Abstract

We propose a phase-shifting interferometer that uses both phase-locked and photothermal modulating techniques. In this interferometer the measurement accuracy is not affected by the intensity modulation that usually appears in current modulation. The surface profile of a diamond-turned aluminum disk was measured; the rms repeatability obtained was λ/460.

© 2001 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. Y. Ishii, J. Chen, K. Murata, “Digital phase-measuring interferometry with a tunable laser diode,” Opt. Lett. 12, 233–235 (1987).
    [CrossRef] [PubMed]
  4. T. Suzuki, O. Sasaki, K. Higuchi, T. Maruyama, “Real-time displacement measurement in sinusoidal phase modulating interferometry,” Appl. Opt. 28, 5270–5274 (1989).
    [CrossRef] [PubMed]
  5. P. Hariharan, “Phase-stepping interferometry with laser diodes: effect of changes in laser power with output wavelength,” Appl. Opt. 28, 27–28 (1989).
    [CrossRef] [PubMed]
  6. Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Laser Eng. 14, 293–309 (1991).
    [CrossRef]
  7. T. Suzuki, M. Matsuda, O. Sasaki, T. Maruyama, “Laser-diode interferometer with a photothermal modulation,” Appl. Opt. 38, 7069–7075 (1999).
    [CrossRef]
  8. T. Suzuki, O. Sasaki, T. Maruyama, “Phase locked laser diode interferometer for surface profile measurement,” Appl. Opt. 28, 4407–4410 (1989).
    [CrossRef] [PubMed]
  9. T. Suzuki, T. Muto, O. Sasaki, T. Maruyama, “Wavelength-multiplexed phase locked laser diode interferometer using a phase-shifting technique,” Appl. Opt. 36, 6196–6201 (1997).
    [CrossRef]
  10. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
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  11. P. Blood, E. D. Fletcher, K. Woodbridge, K. C. Heasman, A. R. Adams, “Influence of the barriers on the temperature dependence of threshold current in GaAs/AlGaAs quantum well lasers,” IEEE J. Quantum Electron. 25, 1459–1468 (1989).
    [CrossRef]
  12. 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 (1991).
    [CrossRef]
  13. 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]

1999 (1)

1997 (1)

1993 (1)

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 (2)

Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Laser Eng. 14, 293–309 (1991).
[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 (1991).
[CrossRef]

1989 (4)

1988 (1)

1987 (2)

1983 (1)

Adams, A. R.

P. Blood, E. D. Fletcher, K. Woodbridge, K. C. Heasman, A. R. Adams, “Influence of the barriers on the temperature dependence of threshold current in GaAs/AlGaAs quantum well lasers,” IEEE J. Quantum Electron. 25, 1459–1468 (1989).
[CrossRef]

Blood, P.

P. Blood, E. D. Fletcher, K. Woodbridge, K. C. Heasman, A. R. Adams, “Influence of the barriers on the temperature dependence of threshold current in GaAs/AlGaAs quantum well lasers,” IEEE J. Quantum Electron. 25, 1459–1468 (1989).
[CrossRef]

Burow, R.

Chen, J.

Elssner, K.-E.

Fletcher, E. D.

P. Blood, E. D. Fletcher, K. Woodbridge, K. C. Heasman, A. R. Adams, “Influence of the barriers on the temperature dependence of threshold current in GaAs/AlGaAs quantum well lasers,” IEEE J. Quantum Electron. 25, 1459–1468 (1989).
[CrossRef]

Grzanna, J.

Hariharan, P.

Heasman, K. C.

P. Blood, E. D. Fletcher, K. Woodbridge, K. C. Heasman, A. R. Adams, “Influence of the barriers on the temperature dependence of threshold current in GaAs/AlGaAs quantum well lasers,” IEEE J. Quantum Electron. 25, 1459–1468 (1989).
[CrossRef]

Higuchi, K.

Ishii, Y.

Maruyama, T.

Matsuda, M.

Merkel, K.

Murata, K.

Muto, T.

Sasaki, O.

Schwider, J.

Spolaczyk, R.

Suzuki, T.

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 (1991).
[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]

Tatsuno, K.

Tsunoda, Y.

Woodbridge, K.

P. Blood, E. D. Fletcher, K. Woodbridge, K. C. Heasman, A. R. Adams, “Influence of the barriers on the temperature dependence of threshold current in GaAs/AlGaAs quantum well lasers,” IEEE J. Quantum Electron. 25, 1459–1468 (1989).
[CrossRef]

Appl. Opt. (8)

IEEE J. Quantum Electron. (1)

P. Blood, E. D. Fletcher, K. Woodbridge, K. C. Heasman, A. R. Adams, “Influence of the barriers on the temperature dependence of threshold current in GaAs/AlGaAs quantum well lasers,” IEEE J. Quantum Electron. 25, 1459–1468 (1989).
[CrossRef]

Opt. Eng. (2)

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 (1991).
[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]

Opt. Laser Eng. (1)

Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Laser Eng. 14, 293–309 (1991).
[CrossRef]

Opt. Lett. (1)

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Figures (8)

Fig. 1
Fig. 1

Experimental setup: Abbreviations are defined in text.

Fig. 2
Fig. 2

Block diagram of the feedback controller. MUL, multiplier; PI, proportional-integral controller; other abbreviations are defined in text.

Fig. 3
Fig. 3

Phase shifting by the transition of feedback signals F i .

Fig. 4
Fig. 4

Intensity changes caused by current modulation. The amount of phase shift is (a) α1 = 0, (b) α2 = π/2, (c) α3 = π, and (d) α4 = 3π/2.

Fig. 5
Fig. 5

Intensity change with photothermal modulation. The amount of phase shift is (a) α1 = 0, (b) α2 = π/2, (c) α3 = π, and (d) α4 = 3π/2.

Fig. 6
Fig. 6

Fringe images observed with the phase shift.

Fig. 7
Fig. 7

Two-dimensional surface profiles of a diamond-turned aluminum disk measured with (a) a Talystep profilometer and (b) our system.

Fig. 8
Fig. 8

Three-dimensional surface profile of a diamond-turned aluminum disk measured with our system.

Equations (13)

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Φx, y=tan-1I2x, y-I4x, yI1x, y-I3x, y,
Iix, y=I0x, y1+Vx, ycosΦx, y+i-1π2i=14,
Vmt=r cosωct+θ.
St=S1+S0 coszcosωct+θ+αFBC,
z=4πr/λ1
αFBC=4πLλ1-4πLλ12 βΔI
Vs1=-As1 cosωct+θ,
Vs2=As2 cos2ωct+2θ,
Vs3=As3 cosωct+θ,
Vs4=-As4 cos2ωct+2θ,
St=S1+S0 cos αFBCJ0z-2J2zcos2ωct+2θ+-S0 sin αFBC2J1zcosωct+θ-2J3zcos3ωct+3θ+,
Fi=Ai sinαFBC-i-1π2 i=14.
ΔΦx, y=Φx, yL ΔL=4πλ1 ΔL-4πλ12 βΔIΔL.

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