Abstract

We introduce a heterodyne interferometer scheme utilizing the double-pass arrangement of the deflected beams of an acousto-optic modulator. To prove our new idea, the interferometer has been applied for measuring small amplitude vibrations. The output intermediate frequency signal from the interferometer is processed by using an I/Q demodulator. In theory, it can provide the quantum noise limited sensitivity, whereas, in our present Letter, the sensitivity of the phase measurement is limited by the resolution of the 16  bit A/D converter used for processing the I/Q signals. Details of our interferometer scheme are discussed.

© 2011 Optical Society of America

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References

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2008 (2)

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[CrossRef]

K. H. Kwon, B. S. Kim, and K. Cho, Opt. Express 16, 13456 (2008).
[CrossRef] [PubMed]

2005 (1)

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, Rev. Sci. Instrum. 76, 063112 (2005).
[CrossRef]

2004 (1)

2003 (1)

2001 (1)

T. Yokoyamal, T. Arakil, S. Yokoyama, and N. Suzuki, Meas. Sci. Technol. 12, 157 (2001).
[CrossRef]

1999 (1)

M. R. Williams, F. Chi, M. T. Cashen, and H. Metcalf, Phys. Rev. A 60, R1763 (1999).
[CrossRef]

1993 (1)

1987 (1)

M. J. Collet, R. Loudon, and C. W. Gardiner, J. Mod. Opt. 34, 881 (1987).
[CrossRef]

1983 (1)

1981 (1)

A. Korpel, Proc. IEEE 69, 48 (1981).
[CrossRef]

1979 (1)

Arain, M. A.

Arakil, T.

T. Yokoyamal, T. Arakil, S. Yokoyama, and N. Suzuki, Meas. Sci. Technol. 12, 157 (2001).
[CrossRef]

Cashen, M. T.

M. R. Williams, F. Chi, M. T. Cashen, and H. Metcalf, Phys. Rev. A 60, R1763 (1999).
[CrossRef]

Chi, F.

M. R. Williams, F. Chi, M. T. Cashen, and H. Metcalf, Phys. Rev. A 60, R1763 (1999).
[CrossRef]

Cho, K.

Collet, M. J.

M. J. Collet, R. Loudon, and C. W. Gardiner, J. Mod. Opt. 34, 881 (1987).
[CrossRef]

Davis, C. C.

Donley, E. A.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, Rev. Sci. Instrum. 76, 063112 (2005).
[CrossRef]

Gardiner, C. W.

M. J. Collet, R. Loudon, and C. W. Gardiner, J. Mod. Opt. 34, 881 (1987).
[CrossRef]

Heavner, T. P.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, Rev. Sci. Instrum. 76, 063112 (2005).
[CrossRef]

Holly, S.

Jefferts, S. R.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, Rev. Sci. Instrum. 76, 063112 (2005).
[CrossRef]

Kaivola, M.

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[CrossRef]

Kim, B. S.

Kokkonen, K.

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[CrossRef]

Korpel, A.

Kwon, K. H.

Levi, F.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, Rev. Sci. Instrum. 76, 063112 (2005).
[CrossRef]

Loudon, R.

M. J. Collet, R. Loudon, and C. W. Gardiner, J. Mod. Opt. 34, 881 (1987).
[CrossRef]

Massie, N. A.

Mazzoni, D. L.

Metcalf, H.

M. R. Williams, F. Chi, M. T. Cashen, and H. Metcalf, Phys. Rev. A 60, R1763 (1999).
[CrossRef]

Nelson, R. D.

Pieper, R. J.

Riza, N. A.

Suzuki, N.

T. Yokoyamal, T. Arakil, S. Yokoyama, and N. Suzuki, Meas. Sci. Technol. 12, 157 (2001).
[CrossRef]

Tataw, M. O.

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, Rev. Sci. Instrum. 76, 063112 (2005).
[CrossRef]

Williams, M. R.

M. R. Williams, F. Chi, M. T. Cashen, and H. Metcalf, Phys. Rev. A 60, R1763 (1999).
[CrossRef]

Wu, C.

Yokoyama, S.

T. Yokoyamal, T. Arakil, S. Yokoyama, and N. Suzuki, Meas. Sci. Technol. 12, 157 (2001).
[CrossRef]

Yokoyamal, T.

T. Yokoyamal, T. Arakil, S. Yokoyama, and N. Suzuki, Meas. Sci. Technol. 12, 157 (2001).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

K. Kokkonen and M. Kaivola, Appl. Phys. Lett. 92, 063502 (2008).
[CrossRef]

J. Mod. Opt. (1)

M. J. Collet, R. Loudon, and C. W. Gardiner, J. Mod. Opt. 34, 881 (1987).
[CrossRef]

Meas. Sci. Technol. (1)

T. Yokoyamal, T. Arakil, S. Yokoyama, and N. Suzuki, Meas. Sci. Technol. 12, 157 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

M. R. Williams, F. Chi, M. T. Cashen, and H. Metcalf, Phys. Rev. A 60, R1763 (1999).
[CrossRef]

Proc. IEEE (1)

A. Korpel, Proc. IEEE 69, 48 (1981).
[CrossRef]

Rev. Sci. Instrum. (1)

E. A. Donley, T. P. Heavner, F. Levi, M. O. Tataw, and S. R. Jefferts, Rev. Sci. Instrum. 76, 063112 (2005).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of experimental arrangement.

Fig. 2
Fig. 2

Oscilloscope traces of the 160 MHz heterodyne beat signals from PD1 and PD2.

Fig. 3
Fig. 3

Measurement results of the small amplitude vibrations using the interferometer (solid curve) and a commercial capacitive sensor (dotted curve) (a) with and (b) without the closed feedback control loop.

Equations (6)

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E 00 = r m E inc cos 2 ( α 2 ) exp { i [ ω 0 t + ω 0 c ( l 1 + 2 l ZO ) + ϕ m ] } ,
E 10 = i r m E inc cos ( α 2 ) sin ( α 2 ) exp { i [ ( ω 0 ω RF ) t + 1 c [ ( ω 0 ω RF ) l 2 + 2 ω 0 l ZO ] + ϕ m ] } ,
E 01 = i E inc cos ( α 2 ) sin ( α 2 ) exp { i [ ( ω 0 + ω RF ) t + ω 0 + ω RF c ( l 2 + 2 l F 0 ) ] } ,
E 11 = E inc sin 2 ( α 2 ) exp { i [ ( ω 0 + 2 ω RF ) t + 1 c [ ( ω 0 + 2 ω RF ) l 1 + 2 ( ω 0 + ω RF ) l F 0 ) ] ] } ,
i 12 = R r m | E inc | 2 [ cos 2 α sin 2 α { cos ( 2 ω RF t + ϕ S + ϕ RF 1 ϕ m ) + cos ( 2 ω RF t + ϕ S + ϕ RF 2 ϕ m ) } ] ,
i 12 = 2 R r m | E inc | 2 cos ( 2 ω RF t + ϕ S + ϕ RF ϕ m ) .

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