Abstract

The maximum measurable range of a spectral interference microscope depends on the coherence length of the light transmitted by its tunable spectral filter. To achieve a large range in step-height measurement we have developed a new tunable spectral filter that uses tandem liquid-crystal Fabry-Perot interferometers (LC-FPIs), which can simultaneously attain both a high spectral resolution and a large tuning range. Fringe visibility measurements were carried out, and it was found that the coherence length of the light transmitted through tandem LC-FPIs is two times larger than that transmitted through a single LC-FPI. Using this novel tunable spectral filter, we developed a new spectral interference microscope for the measurement of three-dimensional shapes of discontinuous objects. Experimental results of step-height measurements both with a single LC-FPI and with tandem LC-FPIs are presented for a combination of standard steel gauge block sets with 1-, 99-, and 100-µm steps. A large range (1–100 µm) of measurement with submicrometer resolution was achieved with tandem LC-FPIs that was not possible with our previous system in which a single LC-FPI was used.

© 2003 Optical Society of America

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References

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  1. M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, T. Kurokawa, “Optical frequency-domain microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device,” Appl. Opt. 38, 7063–7068 (1999).
    [CrossRef]
  2. M. Takeda, H. Ina, S. Kobayashi, “Fourier transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  3. B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
    [CrossRef] [PubMed]
  4. T. Dressel, G. Hausler, H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt. 31, 919–925 (1992).
    [CrossRef]
  5. L. Deck, P. De Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
    [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).
  9. H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
    [CrossRef]
  10. S. Kuwamura, I. Yamaguchi, “Wavelength scanning profilometry for real-time surface shape measurement,” Appl. Opt. 36, 4473–4482 (1997).
    [CrossRef] [PubMed]
  11. A. Yamamoto, C. C. Kuo, K. Sunouchi, S. Wada, I. Yamaguchi, H. Tashiro, “Surface shape measurement by wavelength scanning interferometry using an electronically tuned Ti:sapphire laser,” Opt. Rev. 8, 59–63 (2001).
    [CrossRef]
  12. D. S. Mehta, M. Sugai, H. Hinosugi, S. Saito, M. Takeda, T. Kurokawa, H. Takahashi, M. Ando, M. Shishido, T. Yoshizawa, “Simultaneous three-dimensional step-height measurement and high-resolution tomographic imaging using spectral interferometric microscope,” Appl. Opt. 41, 3874–3885 (2002).
    [CrossRef] [PubMed]
  13. K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable wavelength-selective liquid-crystal filters for 600-channel FDM system,” IEEE Photon. Technol. Lett. 4, 597–599 (1992).
    [CrossRef]
  14. J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
    [CrossRef]
  15. K. Hirabayashi, H. Tsuda, T. Kurokawa, “Narrow-band tunable wavelength-selective filters of Fabry-Perot interferometers with a liquid crystal intracavity,” IEEE Photon. Technol. Lett. 3, 213–215 (1991).
    [CrossRef]
  16. H. Tsuda, K. Hirabayashi, T. Tohmori, T. Kurokawa, “Tunable light source using a liquid-crystal Fabry-Perot interferometer,” IEEE Photon. Technol. Lett. 3, 504–506 (1991).
    [CrossRef]
  17. K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable liquid-crystal Fabry-Perot interferometer filter for wavelength-division multiplexing communication systems,” J. Lightwave Technol. 11, 2033–2043 (1993).
    [CrossRef]
  18. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1999), Chap. 10, p. 175.

2002 (1)

2001 (1)

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

1999 (1)

1997 (2)

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

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

1996 (1)

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

1994 (2)

1993 (1)

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable liquid-crystal Fabry-Perot interferometer filter for wavelength-division multiplexing communication systems,” J. Lightwave Technol. 11, 2033–2043 (1993).
[CrossRef]

1992 (2)

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable wavelength-selective liquid-crystal filters for 600-channel FDM system,” IEEE Photon. Technol. Lett. 4, 597–599 (1992).
[CrossRef]

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

1991 (3)

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]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Narrow-band tunable wavelength-selective filters of Fabry-Perot interferometers with a liquid crystal intracavity,” IEEE Photon. Technol. Lett. 3, 213–215 (1991).
[CrossRef]

H. Tsuda, K. Hirabayashi, T. Tohmori, T. Kurokawa, “Tunable light source using a liquid-crystal Fabry-Perot interferometer,” IEEE Photon. Technol. Lett. 3, 504–506 (1991).
[CrossRef]

1990 (2)

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
[CrossRef]

B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
[CrossRef] [PubMed]

1982 (1)

Ando, M.

Andreadakis, N.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
[CrossRef]

Barnes, T. H.

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

Berreman, D. W.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1999), Chap. 10, p. 175.

De Groot, P.

Deck, L.

Dressel, T.

Eiju, T.

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

Franze, B.

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Haible, P.

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Hausler, G.

Hinosugi, H.

Hirabayashi, K.

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable liquid-crystal Fabry-Perot interferometer filter for wavelength-division multiplexing communication systems,” J. Lightwave Technol. 11, 2033–2043 (1993).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable wavelength-selective liquid-crystal filters for 600-channel FDM system,” IEEE Photon. Technol. Lett. 4, 597–599 (1992).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Narrow-band tunable wavelength-selective filters of Fabry-Perot interferometers with a liquid crystal intracavity,” IEEE Photon. Technol. Lett. 3, 213–215 (1991).
[CrossRef]

H. Tsuda, K. Hirabayashi, T. Tohmori, T. Kurokawa, “Tunable light source using a liquid-crystal Fabry-Perot interferometer,” IEEE Photon. Technol. Lett. 3, 504–506 (1991).
[CrossRef]

Ina, H.

Kinoshita, M.

Kobayashi, S.

Kuo, C. C.

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

Kurokawa, T.

D. S. Mehta, M. Sugai, H. Hinosugi, S. Saito, M. Takeda, T. Kurokawa, H. Takahashi, M. Ando, M. Shishido, T. Yoshizawa, “Simultaneous three-dimensional step-height measurement and high-resolution tomographic imaging using spectral interferometric microscope,” Appl. Opt. 41, 3874–3885 (2002).
[CrossRef] [PubMed]

M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, T. Kurokawa, “Optical frequency-domain microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device,” Appl. Opt. 38, 7063–7068 (1999).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable liquid-crystal Fabry-Perot interferometer filter for wavelength-division multiplexing communication systems,” J. Lightwave Technol. 11, 2033–2043 (1993).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable wavelength-selective liquid-crystal filters for 600-channel FDM system,” IEEE Photon. Technol. Lett. 4, 597–599 (1992).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Narrow-band tunable wavelength-selective filters of Fabry-Perot interferometers with a liquid crystal intracavity,” IEEE Photon. Technol. Lett. 3, 213–215 (1991).
[CrossRef]

H. Tsuda, K. Hirabayashi, T. Tohmori, T. Kurokawa, “Tunable light source using a liquid-crystal Fabry-Perot interferometer,” IEEE Photon. Technol. Lett. 3, 504–506 (1991).
[CrossRef]

Kuwamura, S.

Lee, B. S.

Lin, C.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
[CrossRef]

Matsuda, K.

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

Mehta, D. S.

Patel, J. S.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
[CrossRef]

Saifi, M. A.

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
[CrossRef]

Saito, S.

Shishido, M.

Strand, T. C.

Suematsu, M.

Sugai, M.

Sunouchi, K.

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

Takahashi, H.

Takeda, M.

Tashiro, H.

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

Tiziani, H. J.

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

Tohmori, T.

H. Tsuda, K. Hirabayashi, T. Tohmori, T. Kurokawa, “Tunable light source using a liquid-crystal Fabry-Perot interferometer,” IEEE Photon. Technol. Lett. 3, 504–506 (1991).
[CrossRef]

Tsuda, H.

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable liquid-crystal Fabry-Perot interferometer filter for wavelength-division multiplexing communication systems,” J. Lightwave Technol. 11, 2033–2043 (1993).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable wavelength-selective liquid-crystal filters for 600-channel FDM system,” IEEE Photon. Technol. Lett. 4, 597–599 (1992).
[CrossRef]

H. Tsuda, K. Hirabayashi, T. Tohmori, T. Kurokawa, “Tunable light source using a liquid-crystal Fabry-Perot interferometer,” IEEE Photon. Technol. Lett. 3, 504–506 (1991).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Narrow-band tunable wavelength-selective filters of Fabry-Perot interferometers with a liquid crystal intracavity,” IEEE Photon. Technol. Lett. 3, 213–215 (1991).
[CrossRef]

Venzke, H.

Wada, S.

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

Watanabe, Y.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1999), Chap. 10, p. 175.

Yago, H.

Yamaguchi, I.

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

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

Yamamoto, A.

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

Yamamoto, H.

Yoshizawa, T.

Appl. Opt. (8)

B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
[CrossRef] [PubMed]

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

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

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]

M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, T. Kurokawa, “Optical frequency-domain microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device,” Appl. Opt. 38, 7063–7068 (1999).
[CrossRef]

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

D. S. Mehta, M. Sugai, H. Hinosugi, S. Saito, M. Takeda, T. Kurokawa, H. Takahashi, M. Ando, M. Shishido, T. Yoshizawa, “Simultaneous three-dimensional step-height measurement and high-resolution tomographic imaging using spectral interferometric microscope,” Appl. Opt. 41, 3874–3885 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. S. Patel, M. A. Saifi, D. W. Berreman, C. Lin, N. Andreadakis, “An electrically tunable optical filter for infra-red wavelength using liquid crystals in a Fabry-Perot etalon,” Appl. Phys. Lett. 57, 1718–1720 (1990).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Narrow-band tunable wavelength-selective filters of Fabry-Perot interferometers with a liquid crystal intracavity,” IEEE Photon. Technol. Lett. 3, 213–215 (1991).
[CrossRef]

H. Tsuda, K. Hirabayashi, T. Tohmori, T. Kurokawa, “Tunable light source using a liquid-crystal Fabry-Perot interferometer,” IEEE Photon. Technol. Lett. 3, 504–506 (1991).
[CrossRef]

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable wavelength-selective liquid-crystal filters for 600-channel FDM system,” IEEE Photon. Technol. Lett. 4, 597–599 (1992).
[CrossRef]

J. Lightwave Technol. (1)

K. Hirabayashi, H. Tsuda, T. Kurokawa, “Tunable liquid-crystal Fabry-Perot interferometer filter for wavelength-division multiplexing communication systems,” J. Lightwave Technol. 11, 2033–2043 (1993).
[CrossRef]

J. Mod. Opt. (1)

H. J. Tiziani, B. Franze, P. Haible, “Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser,” J. Mod. Opt. 44, 1485–1496 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Rev. (1)

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

Optik (1)

T. H. Barnes, T. Eiju, K. Matsuda, “Rough surface profile measurement using speckle optical frequency domain reflectometry with an external cavity tunable diode laser,” Optik 103, 93–100 (1996).

Other (1)

M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1999), Chap. 10, p. 175.

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Figures (10)

Fig. 1
Fig. 1

Structure of two stacked LC-FPIs, the top LC-FPI with a large cavity gap and the bottom LC-FPI with a small cavity gap. At the right are the results of simulation of the transmission spectra of the respective LC-FPIs. Bottom right, the transmission spectrum of the tandem LC-FPIs.

Fig. 2
Fig. 2

(a) Optical setup for measuring the spectrum of the tandem LC-FPIs: PBS, polarizing beam splitter; BS, beam splitter; other abbreviations defined in text. (b) Measured spectra of curve (a) the SLD, curve (b) LC-FPI1, curve (c) LC-FPI2, and curve (d) the tandem LC-FPIs.

Fig. 3
Fig. 3

Schematic of the experimental setup for measuring three-dimensional step height by use of tandem LC-FPIs: PBS, polarizing beam splitter; PD, photodetector; BS’s, beam splitters; GG, ground glass; other abbreviations defined in text.

Fig. 4
Fig. 4

Interference fringe patterns obtained by use of (a) single LC-FPI2 and (b) the tandem LC-FPIs and the corresponding Fourier spectra obtained by use of (c) single LC-FPI2 and (d) the tandem LC-FPIs.

Fig. 5
Fig. 5

Interference fringe visibility versus optical path difference.

Fig. 6
Fig. 6

Sketch of the object structure, illustrating three height steps, 1, 99, and 100 µm, formed with standard steel gauge block sets.

Fig. 7
Fig. 7

Example of interference fringe patterns of gauge block sets obtained with (a) single LC-FPI2 and (b) the tandem LC-FPIs. (c), (d) Cross-sectional fringe intensity distributions for (a) and (b), respectively.

Fig. 8
Fig. 8

(a) Comparison of temporal interference fringe signal at an arbitrarily chosen pixel on the top of gauge block [indicated by C in Figs. 7(a) and 7(b)] with 100-µm step height, where the dotted curve is for single LC-FPI2 and the solid curve is for the tandem LC-FPIs. (b) Fourier spectra of the corresponding temporal fringe signals.

Fig. 9
Fig. 9

Comparison of phase profiles of temporal interference fringe signals across a line along the x axis on the top of the gauge block indicated by C in Fig. 7: (a) for single LC-FPI2 and (b) for the tandem LC-FPIs.

Fig. 10
Fig. 10

Three-dimensional object structures obtained with (a) single LC-FPI2 and (b) the tandem LC-FPIs.

Tables (1)

Tables Icon

Table 1 Comparison of Step-Height Measurements with Single LC-FPI2 and the Tandem LC-FPIsa

Equations (4)

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TFV, k=1-R21-R2+4R sin2nVLk,
Vτ=Imax-IminImax+Imin=2I1I2I1+I2 |γτ|,
gx, y; τ=I1+I21+Vτcos2πf0xx+f0yy+ϕ0,
Gfx, fy; τ=I1+I2δfx, fy+½Vτδfx-f0x, fy-f0y+½Vτδfx+f0x, fy+f0y,

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