Abstract

A new signal processing system for real time displacement measurement in sinusoidal phase modulating interferometry is described. Although sinusoidal phase modulating interferometry is effective in measuring with high accuracy the displacement of an object, conventional signal processing takes a long time. In this method, detection of the object's displacement is easily achieved by sampling the interference signal at those times that satisfy certain conditions and by processing the sampled signals with electric circuits in real time. The delay time of this signal processing system is <45 μs.

© 1989 Optical Society of America

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References

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  1. G. E. Sommargren, “Optical Heterodyne Profilometry,” Appl. Opt. 20, 610–618 (1981).
    [CrossRef] [PubMed]
  2. S. Ueha, K. Shiota, T. Okada, J. Tsujiuchi, “Optical Heterodyne Measurement of In-Plane Vibrations,” Opt. Commun. 10, 88–90 (1974).
    [CrossRef]
  3. W. Puschert, “Optical Detection of Amplitude and Phase of Mechanical Displacements in the Angstrom Range,” Opt. Commun. 10, 357–361 (1974).
    [CrossRef]
  4. N. A. Massie, R. D. Nelson, S. Holly, “High-Performance Real-Time Heterodyne Interferometry,” Appl. Opt. 18, 1797–1803 (1979).
    [CrossRef] [PubMed]
  5. N. A. Massie, “Real-Time Digital Heterodyne Interferometry: A System,” Appl. Opt. 19, 154–160 (1980).
    [CrossRef] [PubMed]
  6. O. Sasaki, T. Yagiuchi, “Sinusoidal Phase Modulating Interferometry,” Jpn. J. Opt. 15, 25–30 (1986).
  7. O. Sasaki, H. Okazaki, “Analysis of Measurement Accuracy in Sinusoidal Phase Modulating Interferometry,” Appl. Opt. 25, 3152–3158 (1986).
    [CrossRef] [PubMed]
  8. O. Sasaki, K. Takahashi, “Sinusoidal Phase Modulating Interferometer using Optical Fibers for Displacement Measurement,” Appl. Opt. 27, 4139–4142 (1988).
    [CrossRef] [PubMed]
  9. O. Sasaki, K. Takahashi, “Real-Time Interferometric Displacement Measurement by Fiber-Optic Sinusoidal Phase-Modulation,” Jpn. J. Opt. 17, 472–476 (1988).

1988 (2)

O. Sasaki, K. Takahashi, “Sinusoidal Phase Modulating Interferometer using Optical Fibers for Displacement Measurement,” Appl. Opt. 27, 4139–4142 (1988).
[CrossRef] [PubMed]

O. Sasaki, K. Takahashi, “Real-Time Interferometric Displacement Measurement by Fiber-Optic Sinusoidal Phase-Modulation,” Jpn. J. Opt. 17, 472–476 (1988).

1986 (2)

O. Sasaki, T. Yagiuchi, “Sinusoidal Phase Modulating Interferometry,” Jpn. J. Opt. 15, 25–30 (1986).

O. Sasaki, H. Okazaki, “Analysis of Measurement Accuracy in Sinusoidal Phase Modulating Interferometry,” Appl. Opt. 25, 3152–3158 (1986).
[CrossRef] [PubMed]

1981 (1)

1980 (1)

1979 (1)

1974 (2)

S. Ueha, K. Shiota, T. Okada, J. Tsujiuchi, “Optical Heterodyne Measurement of In-Plane Vibrations,” Opt. Commun. 10, 88–90 (1974).
[CrossRef]

W. Puschert, “Optical Detection of Amplitude and Phase of Mechanical Displacements in the Angstrom Range,” Opt. Commun. 10, 357–361 (1974).
[CrossRef]

Holly, S.

Massie, N. A.

Nelson, R. D.

Okada, T.

S. Ueha, K. Shiota, T. Okada, J. Tsujiuchi, “Optical Heterodyne Measurement of In-Plane Vibrations,” Opt. Commun. 10, 88–90 (1974).
[CrossRef]

Okazaki, H.

Puschert, W.

W. Puschert, “Optical Detection of Amplitude and Phase of Mechanical Displacements in the Angstrom Range,” Opt. Commun. 10, 357–361 (1974).
[CrossRef]

Sasaki, O.

O. Sasaki, K. Takahashi, “Sinusoidal Phase Modulating Interferometer using Optical Fibers for Displacement Measurement,” Appl. Opt. 27, 4139–4142 (1988).
[CrossRef] [PubMed]

O. Sasaki, K. Takahashi, “Real-Time Interferometric Displacement Measurement by Fiber-Optic Sinusoidal Phase-Modulation,” Jpn. J. Opt. 17, 472–476 (1988).

O. Sasaki, T. Yagiuchi, “Sinusoidal Phase Modulating Interferometry,” Jpn. J. Opt. 15, 25–30 (1986).

O. Sasaki, H. Okazaki, “Analysis of Measurement Accuracy in Sinusoidal Phase Modulating Interferometry,” Appl. Opt. 25, 3152–3158 (1986).
[CrossRef] [PubMed]

Shiota, K.

S. Ueha, K. Shiota, T. Okada, J. Tsujiuchi, “Optical Heterodyne Measurement of In-Plane Vibrations,” Opt. Commun. 10, 88–90 (1974).
[CrossRef]

Sommargren, G. E.

Takahashi, K.

O. Sasaki, K. Takahashi, “Real-Time Interferometric Displacement Measurement by Fiber-Optic Sinusoidal Phase-Modulation,” Jpn. J. Opt. 17, 472–476 (1988).

O. Sasaki, K. Takahashi, “Sinusoidal Phase Modulating Interferometer using Optical Fibers for Displacement Measurement,” Appl. Opt. 27, 4139–4142 (1988).
[CrossRef] [PubMed]

Tsujiuchi, J.

S. Ueha, K. Shiota, T. Okada, J. Tsujiuchi, “Optical Heterodyne Measurement of In-Plane Vibrations,” Opt. Commun. 10, 88–90 (1974).
[CrossRef]

Ueha, S.

S. Ueha, K. Shiota, T. Okada, J. Tsujiuchi, “Optical Heterodyne Measurement of In-Plane Vibrations,” Opt. Commun. 10, 88–90 (1974).
[CrossRef]

Yagiuchi, T.

O. Sasaki, T. Yagiuchi, “Sinusoidal Phase Modulating Interferometry,” Jpn. J. Opt. 15, 25–30 (1986).

Appl. Opt. (5)

Jpn. J. Opt. (2)

O. Sasaki, K. Takahashi, “Real-Time Interferometric Displacement Measurement by Fiber-Optic Sinusoidal Phase-Modulation,” Jpn. J. Opt. 17, 472–476 (1988).

O. Sasaki, T. Yagiuchi, “Sinusoidal Phase Modulating Interferometry,” Jpn. J. Opt. 15, 25–30 (1986).

Opt. Commun. (2)

S. Ueha, K. Shiota, T. Okada, J. Tsujiuchi, “Optical Heterodyne Measurement of In-Plane Vibrations,” Opt. Commun. 10, 88–90 (1974).
[CrossRef]

W. Puschert, “Optical Detection of Amplitude and Phase of Mechanical Displacements in the Angstrom Range,” Opt. Commun. 10, 357–361 (1974).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Real time displacement measurement system with synchronous sampling of the sinusoidal phase modulated interference signal.

Fig. 2
Fig. 2

Values of min as a function of the vibration amplitude b for various values of the ratio ωdc.

Fig. 3
Fig. 3

Block diagram of a phase detector.

Fig. 4
Fig. 4

Sinusoidal vibrations measured through (a) the computer processing and (b) the real time signal processor proposed here.

Fig. 5
Fig. 5

Measured sinusoidal vibrations of f = 100 Hz. The amplitude of vibrations are (a) 20 nm and (b) 1.2 μm.

Fig. 6
Fig. 6

Measured (a) triangle vibration of f = 100 Hz and (b) rectangular vibration of f = 40 Hz.

Tables (2)

Tables Icon

Table I Phase Obtained from cosα

Tables Icon

Table II Corrections for the Phase α to Obtain a Continuous Value

Equations (11)

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

I m ( t ) = a cos ω c t .
S ( t ) = S 0 cos [ z cos ω c t + α ( t ) ] ,
α ( t ) = ( 4 π / λ 0 ) [ D 0 + r ( t ) ] .
S 1 ( t ) = cos [ z cos ω c t + α ( t ) ] .
S 1 ( t m ) = cos [ α ( t m ) ] ,
S 2 ( t ) = S 0 { z ω c sin ω c t + [ d α ( t ) / d t ] } × { sin [ z cos ω c t + α ( t ) ] } .
S 2 ( t m ) = ± S 0 sin [ α ( t m ) ] ,
= z ω c [ d α ( t ) / d t ] .
r ( t ) = b cos ω d t ,
min = z ω c 4 π b ω d / λ 0 .
α ( t m ) = a 1 + a 2 π ,

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