ds=2wn-11+ψ+w2n+12n.
Δ=ds-drwn-11+ψ2n+12n 1+4 wψ,
δ=Δn+δn-Δn=δnw1+ψ22 1+1n2 1+4 wψ.
δl=δΔy,
δlmax=δmaxY=Δn+δnmax-ΔnY,
αk=Ir+IoM1/2 n=1M expi2kh+δhnR+βk,
Ik=αk2=Ir+Io+Bk+2IrIoM1/2×Ckcos 2kh-Dksin 2kh,
Bk2IoM n=1M-1 m=n+1M cos2kδhn-δhm,  Ckn=1M cos2k·δhn,  Dkn=1M sin2k·δhn.
Ik=I0k+Akcos2kh+θk,
I0kIr+Io+Bk,  Ak2IrIoM1/2 Ck2+Dk21/2,  θktan-1Dk/Ck.
δh=h·δk/Δk.

Metrics