Abstract

A carousel interferometer is designed to find the unknown angle and axis of rotation simultaneously. A set consisting of a compensator glass plate and a right-angle prism is placed in each of the two arms of the interferometer while located at the same rotational stage. When rotation takes place individual and relative optical path differences are generated in the beams that contribute toward finding out the angle and axis of rotation. Computer simulation shows that error remains less than a nanometer for a 1m length of unknown radius and rotation range of ±15°.

© 2008 Optical Society of America

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References

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2006 (1)

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 45, 043604 (2006).
[CrossRef]

2005 (1)

L. Li, O. Yu, Z. Lei, and J. Li, Acta Opt. Sin. 25, 491 (2005).

2004 (1)

2001 (1)

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 40, 426 (2001).
[CrossRef]

1999 (1)

1996 (1)

L. Zeng, H. Mataumoto, and K. Kawachi, Opt. Eng. 35, 1662 (1996).
[CrossRef]

1995 (2)

1994 (1)

1993 (1)

1992 (2)

1988 (1)

1974 (1)

1970 (1)

Chapman, J. D.

Chiang, H. K.

Dai, X.

Endo, T.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 45, 043604 (2006).
[CrossRef]

Giblin, P. J.

Greivenkamp, J. E.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 45, 043604 (2006).
[CrossRef]

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 40, 426 (2001).
[CrossRef]

X. Dai, O. Sasaki, J. E. Greivenkamp, and T. Suzuki, Appl. Opt. 34, 6380 (1995).
[CrossRef] [PubMed]

Harris, O.

Hartman, N. F.

Huang, P. S.

Hussain, G.

Ikram, M.

Kamada, O.

Kauppinen, J. K.

Kawachi, K.

L. Zeng, H. Mataumoto, and K. Kawachi, Opt. Eng. 35, 1662 (1996).
[CrossRef]

Kenan, R. P.

Kiyano, S.

Lei, Z.

L. Li, O. Yu, Z. Lei, and J. Li, Acta Opt. Sin. 25, 491 (2005).

Li, J.

L. Li, O. Yu, Z. Lei, and J. Li, Acta Opt. Sin. 25, 491 (2005).

Li, L.

L. Li, O. Yu, Z. Lei, and J. Li, Acta Opt. Sin. 25, 491 (2005).

Malacara, D.

Mataumoto, H.

L. Zeng, H. Mataumoto, and K. Kawachi, Opt. Eng. 35, 1662 (1996).
[CrossRef]

Nakamura, H.

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 40, 426 (2001).
[CrossRef]

Partanen, J. O.

Pollick, F. E.

Rycroft, J. E.

Salomaa, I. K.

Sasaki, O.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 45, 043604 (2006).
[CrossRef]

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 40, 426 (2001).
[CrossRef]

X. Dai, O. Sasaki, J. E. Greivenkamp, and T. Suzuki, Appl. Opt. 34, 6380 (1995).
[CrossRef] [PubMed]

Shi, P.

Stijns, E.

Summers, C. J.

Suzuki, T.

T. Suzuki, T. Endo, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 45, 043604 (2006).
[CrossRef]

T. Suzuki, H. Nakamura, O. Sasaki, and J. E. Greivenkamp, Opt. Eng. 40, 426 (2001).
[CrossRef]

X. Dai, O. Sasaki, J. E. Greivenkamp, and T. Suzuki, Appl. Opt. 34, 6380 (1995).
[CrossRef] [PubMed]

Yu, O.

L. Li, O. Yu, Z. Lei, and J. Li, Acta Opt. Sin. 25, 491 (2005).

Zeng, L.

L. Zeng, H. Mataumoto, and K. Kawachi, Opt. Eng. 35, 1662 (1996).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Layout shows a carousel interferometer that measures the angle and axis of rotation. Mirrors, M 1 M 4 ; beam splitters, BS 1 BS 3 ; prisms (hollow), P R 1 , P R 2 . R 1 and R 2 are distances from prism apexes to axis of rotation.

Fig. 2
Fig. 2

Arrangement of compensating glass strips when θ = 0 for minimization of nonlinearity in Δ P 12 ( θ ) , P 1 ( θ ) , and P 2 ( θ ) . Two glass strips are introduced in beams I 1 and I 2 that fill up the length OPD o of air. When rotation takes place OPD o for the two strips changes differently.

Tables (3)

Tables Icon

Table 1 Parameters of the Interferometer

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Table 2 Error in Angle of Rotation

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Table 3 Error in Unknown Axis of Rotation with Glass Strips

Equations (7)

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P 1 ( θ ) = 2 x 1 sin θ + 2 y 1 ( cos θ 1 ) ,
Δ P 12 ( θ ) = 2 Δ x sin θ + 2 Δ y ( cos θ 1 ) ,
L n ( θ ) = ( 2 λ ) Δ P 12 ( θ ) m θ m θ ,
θ r = Δ P 12 ( θ ) ( λ 2 ) m ,
P 1 ( θ ) = 2 x 1 sin θ + 2 y 1 ( cos θ 1 ) + Φ 1 ( θ ) ,
P 2 ( θ ) = 2 x 2 sin θ + 2 y 2 ( cos θ 1 ) + Φ 2 ( θ ) ,
Δ P 12 ( θ ) = 2 Δ x sin θ + 2 Δ y ( cos θ 1 ) + δ Φ ( θ ) .

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