Abstract

Wavelength scanning interferometry (WSI) can be used for surface measurement with discontinuous surface profiles by producing phase shifts without any mechanical scanning process. The choice of algorithms for the WSI to analyze the fringe pattern depends on the desired accuracy and computing speed. This paper provides comparison of four different algorithms to analyze the interference fringe pattern acquired from WSI. The mathematical description of these algorithms, their computing resolution, and speed are presented. Two step-height samples are measured using the WSI. Experimental results demonstrate that the accuracy of measuring surface height varies from micrometer to nanometer value depending on the algorithm used to analyze the captured interferograms.

© 2012 Optical Society of America

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References

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    [CrossRef]
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2012

2010

2002

2001

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

1999

1998

D. Xiaoli and S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

1997

1995

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

1994

1986

1982

1980

Balsubramanian, N.

N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent 4,340,306 (4February1980).

Bucher, E. G.

Carnahan, J. W.

Coupland, J. M.

Davila, A.

de Groot, P.

deLega, X. C.

Gao, F.

Hartmann, M.

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Huntley, J. M.

Ina, H.

Ishii, Y.

Y. Ishii, “Wavelength-tunable laser-diode interferometer,” Opt. Rev. 6, 273–283 (1999).
[CrossRef]

Iwata, K.

Jiang, X.

Katuo, S.

D. Xiaoli and S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Kikuta, H.

Kobayashi, S.

Kramer, J.

Kuo, C.

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

Kuwamura, S.

Muhamedsalih, H.

Nagata, R.

Pallikarakis, C.

Pfeifer, T.

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Ruiz, P. D.

Schwider, J.

Snyder, J. J.

Sunouchi, K.

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

Takeda, M.

Tashiro, H.

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

Thiel, J.

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Turzhitsky, M.

Wada, S.

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

Wang, K.

Whitehouse, D. J.

D. J. Whitehouse, Handbook of Surface and Nanometrology (Taylor & Francis, 2011).

Xiaoli, D.

D. Xiaoli and S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Yamaguchi, I.

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

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

Yamamoto, A.

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

Yamamoto, H.

Zhou, L.

Appl. Opt.

Appl. Spectrosc.

J. Opt. Soc. Am.

Meas. Sci. Technol.

D. Xiaoli and S. Katuo, “High-accuracy absolute distance measurement by means of wavelength scanning heterodyne interferometry,” Meas. Sci. Technol. 9, 1031–1035 (1998).
[CrossRef]

Measurement

J. Thiel, T. Pfeifer, and M. Hartmann, “Interferometric measurement of absolute distances of up to 40 m,” Measurement 16, 1–6 (1995).
[CrossRef]

Opt. Lett.

Opt. Rev.

Y. Ishii, “Wavelength-tunable laser-diode interferometer,” Opt. Rev. 6, 273–283 (1999).
[CrossRef]

A. Yamamoto, C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, and H. Tashiro, “Surface shape by wavelength scanning interferometry using an electrically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
[CrossRef]

Other

D. J. Whitehouse, Handbook of Surface and Nanometrology (Taylor & Francis, 2011).

N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent 4,340,306 (4February1980).

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Figures (10)

Fig. 1.
Fig. 1.

Schematic drawing of a wavelength scanning surface measurement system. AOTF, acousto-optic tunable filter; DAQ, data acquisition card; BS, beam-splitter; and PC, personal computer.

Fig. 2.
Fig. 2.

Interference pattern obtained from a single pixel.

Fig. 3.
Fig. 3.

Fourier power spectral density for different heights.

Fig. 4.
Fig. 4.

Fourier power spectral density for 7490 nm single point height. The dotted curve is the fitted FFT spectrum.

Fig. 5.
Fig. 5.

Interference pattern analysis: (a) corrected interference pattern; (b) phase distribution with discontinuities; (c) 2π stair step function; (d) corrected phase distribution; and (e) fitted phase distribution.

Fig. 6.
Fig. 6.

Convolution output.

Fig. 7.
Fig. 7.

Areal measurement of 4.707 μm step-height standard sample using different algorithms (a) algorithm A; (b) algorithm B; (c) algorithm C; and (d) algorithm D.

Fig. 8.
Fig. 8.

Measurement of 100 nm standard step sample using algorithm B: (a) areal measurement and (b) cross section profile.

Fig. 9.
Fig. 9.

Measurement of 100 nm standard step sample using algorithm C: (a) areal measurement and (b) cross section profile.

Fig. 10.
Fig. 10.

Measurement of 100 nm standard step sample by using algorithm D: (a) areal measurement and (b) cross section profile.

Tables (1)

Tables Icon

Table 1. Measurement Results of a 4.707 μm Step-Height Standard Using the Four Different Algorithmsa

Equations (20)

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

λ=αΔnvafa,
Ixy(λ)=axy(λ)+bxy(λ)cos(ϕxy(λ)),
Δφxy(λ)=4πλshxy,
λs=λmaxλminλmaxλmin.
hxy=Δφλs4π.
δh=δφλs4π,
δh=λs2.
f(x)=ax2+bx+c,
x=b/(2a).
Ixy(i)=axy(i)+12bxyejφ(i)12bxyejφ(i).
Ixy(i)=axy+cxy+cxy*.
FFT[Ixy]=A(f)+C(ffo)+C*(f+fo).
ln(bxyejφ(i))=ln(bxy)+jφ(i).
δφ=2π(N+ε)F,
δh=(N+εF)λs2.
f(x)={10<xB1B<x2B,
h=Npk12(1λm1λn),
h1=(Npk1)2λm2+λmΔλΔλ.
h2=(Npk1)2λm2+λm(Δλδλ)(Δλδλ).
δh=(Npk1)2λm22δλΔλ(Δλδλ).

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