Abstract

A previously proposed double sinusoidal phase-modulating (DSPM) laser-diode interferometer measures distances larger than a half-wavelength by detecting modulation depth. Although it requires a vibrating mirror to provide the second modulation to the interference signal, such vibrations naturally affect measurement accuracy. We propose a static-type DSPM laser-diode interferometer that uses no mechanical modulation. Our experimental results indicate a measurement error of ±1.6 µm.

© 2003 Optical Society of America

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References

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  1. Y.-Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef] [PubMed]
  2. Y.-Y. Cheng, J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,” Appl. Opt. 24, 804–807 (1985).
    [CrossRef] [PubMed]
  3. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [CrossRef]
  4. C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
    [CrossRef]
  5. T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength-multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
    [CrossRef]
  6. O. Sasaki, T. Yoshida, T. Suzuki, “Double sinusoidal phase-modulating laser diode interferometer for distance measurement,” Appl. Opt. 30, 3617–3621 (1991).
    [CrossRef] [PubMed]
  7. O. Sasaki, H. Okazaki, “Sinusoidal phase-modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
    [CrossRef]
  8. G. Mourat, N. Servagent, T. Bosch, “Distance measurement using the self-mixing effect in a three electrode distributed Bragg reflector laser diode,” Opt. Eng. 39, 738–743 (2000).
    [CrossRef]
  9. O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase-modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
    [CrossRef]

2000 (1)

G. Mourat, N. Servagent, T. Bosch, “Distance measurement using the self-mixing effect in a three electrode distributed Bragg reflector laser diode,” Opt. Eng. 39, 738–743 (2000).
[CrossRef]

1996 (1)

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength-multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

1991 (1)

1990 (1)

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase-modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

1988 (1)

1986 (2)

O. Sasaki, H. Okazaki, “Sinusoidal phase-modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef]

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

1985 (1)

1984 (1)

Bosch, T.

G. Mourat, N. Servagent, T. Bosch, “Distance measurement using the self-mixing effect in a three electrode distributed Bragg reflector laser diode,” Opt. Eng. 39, 738–743 (2000).
[CrossRef]

Cheng, Y.-Y.

den Boef, A. J.

Maruyama, T.

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength-multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

Mourat, G.

G. Mourat, N. Servagent, T. Bosch, “Distance measurement using the self-mixing effect in a three electrode distributed Bragg reflector laser diode,” Opt. Eng. 39, 738–743 (2000).
[CrossRef]

Okazaki, H.

Sasaki, O.

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength-multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

O. Sasaki, T. Yoshida, T. Suzuki, “Double sinusoidal phase-modulating laser diode interferometer for distance measurement,” Appl. Opt. 30, 3617–3621 (1991).
[CrossRef] [PubMed]

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase-modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

O. Sasaki, H. Okazaki, “Sinusoidal phase-modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
[CrossRef]

Servagent, N.

G. Mourat, N. Servagent, T. Bosch, “Distance measurement using the self-mixing effect in a three electrode distributed Bragg reflector laser diode,” Opt. Eng. 39, 738–743 (2000).
[CrossRef]

Suzuki, T.

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength-multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

O. Sasaki, T. Yoshida, T. Suzuki, “Double sinusoidal phase-modulating laser diode interferometer for distance measurement,” Appl. Opt. 30, 3617–3621 (1991).
[CrossRef] [PubMed]

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase-modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Takahashi, K.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase-modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

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]

Wyant, J. C.

Yoshida, T.

Appl. Opt. (5)

J. Appl. Phys. (1)

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

Opt. Eng. (3)

T. Suzuki, O. Sasaki, T. Maruyama, “Absolute distance measurement using wavelength-multiplexed phase-locked laser diode interferometry,” Opt. Eng. 35, 492–497 (1996).
[CrossRef]

G. Mourat, N. Servagent, T. Bosch, “Distance measurement using the self-mixing effect in a three electrode distributed Bragg reflector laser diode,” Opt. Eng. 39, 738–743 (2000).
[CrossRef]

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase-modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Experimental setup: M1, M2, mirrors; BS, beam splitter; PD, photodiode; LM, laser-diode modulator; RL, reflection-tuning layer; PL, phase-tuning layer; AL, active layer.

Fig. 2
Fig. 2

Frequency components embraced in S(t). F 1(ω) and F 2(ω) are (a) separated and (b) not separated on the frequency plane.

Fig. 3
Fig. 3

Calculations of (a) Z c and (b) Z b with respect to γb in the conditions of γa = 0.

Fig. 4
Fig. 4

Calculations of (a) Z c and (b) Z b with respect to γa in the conditions of γb = 0.

Fig. 5
Fig. 5

Calculations of Z b in the conditions of ω c = 32ω b , ω c = 64ω b , and ω c = 128ω b .

Fig. 6
Fig. 6

DBR LD wavelength change according to I DBR. The ratio between I pc and I DBR is 1:1.4.

Fig. 7
Fig. 7

Frequency response of the modulation efficiency β.

Fig. 8
Fig. 8

Observed interference signals modulated by (a) I c (t) and (b) I m (t).

Fig. 9
Fig. 9

Observed intensity changes induced by (a) I c (t) and (b) I m (t).

Fig. 10
Fig. 10

Schematic of the signal processing: (a) DSPM interference signal S(t), (b) result of the Fourier transform of S(t), (c) phase Φ(t) calculated from F 1(ω) and F 2(ω), and (d) amplitude Z b of Φ(t) calculated by the Fourier transform.

Fig. 11
Fig. 11

Relationship between ΔL and Z b .

Fig. 12
Fig. 12

Distances measured at intervals of ΔL = 0.1 mm.

Fig. 13
Fig. 13

Temporal fluctuations of Z b at three kinds of OPD.

Equations (19)

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Ict=a cosωct+θ,
Imt=b cos ωbt,
λt=λ0+Δλa cosωct+θ+Δλb cos ωbt
gt=g01+γa cosωct+θ+γb cos ωbt,
St=gt1+V cosZc cosωct+θ+Φt,
Zc=4πΔλaL/λ02,
Φt=Zb cos ωbt+α,
Zb=4πΔλbL/λ02,
α=4πL/λ0,
L=λ024πΔλb Zb.
St=gt+gtV cos ΦtJ0Zc-2J2Zccos2ωct+2θ+-gtV sin Φt2J1Zccosωct+θ-2J3Zccos3ωct+3θ+
Fω=gt+gtV cosΦt* m=--1mJ|2m|Zcexpj2mθδω-2mωc+gtV sinΦt* m=--1mJ|2m-1|Zcexpj2m-1θ×δω-2m-1ωc,
gtV sin Φt=0 |ω|>ωc/2,
gtV cos Φt=0 |ω|>ωc/2
F1ω+ωc=-J1ZcexpjθgtV sin Φt,
F2ω+2ωc=-J2Zcexpj2θgtV cos Φt.
Φt=tan-1gtV sin ΦtgtV cos Φt =tan-1-1F1ω+ωc/J1Zcexpjθ-1F2ω+2ωc/J2Zcexpj2θ,
δL=λ024πΔλbδZb.
λ024πΔλa Zc minLλ024πΔλb Zb max.

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