Abstract

Multiple-wavelength backpropagation interferometry based on a spectral interferometer is proposed for measuring thin glass sheets with nanometer accuracy. The multiwavelength backpropagation method introduced to the spectral interferometer eliminates time-encoded wavelength sweeping and mechanical scanning, which enables high-speed profile measurements. The applicability of the proposed method is experimentally demonstrated through cross-sectional profile and vibrating surface displacement measurements of a glass sheet.

© 2013 Optical Society of America

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References

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2012 (1)

2007 (3)

P. Bu, X. Wang, and O. Sasaki, “Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” Opt. Eng. 46, 105603 (2007).
[Crossref]

P. Bu, X. Wang, and O. Sasaki, “Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” J. Opt. A 9, 422–426 (2007).
[Crossref]

O. Sasaki, H. Tai, and T. Suzuki, “Step-profile measurement by backpropagation of multiple-wavelength optical field,” Opt. Lett. 32, 2683–2685 (2007).
[Crossref]

2006 (1)

2003 (1)

1999 (1)

1998 (1)

G. Hausler and M. W. Lindner, “‘Coherence radar’ and ‘spectral radar’-new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–23 (1998).
[Crossref]

1995 (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[Crossref]

1994 (1)

1988 (1)

1986 (1)

1979 (1)

Bajraszewski, T.

Bu, P.

P. Bu, X. Wang, and O. Sasaki, “Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” Opt. Eng. 46, 105603 (2007).
[Crossref]

P. Bu, X. Wang, and O. Sasaki, “Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” J. Opt. A 9, 422–426 (2007).
[Crossref]

Cobb, M. J.

de Groot, P.

Deck, L.

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[Crossref]

Fercher, A. F.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[Crossref]

Hausler, G.

G. Hausler and M. W. Lindner, “‘Coherence radar’ and ‘spectral radar’-new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–23 (1998).
[Crossref]

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[Crossref]

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[Crossref]

Kim, G. H.

Kim, S. W.

Kowalczyk, A.

Lee, C. C.

Li, M. C.

Li, X.

Lindner, M. W.

G. Hausler and M. W. Lindner, “‘Coherence radar’ and ‘spectral radar’-new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–23 (1998).
[Crossref]

MacDonald, D. J.

Okazaki, H.

Post, D.

Ren, H.

Sasaki, O.

P. Bu, X. Wang, and O. Sasaki, “Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” Opt. Eng. 46, 105603 (2007).
[Crossref]

P. Bu, X. Wang, and O. Sasaki, “Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” J. Opt. A 9, 422–426 (2007).
[Crossref]

O. Sasaki, H. Tai, and T. Suzuki, “Step-profile measurement by backpropagation of multiple-wavelength optical field,” Opt. Lett. 32, 2683–2685 (2007).
[Crossref]

O. Sasaki and K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27, 4139–4142 (1988).
[Crossref]

O. Sasaki and H. Okazaki, “Analysis of measurement accuracy in sinusoidal phase modulating interferometry,” Appl. Opt. 25, 3152–3158 (1986).
[Crossref]

Sun, T.

Suzuki, T.

Tai, H.

Takahashi, K.

Targowski, P.

Wan, D. S.

Wang, X.

P. Bu, X. Wang, and O. Sasaki, “Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” J. Opt. A 9, 422–426 (2007).
[Crossref]

P. Bu, X. Wang, and O. Sasaki, “Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” Opt. Eng. 46, 105603 (2007).
[Crossref]

Wojtkowski, M.

Appl. Opt. (6)

J. Biomed. Opt. (1)

G. Hausler and M. W. Lindner, “‘Coherence radar’ and ‘spectral radar’-new tools for dermatological diagnosis,” J. Biomed. Opt. 3, 21–23 (1998).
[Crossref]

J. Opt. A (1)

P. Bu, X. Wang, and O. Sasaki, “Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” J. Opt. A 9, 422–426 (2007).
[Crossref]

Opt. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117, 43–48 (1995).
[Crossref]

Opt. Eng. (1)

P. Bu, X. Wang, and O. Sasaki, “Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry,” Opt. Eng. 46, 105603 (2007).
[Crossref]

Opt. Lett. (3)

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Figures (7)

Fig. 1.
Fig. 1.

Spectral interferometer using MWB interferometer. SLD, superluminescent laser diode; OL, object lens; CL, cylindrical lens; PZT, piezoelectric transducer; M, mirrors; L, lenses; BS, beam splitter; G, grating; PL, projection lens; P, surfaces.

Fig. 2.
Fig. 2.

Interference amplitude and phase distributions reconstructed by the backpropagated optical field of multiple wavenumbers for a glass sheet including two reflecting surfaces.

Fig. 3.
Fig. 3.

Simulated measurement error caused by the overlapping of the optical fields reflecting from two surfaces in the case of P=2.

Fig. 4.
Fig. 4.

(a) Amplitude distribution of the reconstructed field U(LB) and (b) its distribution along the depth direction at y=0.48 mm in (a).

Fig. 5.
Fig. 5.

Amplitude and phase distributions near the peak positions shown in Fig. 4(b). (a) Front surface, p=1 and (b) rear surface, p=2.

Fig. 6.
Fig. 6.

Measured profiles of (a) front, (b) rear surfaces, and (c) optical thickness distribution of the glass sheet along the y axis.

Fig. 7.
Fig. 7.

Measured time-varying surface profiles of a glass plate vibrating at a frequency of 15 Hz: (a) front surface and (b) rear surface.

Equations (3)

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S(k,t)=A(km)+B(km)cos[ϕ(km)+Zcos(2πfct)],
Up(LB)=m=1MB(km)exp{jϕ(km)j2πkmLB}=m=1MB(km)exp{j2πkm(LpLB)}=|Up(LB)|exp{jΦp(LB)},
U(LB)=p=1PUp(LB)=p=1P|Up(LB)|exp{jΦp(LB)}=|U(LB)|exp{jΦ(LB)},

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