Abstract

Subdivision is one of the essential methods to improve the measurement resolution of optical instruments. A new method is proposed to solve λ/16 bidirectional subdivision and direction recognition for orthogonal interference signals by constructing two sets of reference signals and using zero-cross detection. The experimental results prove that the method is efficient for orthogonal signals and has good real-time performance by field-programmable gate array realization. This method is easy to realize by use of electronic design automation tools and can be widely used in the signal processing system of optical measurement instruments such as a moiré fringe measurement system and laser interferometer.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. X. Chu, H. Lü, and J. Cao, “Research on direction recognizing and subdividing method for Moiré (interference) fringes,” Chin. Opt. Lett. 1, 692-694 (2003).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems,” Appl. Opt. 43, 2443-2448 (2004).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

2004 (1)

2003 (1)

2000 (1)

S. Su, H. Lü, W. Zhou, and G. Wang, “A software solution to counting and subdivision of Moiré fringe with wide dynamic range,” Proc. SPIE 4222, 308-312 (2000).
[CrossRef]

1994 (1)

1990 (1)

K. P. Birch, “Optical fringe subdivision with nanometric accuracy,” Precis. Eng. 12, 195-198 (1990).
[CrossRef]

1983 (1)

M. J. Downs and K. P. Birch, “Bi-directional fringe counting interference refractometer,” Precis. Eng. 5, 105-110 (1983).
[CrossRef]

Barone, F.

Birch, K. P.

K. P. Birch, “Optical fringe subdivision with nanometric accuracy,” Precis. Eng. 12, 195-198 (1990).
[CrossRef]

M. J. Downs and K. P. Birch, “Bi-directional fringe counting interference refractometer,” Precis. Eng. 5, 105-110 (1983).
[CrossRef]

Calloni, E.

Cao, J.

Chen, B.

Cheng, Z.

Chu, X.

Downs, M. J.

M. J. Downs and K. P. Birch, “Bi-directional fringe counting interference refractometer,” Precis. Eng. 5, 105-110 (1983).
[CrossRef]

Fiore, L. D.

Fusco, F.

Gao, H.

Gonda, S.

Hou, W.

H. Hu, W. Hou, J. Wang, and X. Qiu, “A new subdivision algorithm for orthogonal signals in nanometric interferometer,” in Proceedings of the First International Symposium on Photonics and Optoelectronics (IEEE, 2009).
[CrossRef]

Hu, H.

H. Hu, W. Hou, J. Wang, and X. Qiu, “A new subdivision algorithm for orthogonal signals in nanometric interferometer,” in Proceedings of the First International Symposium on Photonics and Optoelectronics (IEEE, 2009).
[CrossRef]

Huang, H.

Huang, Q.

Keem, T.

Kurosawa, T.

Li, D.

Lü, H.

X. Chu, H. Lü, and J. Cao, “Research on direction recognizing and subdividing method for Moiré (interference) fringes,” Chin. Opt. Lett. 1, 692-694 (2003).

S. Su, H. Lü, W. Zhou, and G. Wang, “A software solution to counting and subdivision of Moiré fringe with wide dynamic range,” Proc. SPIE 4222, 308-312 (2000).
[CrossRef]

Luo, J.

Milano, L.

Misumi, I.

Qiu, X.

H. Hu, W. Hou, J. Wang, and X. Qiu, “A new subdivision algorithm for orthogonal signals in nanometric interferometer,” in Proceedings of the First International Symposium on Photonics and Optoelectronics (IEEE, 2009).
[CrossRef]

Rosa, R. D.

Russo, G.

Su, S.

S. Su, H. Lü, W. Zhou, and G. Wang, “A software solution to counting and subdivision of Moiré fringe with wide dynamic range,” Proc. SPIE 4222, 308-312 (2000).
[CrossRef]

Wang, G.

S. Su, H. Lü, W. Zhou, and G. Wang, “A software solution to counting and subdivision of Moiré fringe with wide dynamic range,” Proc. SPIE 4222, 308-312 (2000).
[CrossRef]

Wang, J.

H. Hu, W. Hou, J. Wang, and X. Qiu, “A new subdivision algorithm for orthogonal signals in nanometric interferometer,” in Proceedings of the First International Symposium on Photonics and Optoelectronics (IEEE, 2009).
[CrossRef]

Zhang, Z.

Zhou, W.

S. Su, H. Lü, W. Zhou, and G. Wang, “A software solution to counting and subdivision of Moiré fringe with wide dynamic range,” Proc. SPIE 4222, 308-312 (2000).
[CrossRef]

Zhu, J.

Appl. Opt. (4)

Chin. Opt. Lett. (1)

Precis. Eng. (2)

K. P. Birch, “Optical fringe subdivision with nanometric accuracy,” Precis. Eng. 12, 195-198 (1990).
[CrossRef]

M. J. Downs and K. P. Birch, “Bi-directional fringe counting interference refractometer,” Precis. Eng. 5, 105-110 (1983).
[CrossRef]

Proc. SPIE (1)

S. Su, H. Lü, W. Zhou, and G. Wang, “A software solution to counting and subdivision of Moiré fringe with wide dynamic range,” Proc. SPIE 4222, 308-312 (2000).
[CrossRef]

Other (1)

H. Hu, W. Hou, J. Wang, and X. Qiu, “A new subdivision algorithm for orthogonal signals in nanometric interferometer,” in Proceedings of the First International Symposium on Photonics and Optoelectronics (IEEE, 2009).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Forward orthogonal signals and reference signals for the λ / 8 subdivision.

Fig. 2
Fig. 2

Backward orthogonal signals and reference signals for the λ / 8 subdivision.

Fig. 3
Fig. 3

Forward orthogonal signals and reference signals for the λ / 16 subdivision.

Fig. 4
Fig. 4

Backward orthogonal signals and reference signals for the λ / 16 subdivision.

Fig. 5
Fig. 5

Experimental system used to test the λ / 16 subdivision method.

Fig. 6
Fig. 6

Schematic of the calculation of the reference signals.

Fig. 7
Fig. 7

Two forward orthogonal signals.

Fig. 8
Fig. 8

Output of forward counting.

Fig. 9
Fig. 9

Two backward orthogonal signals.

Fig. 10
Fig. 10

Output of backward counting.

Tables (1)

Tables Icon

Table 1 Bidirectional Counting Principle of the Proposed Method

Equations (19)

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I 1 = A 1 + B 1 sin θ , I 2 = A 2 B 2 cos θ , I 3 = A 3 B 3 sin θ , I 4 = A 4 + B 4 cos θ ,
θ = 4 π λ Δ L ,
I y = I 1 I 3 , I x = I 4 I 2 .
I y = A 1 A 3 + ( B 1 + B 3 ) sin θ , I x = A 4 A 2 + ( B 2 + B 4 ) cos θ ,
I y = B sin θ , I x = B cos θ ,
I 1 = A 1 + B 1 sin θ , I 2 = A 2 + B 2 cos θ , I 3 = A 3 B 3 sin θ , I 4 = A 4 B 4 cos θ ,
I y = B sin θ , I x = B cos θ ,
Δ L = λ 2 N + ε
ε = Δ θ 4 π λ ,
u 1 f = U 0 sin θ , u 2 f = U 0 cos θ ,
r 11 f = U 0 sin θ + U 0 cos θ , r 12 f = U 0 sin θ U 0 cos θ .
u 1 b = U 0 sin θ , u 2 b = U 0 cos θ .
r 11 b = U 0 sin θ U 0 cos θ , r 12 b = U 0 sin θ + U 0 cos θ .
r 11 = u 1 + u 2 , r 12 = u 1 u 2 .
r 11 f = U 0 sin θ + U 0 cos θ , r 12 f = U 0 sin θ U 0 cos θ ,
r 21 f = U 0 sin 2 θ + U 0 cos 2 θ , r 22 f = U 0 sin 2 θ U 0 cos 2 θ .
r 21 f = U 0 sin 2 θ + U 0 cos 2 θ = U 0 [ 2 cos θ ( sin θ + cos θ ) 1 ] .
r 22 f = U 0 [ 2 sin θ ( sin θ + cos θ ) 1 ] .
r 21 = 2 u 2 U 0 ( u 1 + u 2 ) U 0 , r 22 = 2 u 1 U 0 ( u 1 + u 2 ) U 0 .

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