Abstract

Sinusoidal phase-modulating interferometry is used to detect exactly the sinusoidal phase variation of an interference signal even when the amplitude of the interference signal is varied by modulation of the injection current. We can easily provide a sinusoidal phase-modulating interferometer with a feedback control system that eliminates the phase fluctuations caused by mechanical vibrations. The methods using sinusoidal phase-modulating interferometry improve the resolution of distance measurements. Experimental results show that the thickness of gauge blocks is measured with a resolution of ∼0.5 μm.

© 1991 Optical Society of America

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References

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  1. C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
    [CrossRef]
  2. A. J. den Boef, “Two-Wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [CrossRef]
  3. G. Beheim, K. Fritsch, “Range finding using frequency-modulated laser diode,” Appl. Opt. 25, 1439–1442 (1986).
    [CrossRef] [PubMed]
  4. H. Kikuta, K. Iwata, R. Nagata, “Distance measurement by the wavelength shift of laser diode light,” Appl. Opt. 25, 2976–2980 (1986).
    [CrossRef] [PubMed]
  5. A. J. den Boef, “Interferometric laser rangefinder using a frequency modulated diode laser,” Appl. Opt. 26, 4545–4550 (1987).
    [CrossRef]
  6. O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
    [CrossRef] [PubMed]
  7. O. Sasaki, K. Takahashi, “Sinusoidal phase modulating interferometer using optical fibers for displacement measurement,” Appl. Opt. 27, 4139–4142 (1988).
    [CrossRef] [PubMed]

1988

1987

1986

Beheim, G.

den Boef, A. J.

Fritsch, K.

Iwata, K.

Kikuta, H.

Nagata, R.

Okazaki, H.

Sasaki, O.

Takahashi, K.

Wickramasinghe, H. K.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Williams, C. C.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Basic setup of a double SPM laser diode interferometer for distance measurements.

Fig. 2
Fig. 2

Experimental setup where the feedback control system is provided to eliminate phase fluctuations caused by mechanical vibrations.

Fig. 3
Fig. 3

Signal processing to obtain amplitude zb of the sinusoidal phase variation: (a) detected signal S(t) given by Eq. (4); (b) amplitude of the Fourier transform of signal S(t); (c) phase variation Φ(t) obtained from the frequency components of F1(ω) and F2(ω); (d) Fourier transform of the phase variation Φ(t).

Fig. 4
Fig. 4

Measured relationship between the optical path difference and the amplitude of the sinusoidal phase variation at b = 10 mA.

Fig. 5
Fig. 5

Measured relationship between the optical path difference and the amplitude of the sinusoidal phase variation at b = 5 mA.

Fig. 6
Fig. 6

Double SPM laser diode interferometer for thickness measurement of gauge blocks.

Tables (1)

Tables Icon

Table I Thickness Measurement Results of Gauge Blocks

Equations (12)

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g ( t ) = g 0 [ 1 + m cos ( w b t ) ] , λ ( t ) = λ 0 + β b cos ( ω b t ) ,
S ( t ) = g ( t ) + g ( t ) cos [ z c cos ( ω c t + θ ) + z b cos ( ω b t ) + α ] ,
z c = ( 4 π / λ 0 ) a , z b = ( 2 π β b / λ 0 2 ) Δ l , α = ( 2 π / λ 0 ) Δ l .
S ( t ) = g ( t ) cos [ z c cos ( ω c t + θ ) + Φ ( t ) ] .
S ( t ) = cos [ z c cos ( ω c t + θ ) + α ] .
S ( t ) = { g ( t ) cos [ Φ ( t ) ] } [ J 0 ( z c ) 2 J 2 ( z c ) cos ( 2 ω c t + 2 θ ) + ] { g ( t ) sin [ Φ ( t ) ] } [ 2 J 1 ( z c ) cos ( ω c t + θ ) ] ,
{ g ( t ) cos [ Φ ( t ) ] } = 0 , { g ( t ) sin [ Φ ( t ) ] } = 0 , | ω | > ω c / 2 ,
F 1 ( ω + ω c ) = J 1 ( z c ) exp ( j θ ) { g ( t ) sin [ Φ ( t ) ] } , F 2 ( ω + 2 ω c ) = J 2 ( z c ) exp ( j 2 θ ) { g ( t ) cos [ Φ ( t ) ] } , | ω | < ω c / 2 .
F 1 ( ω + ω c ) / J 1 ( z c ) exp ( j θ ) , F 2 ( ω + 2 ω c ) / J 2 ( z c ) exp ( j 2 θ ) .
J 2 ( z c ) g ( t ) cos [ Φ ( t ) ] , J 1 ( z c ) g ( t ) sin [ Φ ( t ) ] .
h 1 ( t ) = J 2 ( z c ) J 0 ( z b ) cos α m J 2 ( z c ) J 1 ( z b ) sin α , h 2 ( t ) = J 1 ( z c ) J 0 ( z b ) sin α + m J 1 ( z c ) J 1 ( z b ) cos α .
J 1 ( z c ) h 1 ( t ) J 2 ( z c ) h 2 ( t ) cos ( α + π / 4 ) .

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