Abstract

We describe an interferometer system that uses two separate wavelengths to measure step height. The overlapping interference images detected by a CCD camera are easily separated by an ordinary integrating-bucket method and time-sharing sinusoidal phase modulation, in which two laser diodes are alternately modulated with a sinusoidal signal. A phase map is obtained only for the laser diode into which the modulation signal is injected. In this instance, a 1-µm step height was accurately detected.

© 2002 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. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef] [PubMed]
  4. G. Beheim, “Fiber-optic interferometer using frequency-modulated laser diodes,” Appl. Opt. 25, 3469–3472 (1986).
    [CrossRef] [PubMed]
  5. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [CrossRef]
  6. Y. Ishii, R. Onodera, “Two-wavelength laser-diode interferometry that uses a phase-shifting technique,” Opt. Lett. 16, 1523–1525 (1991).
    [CrossRef] [PubMed]
  7. 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]
  8. R. Onodera, Y. Ishii, “Time-multiplex two-wavelength heterodyne interferometer with frequency-ramped laser diode,” Opt. Commun. 167, 47–51 (1999).
    [CrossRef]
  9. 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]
  10. T. Suzuki, K. Kobayashi, O. Sasaki, “Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode interferometer,” Appl. Opt. 39, 2646–2652 (2000).
    [CrossRef]
  11. R. Onodera, Y. Ishii, “Two-wavelength interferometry that uses a Fourier-transform method,” Appl. Opt. 37, 7988–7994 (1998).
    [CrossRef]
  12. O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
    [CrossRef] [PubMed]
  13. T. Suzuki, O. Sasaki, J. Kaneda, T. Maruyama, “Real-time two-dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer,” Opt. Eng. 33, 2754–2759 (1994).
    [CrossRef]
  14. O. Sasaki, H. Okazaki, “Sinusoidal phase modulating interferometry for surface profile measurement,” Appl. Opt. 25, 3137–3140 (1986).
    [CrossRef] [PubMed]
  15. T. Suzuki, H. Nakamura, O. Sasaki, “Small-rotation angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2000).
    [CrossRef]
  16. T. Suzuki, T. Maki, O. Sasaki, “High-speed sinusoidal phase modulating laser diode interferometer with a feedback control to eliminate external disturbance,” in International Symposium on Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 392–396 (2001).
    [CrossRef]

2000 (2)

1999 (1)

R. Onodera, Y. Ishii, “Time-multiplex two-wavelength heterodyne interferometer with frequency-ramped laser diode,” Opt. Commun. 167, 47–51 (1999).
[CrossRef]

1998 (1)

1994 (1)

T. Suzuki, O. Sasaki, J. Kaneda, T. Maruyama, “Real-time two-dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer,” Opt. Eng. 33, 2754–2759 (1994).
[CrossRef]

1991 (3)

1988 (1)

1987 (2)

1986 (2)

1973 (1)

1971 (1)

Beheim, G.

Creath, K.

den Boef, A. J.

Fischer, E.

Ishii, Y.

Ittner, T.

Kaneda, J.

T. Suzuki, O. Sasaki, J. Kaneda, T. Maruyama, “Real-time two-dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer,” Opt. Eng. 33, 2754–2759 (1994).
[CrossRef]

Kobayashi, K.

Maki, T.

T. Suzuki, T. Maki, O. Sasaki, “High-speed sinusoidal phase modulating laser diode interferometer with a feedback control to eliminate external disturbance,” in International Symposium on Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 392–396 (2001).
[CrossRef]

Maruyama, T.

T. Suzuki, O. Sasaki, J. Kaneda, T. Maruyama, “Real-time two-dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer,” Opt. Eng. 33, 2754–2759 (1994).
[CrossRef]

Nakamura, H.

T. Suzuki, H. Nakamura, O. Sasaki, “Small-rotation angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2000).
[CrossRef]

Okazaki, H.

Onodera, R.

Polhemus, C.

Sakai, M.

Sasaki, O.

T. Suzuki, H. Nakamura, O. Sasaki, “Small-rotation angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2000).
[CrossRef]

T. Suzuki, K. Kobayashi, O. Sasaki, “Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode interferometer,” Appl. Opt. 39, 2646–2652 (2000).
[CrossRef]

T. Suzuki, O. Sasaki, J. Kaneda, T. Maruyama, “Real-time two-dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer,” Opt. Eng. 33, 2754–2759 (1994).
[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, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
[CrossRef] [PubMed]

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

T. Suzuki, T. Maki, O. Sasaki, “High-speed sinusoidal phase modulating laser diode interferometer with a feedback control to eliminate external disturbance,” in International Symposium on Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 392–396 (2001).
[CrossRef]

Sasazaki, H.

Sodnik, Z.

Suzuki, T.

T. Suzuki, H. Nakamura, O. Sasaki, “Small-rotation angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2000).
[CrossRef]

T. Suzuki, K. Kobayashi, O. Sasaki, “Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode interferometer,” Appl. Opt. 39, 2646–2652 (2000).
[CrossRef]

T. Suzuki, O. Sasaki, J. Kaneda, T. Maruyama, “Real-time two-dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer,” Opt. Eng. 33, 2754–2759 (1994).
[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]

T. Suzuki, T. Maki, O. Sasaki, “High-speed sinusoidal phase modulating laser diode interferometer with a feedback control to eliminate external disturbance,” in International Symposium on Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 392–396 (2001).
[CrossRef]

Tiziani, H. J.

Wyant, J. C.

Appl. Opt. (11)

J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
[CrossRef] [PubMed]

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
[CrossRef] [PubMed]

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

G. Beheim, “Fiber-optic interferometer using frequency-modulated laser diodes,” Appl. Opt. 25, 3469–3472 (1986).
[CrossRef] [PubMed]

A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
[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]

T. Suzuki, K. Kobayashi, O. Sasaki, “Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode interferometer,” Appl. Opt. 39, 2646–2652 (2000).
[CrossRef]

R. Onodera, Y. Ishii, “Two-wavelength interferometry that uses a Fourier-transform method,” Appl. Opt. 37, 7988–7994 (1998).
[CrossRef]

O. Sasaki, H. Okazaki, M. Sakai, “Sinusoidal phase modulating interferometer using the integrating-bucket method,” Appl. Opt. 26, 1089–1093 (1987).
[CrossRef] [PubMed]

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]

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

Opt. Commun. (1)

R. Onodera, Y. Ishii, “Time-multiplex two-wavelength heterodyne interferometer with frequency-ramped laser diode,” Opt. Commun. 167, 47–51 (1999).
[CrossRef]

Opt. Eng. (2)

T. Suzuki, H. Nakamura, O. Sasaki, “Small-rotation angle measurement using an imaging method,” Opt. Eng. 40, 426–432 (2000).
[CrossRef]

T. Suzuki, O. Sasaki, J. Kaneda, T. Maruyama, “Real-time two-dimensional surface profile measurement in a sinusoidal phase modulating laser diode interferometer,” Opt. Eng. 33, 2754–2759 (1994).
[CrossRef]

Opt. Lett. (1)

Other (1)

T. Suzuki, T. Maki, O. Sasaki, “High-speed sinusoidal phase modulating laser diode interferometer with a feedback control to eliminate external disturbance,” in International Symposium on Optical Engineering for Sensing and Nanotechnology, K. Iwata, ed., Proc. SPIE4416, 392–396 (2001).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental setup for a two-wavelength LD interferometer that uses time-sharing sinusoidal phase-modulation: M1, M2, mirrors; BS2, BS3, beam splitters; L1, L2, lenses; PC, personal computer; other abbreviations defined in text.

Fig. 2
Fig. 2

Test surface made from gauge blocks.

Fig. 3
Fig. 3

Timing chart of integrating-bucket method for measuring profile with (a) the ordinary modulating technique and (b) time-sharing sinusoidal phase modulation.

Fig. 4
Fig. 4

Timing chart of the modulation process in the experiment.

Fig. 5
Fig. 5

Block diagram of the modulating-signal generator.

Fig. 6
Fig. 6

Fringes (a) captured with the CCD camera, (b) calculated for λ1, and (c) calculated for λ2.

Fig. 7
Fig. 7

Surface profile of the flat mirror measured with a single wavelength.

Fig. 8
Fig. 8

Result of the step-height measurement.

Equations (12)

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

Imit=mi cosωct+θ i=1, 2
Sit, x, y=aix, y+bix, ycoszi cosωct+θ+αix, y i=1, 2,
zi=2πmiβiL0/λi2 i=1, 2
αix, y=4πLx, y/λi i=1, 2
pix, y=T/4i-1T/4i St, x, ydt i=1–4,
p1+p2-p3-p4=As sin αx, y,
p1-p2+p3-p4=Ac cos αx, y.
αx, y=tan-1p1+p2-p3-p4p1-p2+p3-p4.
Δαx, y=α1x, y-α2x, y=4πLx, y/Λ,
Λ=λ1λ2/ λ1-λ2
α1=α1x, y+2nπ,
Lx, y= λ1α1x, y+2π INTRΔαx, y-α1x, y/2π4π,

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