Abstract

A phase-shifting interferometer with feedback control using heterodyne phase detection was developed. A composite heterodyne phase detection method for obtaining feedback signals was proposed. Interference fringe stabilization and accurate π2 phase shifts under micrometer-order vibrations were successfully demonstrated using a digital high-speed lock-in amplifier.

© 2008 Optical Society of America

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References

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2006 (1)

2005 (1)

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, Opt. Eng. (Bellingham) 44, 125602 (2005).
[CrossRef]

2003 (2)

1998 (1)

1996 (1)

1995 (1)

1987 (2)

Asaka, A.

Chen, J.

de Groot, P.

Deck, L. L.

Eiju, T.

Farrant, D. I.

Hariharan, P.

He, L.

Hibino, K.

Ishii, Y.

Larkin, K. G.

Masutomi, T.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, Opt. Eng. (Bellingham) 44, 125602 (2005).
[CrossRef]

Murata, K.

Onodera, R.

Oreb, B. F.

Sasaki, O.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, Opt. Eng. (Bellingham) 44, 125602 (2005).
[CrossRef]

Suzuki, T.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, Opt. Eng. (Bellingham) 44, 125602 (2005).
[CrossRef]

Yamaguchi, H.

Yokota, M.

Yoshino, T.

Zhao, X.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, Opt. Eng. (Bellingham) 44, 125602 (2005).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic setup for the phase-shifting interferometer with feedback control using heterodyne phase detection. Abbreviations defined in text.

Fig. 2
Fig. 2

Time variations of the phase output under the sinusoidal vibration (a) without and (b) with feedback control.

Fig. 3
Fig. 3

Interference fringe patterns of the mirror surface observed (a) without vibration and feedback control, (b) with vibration and without feedback control, and (c) with vibration and feedback control. The additional phase shifts of (d) π 2 , (e) π, and (f) 3 π 2 were given for Fig. 3c.

Fig. 4
Fig. 4

Time variation of the phase output with feedback control when the optical path difference was approximately 2 m .

Fig. 5
Fig. 5

Phase distribution of the low-quality mirror surface calculated by a five-step algorithm under vibration with feedback control.

Equations (2)

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I 1 = A 1 + B 1 cos ( 2 π f t + ϕ 80 ϕ R ) ,
I 2 = A 2 + B 2 cos ( 2 π f t + ϕ 80 ϕ M ) ,

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