Abstract

A fast ferroelectric liquid-crystal spatial light modulator, originally developed for optical computing, has found a new application in vibrometry. A new scheme of vibration-synchronized double-exposure holographic interferometry is proposed that makes full use of the speed of the ferroelectric liquid-crystal spatial light modulator. Preliminary experiments were performed that demonstrate virtually continuous real-time vibrometric data acquisition.

© 1998 Optical Society of America

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References

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  1. See, for example, C. S. Vikram, “Study of vibrations,” in Holographic InterferometryP. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), pp. 293–318; T. Kreis, Holographic Interferometry (Akademie-Verlag, Berlin, 1996), pp. 198–207.
  2. S. Nakadate, M. Isshiki, “Real-time vibration measurement by a spatial phase-shifting technique with a tilted holographic interferogram,” Appl. Opt. 36, 281–284 (1997).
    [CrossRef] [PubMed]
  3. R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
    [CrossRef]
  4. Y. Kobayashi, T. Takemori, N. Mukozaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
    [CrossRef] [PubMed]
  5. S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–797 (1991).
    [CrossRef]
  6. T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystal,” Opt. Quantum Electron. 24, 1151–1163 (1992).
    [CrossRef]
  7. H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
    [CrossRef]
  8. See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), pp. 435–437.
  9. 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]
  10. D. J. Bone, H.-A. Bachor, R. J. Sandeman, “Fringe-pattern analysis using 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
    [CrossRef] [PubMed]
  11. C. Roddier, F. Roddier, “Interferogram analysis using Fourier transform techniques,” Appl. Opt. 26, 1668–1673 (1987).
    [CrossRef] [PubMed]
  12. T. Kreis, “Digital holographic interference phase measurement using the Fourier transform method,” J. Opt. Soc. Am. A 3, 847–855 (1986).
    [CrossRef]

1997 (1)

1995 (1)

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

1994 (2)

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Y. Kobayashi, T. Takemori, N. Mukozaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
[CrossRef] [PubMed]

1992 (1)

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystal,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

1991 (1)

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–797 (1991).
[CrossRef]

1987 (1)

1986 (2)

1982 (1)

Bachor, H.-A.

Black, T. D.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Bone, D. J.

Burckhardt, C. B.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), pp. 435–437.

Collier, R. J.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), pp. 435–437.

Fukushima, S.

Y. Kobayashi, T. Takemori, N. Mukozaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
[CrossRef] [PubMed]

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystal,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–797 (1991).
[CrossRef]

Haflz, A.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Haji-Sheikh, A.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Hara, T.

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

Ina, H.

Isshiki, M.

Kobayashi, S.

Kobayashi, Y.

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

Y. Kobayashi, T. Takemori, N. Mukozaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
[CrossRef] [PubMed]

Konecni, S.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Kreis, T.

Kurokawa, T.

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystal,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–797 (1991).
[CrossRef]

Lin, L. H.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), pp. 435–437.

Magnusson, R.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Mukozaka, N.

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

Y. Kobayashi, T. Takemori, N. Mukozaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
[CrossRef] [PubMed]

Nakadate, S.

Ohno, M.

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–797 (1991).
[CrossRef]

Ohno, T.

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

Roddier, C.

Roddier, F.

Sandeman, R. J.

Takeda, M.

Takemori, T.

Tello, L. N.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Toyoda, H.

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

Vikram, C. S.

See, for example, C. S. Vikram, “Study of vibrations,” in Holographic InterferometryP. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), pp. 293–318; T. Kreis, Holographic Interferometry (Akademie-Verlag, Berlin, 1996), pp. 198–207.

Wang, X.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Wilson, D. R.

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Yoshida, N.

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

Y. Kobayashi, T. Takemori, N. Mukozaka, N. Yoshida, S. Fukushima, “Real-time velocity measurement by the use of a speckle-pattern correlation system that incorporates a ferroelectric liquid-crystal spatial light modulator,” Appl. Opt. 33, 2785–2794 (1994).
[CrossRef] [PubMed]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–797 (1991).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

H. Toyoda, Y. Kobayashi, N. Mukozaka, N. Yoshida, T. Hara, T. Ohno, “Frame-rate displacement measurement system utilizing an ultra-fast-speed shutter camera and an optical correlator,” IEEE Trans. Instrum. Meas. 44, 755–757 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

R. Magnusson, X. Wang, A. Haflz, T. D. Black, L. N. Tello, A. Haji-Sheikh, S. Konecni, D. R. Wilson, “Experiments with photorefractive crystals for holographic interferometry,” Opt. Eng. 33, 596–607 (1994).
[CrossRef]

Opt. Quantum Electron. (1)

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystal,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

Other (2)

See, for example, C. S. Vikram, “Study of vibrations,” in Holographic InterferometryP. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), pp. 293–318; T. Kreis, Holographic Interferometry (Akademie-Verlag, Berlin, 1996), pp. 198–207.

See, for example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, San Diego, Calif., 1971), pp. 435–437.

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Figures (8)

Fig. 1
Fig. 1

(a) Structure and (b) signal time chart of FLC-SLM.

Fig. 2
Fig. 2

Experimental setup.

Fig. 3
Fig. 3

PZT disk with a micromirror attached to its center. Only the small area indicated by the white circle is illuminated with the laser beam.

Fig. 4
Fig. 4

Signal time charts.

Fig. 5
Fig. 5

Fringe contours generated by a lensless Fourier transform hologram recorded with a double-exposure interval of T1 = 1.7 ms and a triggering timing of T2 = 1.4 ms: (a) no vibration, (b) a 74-V (peak-to-valley) driving voltage applied to the PZT, and (c) a 140-V (peak-to-valley) driving voltage applied to the PZT. The vibration cycle and the FLC-SLM’s refresh cycle have the same period of T = 6.2 ms.

Fig. 6
Fig. 6

Fourier fringe analysis to extract the phase from a fringe pattern obtained through SLM-based vibration-synchronized holographic interferometry: (a) contour fringe pattern, (b) Fourier spectra of the fringe pattern, (c) filtered spectrum, and (d) phase distribution.

Fig. 7
Fig. 7

(a) Fringe signal from a Michelson interferometer, and (b) displacement of the mirror obtained with Fourier fringe analysis.

Fig. 8
Fig. 8

Mirror displacement plotted against fringe spatial frequency. The line shows a least-squares fit.

Equations (15)

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g H x ,   y ;   t 1 ,   t 2 = a H x ,   y ;   t 1 ,   t 2 + b H x ,   y ;   t 1 ,   t 2 × cos Δ ϕ H x ,   y ;   t 1 ,   t 2 ,
Δ ϕ H x ,   y ;   t 1 ,   t 2 = k s 1 - s 2 · n Δ h x ,   y ;   t 1 ,   t 2 ,
G H f x ,   f y ;   t 1 ,   t 2 = - -   g H x ,   y ;   t 1 ,   t 2 × exp - 2 π i f x x + f y y d x d y
= A H f x ,   f y ;   t 1 ,   t 2 + C H f x ,   f y ;   t 1 ,   t 2 + C H * - f x ,   - f y ;   t 1 ,   t 2 ,
c H x ,   y ;   t 1 ,   t 2 = 1 / 2 b H x ,   y ;   t 1 ,   t 2 × exp i Δ ϕ H x ,   y ;   t 1 ,   t 2 .
Δ ϕ H x ,   y ;   t 1 ,   t 2 = tan - 1 Im c H x ,   y ;   t 1 ,   t 2 Re c H x ,   y ;   t 1 ,   t 2 ,
g M t = a M + b M   cos ϕ M t ,
Δ ϕ M t 1 ,   t 2 = ϕ M t 2 - ϕ M t 1
= 2 k Δ h x c ,   y c ;   t 1 ,   t 2 ,
Δ h r ;   t 1 ,   t 2 = R - r R   Δ h 0 ;   t 1 ,   t 2 ,
Δ ϕ H r ;   t 1 ,   t 2 = k s 1 - s 2 · n Δ h 0 ;   t 1 ,   t 2 1 - r R .
f r ;   t 1 ,   t 2     - 1 2 π d d r Δ ϕ H r ;   t 1 ,   t 2
= 1 λ R s 1 - s 2 · n Δ h 0 ;   t 1 ,   t 2 .
Δ h 0 ;   t 1 ,   t 2 = α f r ;   t 1 ,   t 2 ,
α = λ R s 1 - s 2 · n .

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