Abstract

A phase-shifting homodyne interferometer with feedback control by heterodyne phase detection is developed. The backreflected beam from a reference flat with a small wedge angle and an internal heterodyne detection system are utilized to obtain heterodyne beat signals for the feedback error signal. Using a digital high-speed lock-in amplifier, interference fringe stabilization, and accurate π/2 phase shifts when micrometer-order vibrations are applied have been successfully demonstrated with a general nonpolarizing homodyne interferometer configuration.

© 2008 Optical Society of America

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References

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2008 (3)

R. Doloca, H. Broistedt, and R. Tutsch, “Phase-shift Fizeau interferometer in presence of vibration,” Proc. SPIE 7064, 706403 (2008).
[CrossRef]

R. Schödel, “Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer,” Meas. Sci. Technol. 19, 084003 (2008).
[CrossRef]

Y. Bitou, “Phase-shifting interferometry with feedback control using heterodyne phase detection,” Opt. Lett. 33, 1777-1779(2008).
[CrossRef] [PubMed]

2006 (2)

2005 (3)

2003 (2)

1998 (1)

1996 (1)

1995 (1)

1987 (2)

1982 (1)

Asaka, A.

Bitou, Y.

Broistedt, H.

R. Doloca, H. Broistedt, and R. Tutsch, “Phase-shift Fizeau interferometer in presence of vibration,” Proc. SPIE 7064, 706403 (2008).
[CrossRef]

Chen,

de Groot, P.

Deck, L. L.

Doloca, R.

R. Doloca, H. Broistedt, and R. Tutsch, “Phase-shift Fizeau interferometer in presence of vibration,” Proc. SPIE 7064, 706403 (2008).
[CrossRef]

R. Doloca and R. Tutsch, “Vibration induced phase-shift interferometer,” Proc. SPIE 6292, 62920Y (2006).

Eiju, T.

Farrant, D. I.

Hariharan, P.

He, L.

Hibino, K.

Hong, F.-L.

Ina, H.

Inaba, H.

Ishii, Y.

J,

Kihm, H.

Kim, S.-W.

Kobayashi, S.

Larkin, K. G.

Masutomi, T.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44, 125602 (2005).
[CrossRef]

Murata, K.

Onae, A.

Onodera, R.

Oreb, B. F.

Sasaki, O.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44, 125602 (2005).
[CrossRef]

Schödel, R.

R. Schödel, “Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer,” Meas. Sci. Technol. 19, 084003 (2008).
[CrossRef]

Suzuki, T.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44, 125602 (2005).
[CrossRef]

Takatsuji, T.

Takeda, M.

Tutsch, R.

R. Doloca, H. Broistedt, and R. Tutsch, “Phase-shift Fizeau interferometer in presence of vibration,” Proc. SPIE 7064, 706403 (2008).
[CrossRef]

R. Doloca and R. Tutsch, “Vibration induced phase-shift interferometer,” Proc. SPIE 6292, 62920Y (2006).

Yamaguchi, H.

Yokota, M.

Yoshino, T.

Zhao, X.

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44, 125602 (2005).
[CrossRef]

Appl. Opt. (6)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

R. Schödel, “Ultra-high accuracy thermal expansion measurements with PTB's precision interferometer,” Meas. Sci. Technol. 19, 084003 (2008).
[CrossRef]

Opt. Eng. (1)

X. Zhao, T. Suzuki, T. Masutomi, and O. Sasaki, “Sinusoidal phase modulating laser diode interferometer for on-machine surface profile measurement,” Opt. Eng. 44, 125602 (2005).
[CrossRef]

Opt. Lett. (4)

Proc. SPIE (2)

R. Doloca and R. Tutsch, “Vibration induced phase-shift interferometer,” Proc. SPIE 6292, 62920Y (2006).

R. Doloca, H. Broistedt, and R. Tutsch, “Phase-shift Fizeau interferometer in presence of vibration,” Proc. SPIE 7064, 706403 (2008).
[CrossRef]

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Figures (6)

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 heterodyne beat signals (a)  S 1 , (b)  S 3 close , and (c)  S 3 open .

Fig. 3
Fig. 3

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

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

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. Additional phase shifts of (d)  π / 2 , (e) π, and (f)  3 π / 2 were given for Fig. 5c.

Fig. 6
Fig. 6

Phase distribution of the Al-coated mirror surface calculated using a five-step algorithm under vibration with feedback control.

Equations (7)

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S 1 = A 1 cos ( 2 π f t + ϕ B ϕ 100 k B ) ,
S 1 = A 1 cos ( 2 π f t + ϕ B ϕ 100   k B + ϕ P ) ,
S 2 close = A 2 cos ( 2 π f t + ϕ R ϕ 100 k ) ,
S 2 open = S 2 close + A 3 cos ( 2 π f t + ϕ M ϕ 100 k ) ,
S 3 open = A 3 cos ( 2 π f t + ϕ M ϕ 100 k ) .
ϕ L = ϕ M ϕ B + ϕ 100 k B ϕ 100 k .
ϕ L = ϕ M ϕ R + ϕ C ,

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