Abstract

We demonstrate the use of temporal phase unwrapping in combination with wavelength-scanning interferometry. Two unwrapping strategies are considered: fitting to a reversed exponential sequence and complex Fourier-transform ranging. Measurement of a 10-µm step by use of an external-cavity laser diode is discussed.

© 2000 Optical Society of America

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References

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  1. 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).
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    [CrossRef] [PubMed]
  3. I. Yamaguchi, A. Yamamoto, S. Kuwamura, “Speckle decorrelation in surface profilometry by wavelength scanning interferometry,” Appl. Opt. 37, 6721–6728 (1998).
    [CrossRef]
  4. I. Yamaguchi, A. Yamamoto, M. Yano, “Surface profilometry by wavelength scanning interferometry,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 141–146 (1998).
    [CrossRef]
  5. H. J. Tiziani, B. Franze, P. Haible, C. Joenathan, “Surface topometry by multi-wavelength technique and temporal Fourier transformation,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 96–103 (1998).
    [CrossRef]
  6. J. Kato, I. Yamaguchi, “Height gauging by wavelength-scanning interferometry with phase detection,” in Optical Engineering for Sensing and Nanotechnology (ICOSN’99), I. Yamaguchi, ed., Proc. SPIE3740, 594–597 (1999).
    [CrossRef]
  7. H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
    [CrossRef] [PubMed]
  8. H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator–based fringe projector,” Opt. Eng. 36, 610–615 (1997).
    [CrossRef]
  9. J. M. Huntley, H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. A 14, 3188–3196 (1997).
    [CrossRef]
  10. J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 86–93 (1998).
    [CrossRef]
  11. J. Burke, H. Helmers, “Complex division as a common basis for calculating phase differences in electronic speckle pattern interferometry in one step,” Appl. Opt. 37, 2589–2590 (1998).
    [CrossRef]

1998

1997

1994

Burke, J.

Coggrave, C. R.

J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 86–93 (1998).
[CrossRef]

Franze, B.

H. J. Tiziani, B. Franze, P. Haible, C. Joenathan, “Surface topometry by multi-wavelength technique and temporal Fourier transformation,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 96–103 (1998).
[CrossRef]

Haible, P.

H. J. Tiziani, B. Franze, P. Haible, C. Joenathan, “Surface topometry by multi-wavelength technique and temporal Fourier transformation,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 96–103 (1998).
[CrossRef]

Helmers, H.

Huntley, J. M.

H. O. Saldner, J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36, 2770–2775 (1997).
[CrossRef] [PubMed]

J. M. Huntley, H. O. Saldner, “Error-reduction methods for shape measurement by temporal phase unwrapping,” J. Opt. Soc. Am. A 14, 3188–3196 (1997).
[CrossRef]

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator–based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 86–93 (1998).
[CrossRef]

Joenathan, C.

H. J. Tiziani, B. Franze, P. Haible, C. Joenathan, “Surface topometry by multi-wavelength technique and temporal Fourier transformation,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 96–103 (1998).
[CrossRef]

Kato, J.

J. Kato, I. Yamaguchi, “Height gauging by wavelength-scanning interferometry with phase detection,” in Optical Engineering for Sensing and Nanotechnology (ICOSN’99), I. Yamaguchi, ed., Proc. SPIE3740, 594–597 (1999).
[CrossRef]

Kuwamura, S.

Saldner, H. O.

Takeda, M.

Tiziani, H. J.

H. J. Tiziani, B. Franze, P. Haible, C. Joenathan, “Surface topometry by multi-wavelength technique and temporal Fourier transformation,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 96–103 (1998).
[CrossRef]

Yamaguchi, I.

I. Yamaguchi, A. Yamamoto, S. Kuwamura, “Speckle decorrelation in surface profilometry by wavelength scanning interferometry,” Appl. Opt. 37, 6721–6728 (1998).
[CrossRef]

S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
[CrossRef] [PubMed]

J. Kato, I. Yamaguchi, “Height gauging by wavelength-scanning interferometry with phase detection,” in Optical Engineering for Sensing and Nanotechnology (ICOSN’99), I. Yamaguchi, ed., Proc. SPIE3740, 594–597 (1999).
[CrossRef]

I. Yamaguchi, A. Yamamoto, M. Yano, “Surface profilometry by wavelength scanning interferometry,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 141–146 (1998).
[CrossRef]

Yamamoto, A.

I. Yamaguchi, A. Yamamoto, S. Kuwamura, “Speckle decorrelation in surface profilometry by wavelength scanning interferometry,” Appl. Opt. 37, 6721–6728 (1998).
[CrossRef]

I. Yamaguchi, A. Yamamoto, M. Yano, “Surface profilometry by wavelength scanning interferometry,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 141–146 (1998).
[CrossRef]

Yamamoto, H.

Yano, M.

I. Yamaguchi, A. Yamamoto, M. Yano, “Surface profilometry by wavelength scanning interferometry,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 141–146 (1998).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

H. O. Saldner, J. M. Huntley, “Profilometry using temporal phase unwrapping and a spatial light modulator–based fringe projector,” Opt. Eng. 36, 610–615 (1997).
[CrossRef]

Other

J. M. Huntley, C. R. Coggrave, “Progress in phase unwrapping,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 86–93 (1998).
[CrossRef]

I. Yamaguchi, A. Yamamoto, M. Yano, “Surface profilometry by wavelength scanning interferometry,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 141–146 (1998).
[CrossRef]

H. J. Tiziani, B. Franze, P. Haible, C. Joenathan, “Surface topometry by multi-wavelength technique and temporal Fourier transformation,” in International Conference on Applied Optical Metrology, F. Gyimesi, K. Rastogi, eds., Proc. SPIE3407, 96–103 (1998).
[CrossRef]

J. Kato, I. Yamaguchi, “Height gauging by wavelength-scanning interferometry with phase detection,” in Optical Engineering for Sensing and Nanotechnology (ICOSN’99), I. Yamaguchi, ed., Proc. SPIE3740, 594–597 (1999).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Basic setup of a wavelength-scanning interferometer for surface profilometer: HM, half mirror; pL1, 2, polarizers.

Fig. 2
Fig. 2

Results from the measurement of a 10-µm step on a specular object by (a) method D with a tuning range of 6.4 nm and (b) method E with a tuning range of 6.2 nm. Every eighth point in the x and y directions is shown. The field of view was 7.2 mm × 7.2 mm.

Equations (8)

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Ix, y; k=IR+Iox, y; k+2IRkIox, y; k1/2 cos2khx, y+α,
P=2Δkhx, y,
hx, y=ωλ24π
hmax=λ24Δλmin
ΔΩuλe-tΔλmin, λe-2tΔλmin=UΔΩwλe-tΔλmin, λe-2tΔλmin, ΔΩuλe, λe-tΔλmin,
ΔΩuλe, λe-2tΔλmin=ΔΩuλe-tΔλmin, λe-2tΔλmin+ΔΩuλe, λe-tΔλmin
UΩ1, Ω2=Ω1-2πNINTΩ1-Ω22π,
ω=2πκsΔλmin,

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