Abstract

To stabilize the phase-shifting Fizeau-type interferometer against environmental disturbances (namely, vibration and temperature variations), the feedback scheme that uses the current-induced frequency modulation of a laser diode (λ = 633 nm) and the two-frequency optical heterodyne method has been investigated, with particular attention to improvement of the achievable stabilization. It is demonstrated that introduction of the proportional-integral control into the feedback system improves stabilization against the proportional control case; e.g., stabilization is improved 5 times for 100-nmp-p vibration at the frequency range at 30 Hz. The surface profile measurement for a sample mirror was conducted with a reproducibility of 6.8 nm in the root mean square under the subwavelength-amplitude vibration at 100 Hz.

© 2003 Optical Society of America

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References

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2001 (1)

1999 (1)

Y. Ishii, “Wavelength-tunable laser-diode interferometer,” Opt. Rev. 6, 273–283 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (1)

J. Liu, I. Yamaguchi, J. Kato, T. Nakajima, “Active phase-shifting interferometer using current modulation of a laser diode,” Opt. Rev. 3, 287–292 (1996).
[CrossRef]

1989 (1)

1987 (1)

1974 (1)

Asaka, A.

Brangaccio, D.

Bruning, J.

Gallagher, J.

Hariharan, P.

Herriott, D.

Ishii, Y.

Y. Ishii, “Wavelength-tunable laser-diode interferometer,” Opt. Rev. 6, 273–283 (1999).
[CrossRef]

Kato, J.

J. Liu, I. Yamaguchi, J. Kato, T. Nakajima, “Active phase-shifting interferometer using current modulation of a laser diode,” Opt. Rev. 3, 287–292 (1996).
[CrossRef]

Lee, B. S.

Liu, J.

J. Liu, I. Yamaguchi, J. Kato, T. Nakajima, “Active phase-shifting interferometer using current modulation of a laser diode,” Opt. Rev. 3, 287–292 (1996).
[CrossRef]

Mnatzakanian, S.

Nakajima, T.

J. Liu, I. Yamaguchi, J. Kato, T. Nakajima, “Active phase-shifting interferometer using current modulation of a laser diode,” Opt. Rev. 3, 287–292 (1996).
[CrossRef]

Nara, M.

Ohde, N.

Rosenfeld, D.

Strand, T.

Takahashi, Y.

White, A.

Yamaguchi, H.

Yamaguchi, I.

J. Liu, I. Yamaguchi, J. Kato, T. Nakajima, “Active phase-shifting interferometer using current modulation of a laser diode,” Opt. Rev. 3, 287–292 (1996).
[CrossRef]

Yokota, M.

Yoshino, T.

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Figures (6)

Fig. 1
Fig. 1

Output of the phase meter in the interferometer subject to 30-Hz vibrational disturbance with feedback on and off. The voltage gains of PI-feedback control of G p and G i are 1.0 and 20.0, respectively.

Fig. 2
Fig. 2

Measured dependence of stabilization factor S on applied vibration frequency for several voltage gains of the PIC.

Fig. 3
Fig. 3

Measured dependence of stabilization factor S against applied vibration at 30 Hz on the voltage gain of G i for two voltage gains of G p = 0.6 and 1.0.

Fig. 4
Fig. 4

Measured and calculated dependences of stabilization S on applied vibration frequency. The feedback gains of G p = 1.0 and G i = 20.0 were used.

Fig. 5
Fig. 5

Measured height profile of a beam splitter without mechanical vibration by a speaker.

Fig. 6
Fig. 6

Measured height profile of a beam splitter with a 100-Hz mechanical vibration by a speaker.

Equations (5)

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

g=ΔV/ΔOPDPMΔI/ΔVFBΔf/ΔILD×ΔOPD/ΔfOPD,
Gs=B/1+sTpAGp+Gi/1+sTiχ4πndf/c,
Ss=δoffs/δons,
Ss=1+Gs.
Ss= 1+αGp+Gi+β+αGpTis+γs2+TpTiTfs31+βs+γs2+TpTiTfs3,

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