Abstract

A two-wavelength moire phase-shifting interferometer that uses a superimposed grating has been developed. The optical phase shifts for the two wavelengths are given by digital phase shifts of a superimposed grating displayed on a liquid-crystal spatial light modulator. A phase shift of the moire fringe is achieved by equal phase shifts with opposite signs in the two gratings. A moire phase-shifting interferometer with no moving parts and no requirement for calibration of the value of the phase shifts was obtained. Our experimental result shows measurements of the profile of a step object with a 2.65-μm synthetic wavelength.

© 2005 Optical Society of America

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References

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2003 (1)

2002 (1)

1999 (2)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

1997 (1)

R. Onodera, Y. Ishii, “Fourier description of the phase-measuring process in two-wavelength phase-shifting interferometry,” Opt. Commun. 137, 27–30 (1997).
[CrossRef]

1996 (1)

1994 (1)

1991 (1)

1988 (2)

1987 (2)

1985 (1)

1984 (1)

1973 (1)

Bitou, Y.

Chen, J.

Cheng, Y.-Y.

Creath, K.

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland/Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

Dandliker, R.

den Boef, A. J.

Fercher, A. F.

Hara, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Hu, H. Z.

Igasaki, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Inoue, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Ishii, Y.

Iwasaki, S.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

Kobayashi, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Li, F.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Maier, N.

Matsumoto, H.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

Mukohzaka, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Murata, K.

Ohnishi, J.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

Onodera, R.

Polhemus, C.

Prongué, D.

Rothe, A.

Sasaki, O.

Seta, K.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

Suzuki, N.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

Suzuki, T.

Thalmann, R.

Tiziani, H. J.

Toyoda, H.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Vry, U.

Wyant, J. C.

Yazawa, T.

Yokoyama, S.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

Yoshida, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Appl. Opt. (8)

Meas. Sci. Technol. (1)

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239 (1999).
[CrossRef]

Opt. Commun. (1)

R. Onodera, Y. Ishii, “Fourier description of the phase-measuring process in two-wavelength phase-shifting interferometry,” Opt. Commun. 137, 27–30 (1997).
[CrossRef]

Opt. Lett. (4)

Opt. Rev. (1)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev. 6, 339–344 (1999).
[CrossRef]

Other (1)

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland/Elsevier, Amsterdam, 1988), Vol. 26, pp. 349–393.
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic setup for the two-wavelength moire PSI with the LCD-coupled PAL-SLM. Abbreviations are defined in text.

Fig. 2
Fig. 2

Spatial variation of the phase-modulation level of the displayed pattern (superimposed grating).

Fig. 3
Fig. 3

Diffraction patterns of the superimposed grating for wavelengths (a) λ1 and (b) λ2.

Fig. 4
Fig. 4

Four moire fringe patterns of the mirror surface observed at additional phase shifts of (a) 0, (b) π/2, (c) π, and (d) 3π/2.

Fig. 5
Fig. 5

Three-dimensional phase map of the step-height object made by use of a four-step algorithm.

Equations (4)

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d 1 d 2 = λ 1 λ 2 ,
I 1 = A 1 + B 1 cos [ 4 π W ( x ,     y ) / λ 1 + Φ 1 + ϕ G 1 ] ,
I 2 = A 2 + B 2 cos [ 4 π W ( x ,     y ) / λ 2 + Φ 2 + ϕ G 2 ] ,
i = a + b cos [ 2 π W ( x , y ) / Γ + Φ ] cos [ 2 π W ( x , y ) / Λ + θ + ϕ G 1 ] ,

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