Abstract

A two-wavelength interferometer that uses two separate modulating currents with different phases but the same frequencies to detect a greater degree of object displacement in real time is proposed and demonstrated. The measurement error was 57 nm, roughly 1/80 of the synthetic wavelength. We have confirmed that this modulating technique enables us to equip our prototype interferometer with a simple feedback-control system that eliminates external disturbance.

© 2000 Optical Society of America

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References

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  1. J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
    [CrossRef] [PubMed]
  2. C. Polhemus, “Two-wavelength Interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  3. Y.-Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef] [PubMed]
  4. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef] [PubMed]
  5. A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  6. Z. Sodnik, E. Fischer, T. Ittner, H. J. Tiziani, “Two-wavelength double heterodyne interferometry using a matched grating technique,” Appl. Opt. 30, 3139–3144 (1991).
    [CrossRef] [PubMed]
  7. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [CrossRef]
  8. C. C. Williams, K. Wickramasinghe, “Absolute optical ranging with 200-nm resolution,” Opt. Lett. 14, 542–544 (1989).
    [CrossRef] [PubMed]
  9. Y. Ishii, R. Onodera, “Two-wavelength laser-diode interferometry that uses phase-shifting techniques,” Opt. Lett. 16, 1523–1525 (1991).
    [CrossRef] [PubMed]
  10. R. Onodera, I. Yukihiro, “Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes,” Appl. Opt. 33, 5052–5061 (1994).
    [CrossRef] [PubMed]
  11. O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
    [CrossRef] [PubMed]
  12. T. Suzuki, O. Sasaki, S. Takayama, T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32, 1033–1037 (1993).
    [CrossRef]
  13. 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]
  14. T. Suzuki, T. Okada, O. Sasaki, T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997).
    [CrossRef]

1997

T. Suzuki, T. Okada, O. Sasaki, T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997).
[CrossRef]

1994

1993

T. Suzuki, O. Sasaki, S. Takayama, T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32, 1033–1037 (1993).
[CrossRef]

1991

1990

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]

1989

1988

1987

1985

1984

1973

1971

Cheng, Y.-Y.

Creath, K.

den Boef, A. J.

Fercher, A. F.

Fischer, E.

Hu, H. Z.

Ishii, Y.

Ittner, T.

Maruyama, T.

T. Suzuki, T. Okada, O. Sasaki, T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997).
[CrossRef]

T. Suzuki, O. Sasaki, S. Takayama, T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32, 1033–1037 (1993).
[CrossRef]

Okada, T.

T. Suzuki, T. Okada, O. Sasaki, T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997).
[CrossRef]

Onodera, R.

Polhemus, C.

Sasaki, O.

T. Suzuki, T. Okada, O. Sasaki, T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997).
[CrossRef]

T. Suzuki, O. Sasaki, S. Takayama, T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32, 1033–1037 (1993).
[CrossRef]

O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (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]

Sasazaki, H.

Sodnik, Z.

Suzuki, T.

T. Suzuki, T. Okada, O. Sasaki, T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997).
[CrossRef]

T. Suzuki, O. Sasaki, S. Takayama, T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32, 1033–1037 (1993).
[CrossRef]

O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (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]

Takayama, S.

T. Suzuki, O. Sasaki, S. Takayama, T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32, 1033–1037 (1993).
[CrossRef]

Tiziani, H. J.

Vry, U.

Wickramasinghe, K.

Williams, C. C.

Wyant, J. C.

Yukihiro, I.

Appl. Opt.

Opt. Eng.

T. Suzuki, O. Sasaki, S. Takayama, T. Maruyama, “Real-time displacement measurement using synchronous detection in a sinusoidal phase modulating interferometer,” Opt. Eng. 32, 1033–1037 (1993).
[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]

T. Suzuki, T. Okada, O. Sasaki, T. Maruyama, “Real-time vibration measurement using a feedback type of laser diode interferometer with an optical fiber,” Opt. Eng. 36, 2496–2502 (1997).
[CrossRef]

Opt. Lett.

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental setup: M’s, mirrors; OSC, oscillator; other abbreviations defined in text.

Fig. 2
Fig. 2

Block diagram of the phase detector: AMP, differential amplifier; other abbreviations defined in text.

Fig. 3
Fig. 3

Block diagram of the FBC: F(t), feedback signal; other abbreviations defined in text.

Fig. 4
Fig. 4

Calculation of the Bessel functions J 1(z), J 2(z), and J 1(z)J 2(z) with respect to modulation depth z. J 1(z)J 2(z) takes its maximum at point P. J 1(z) and J 2(z) take the same values at point Q, which is very close to point P.

Fig. 5
Fig. 5

Interference signals observed by the photodetector (a) without feedback control and (b) with feedback control.

Fig. 6
Fig. 6

Illustration of the extracted quadratic signals with respect to (a) the triangular displacement of mirror M3. The phase difference between signals (b) S g 2 and (c) S h 2 is π/2.

Fig. 7
Fig. 7

Illustration of the extracted quadratic signals with respect to (a) the triangular displacement of mirror M3. The phase difference between signals (b) S g 1 and (c) S h 1 is π/2.

Fig. 8
Fig. 8

Measurement of the large triangular displacement: (a) the displacement of mirror M3, (b) the output signal from the phase detector, (c) the displacement measured with the help of computer.

Equations (33)

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Imit=mi cosωct+θi  i=1, 2
Sit=ai+bi coszi cosωct+θi+αit+δit  i=1, 2,
zi=4πmiβiD0+dt/λi2,
αit=4πD0+dt/λi,
Δαt=α1t-α2t=4πD0/Λ+4πdt/Λ
Λ=λ1λ2/|λ1-λ2|
dt=Λ4π Δαt,
St=i Sit.
git=mi sinωct+θi,
hit=Imit×git=mi2/2sin 2ωct+θi
Sg1t=-b2m1J1z2sinθ1-θ2sin α2t
Sg2t=-b1m2J1z1sinθ1-θ2sin α1t,
Sh1t=-b2m12J2z2/2sin 2θ1-θ2cos α2t,
Sh2t=-b1m22J2z1/2sin 2θ1-θ2cos α1t,
Sg1t×Sh2t=U1m1m22b1b2J1z2J2z1/2×C cos α1tsin α2t,
Sg2t×Sh1t=U2m12m2b1b2J1z1J2z2/2×C sin α1tcos α2t,
C=sinθ1-θ2sin 2θ1-θ2
SΔαt=Sg2t×Sh1t-Sg1t×Sh2t=K sin Δαt,
K=A/2b1b2CJ1zJ2z
dt=Λ4π sin-1SΔαtK.
Ft=a1+a2+b1 cosα1+δ1t+b2 cosz2 sinθ1-θ2+α2+δ2t,
αi=4πD0/λi  i=1, 2.
Fti kibiδit  0<ki<1,
SFBt=i ai+bi coszi cosωct+θi+αi+δit-αcit,
αci=4πD0/λi2Δλi
Jizz Δz  i=1, 2.
S1t=a1+b1cos α1J0z1-2J2z1cos 2ωct+θ1+-sin α12J1z1cosωct+θ1-2J3z1cos 3ωct+θ1+,
S2t=a2+b2cos α2J0z2-2J2z2cos 2ωct+θ2+-sin α22J1z2cosωct+θ2-2J3z2cos 3ωct+θ2+.
-2b1J1z1sin α1 cosωct+θ1×m1 sinωct+θ1=-b1m1J1z1sin α1 sin 2ωct+θ1,
-2b2J1z2sin α2 cosωct+θ2×m1 sinωct+θ1=-b2m1J1z2sin α2sin2ωct+θ1+θ2+sinθ1-θ2
coskωct+θi×sinkωct+θj=sin2kωct+θi+θj+sinθi-θj2  k=1, 2,
fx=sin x sin 2x=2 sin2 x cos x.
fx=2 sin x2-3 sin2 x.

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