Abstract

Optical interferometers for surface metrology require high immunity to vibration when they are to be used outside the laboratory environment. Here we describe a continuous phase-shifting method as a means of vibration suppression, which implements phase shifting uninterruptedly while capturing resulting interference fringes at a high rate. The continuous phase shifting allows the interference initial phase under measurement to be locked to a single temporal frequency in captured fringes, thereby being recovered free from vibration by Fourier-based postprocessing. This continuous phase-shifting method can be realized with any phase-shifting interferometers by incorporating a high-speed digital camera with good intensity-to-voltage conversion linearity.

© 2009 Optical Society of America

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References

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  1. O. Y. Kwon, Opt. Lett. 9, 59 (1984).
    [CrossRef] [PubMed]
  2. D. Malacara, Optical Shop Testing (Wiley, 1992), pp. 123-172.
  3. M. B. North-Morris, J. VanDelden, and J. C. Wyant, Appl. Opt. 41, 668 (2002).
    [CrossRef] [PubMed]
  4. I. Yamaguchi, J. Liu, and J.-I. Kato, Opt. Eng. 35, 2930 (1996).
    [CrossRef]
  5. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  6. R. Smythe and R. Moore, Opt. Eng. 23, 361 (1984).
  7. J. E. Millerd and N. J. Brock, U.S. patent 6,304,330 (Oct. 16, 2001).
  8. J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
    [CrossRef]
  9. M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, Appl. Opt. 44, 6861 (2005).
    [CrossRef] [PubMed]
  10. P. de Groot, Appl. Opt. 34, 4723 (1995).
    [CrossRef]

2005 (1)

2004 (1)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

2002 (1)

1996 (1)

I. Yamaguchi, J. Liu, and J.-I. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

1995 (1)

1984 (2)

O. Y. Kwon, Opt. Lett. 9, 59 (1984).
[CrossRef] [PubMed]

R. Smythe and R. Moore, Opt. Eng. 23, 361 (1984).

1982 (1)

Brock, N.

Brock, N. J.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

J. E. Millerd and N. J. Brock, U.S. patent 6,304,330 (Oct. 16, 2001).

de Groot, P.

Hayes, J.

Hayes, J. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Ina, H.

Kato, J.-I.

I. Yamaguchi, J. Liu, and J.-I. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

Kobayashi, S.

Kwon, O. Y.

Liu, J.

I. Yamaguchi, J. Liu, and J.-I. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, 1992), pp. 123-172.

Millerd, J.

Millerd, J. E.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

J. E. Millerd and N. J. Brock, U.S. patent 6,304,330 (Oct. 16, 2001).

Moore, R.

R. Smythe and R. Moore, Opt. Eng. 23, 361 (1984).

North-Morris, M.

North-Morris, M. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

M. B. North-Morris, J. VanDelden, and J. C. Wyant, Appl. Opt. 41, 668 (2002).
[CrossRef] [PubMed]

Novak, M.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, Appl. Opt. 44, 6861 (2005).
[CrossRef] [PubMed]

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Smythe, R.

R. Smythe and R. Moore, Opt. Eng. 23, 361 (1984).

Takeda, M.

VanDelden, J.

Wyant, J.

Wyant, J. C.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

M. B. North-Morris, J. VanDelden, and J. C. Wyant, Appl. Opt. 41, 668 (2002).
[CrossRef] [PubMed]

Yamaguchi, I.

I. Yamaguchi, J. Liu, and J.-I. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. Eng. (2)

R. Smythe and R. Moore, Opt. Eng. 23, 361 (1984).

I. Yamaguchi, J. Liu, and J.-I. Kato, Opt. Eng. 35, 2930 (1996).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Other (2)

D. Malacara, Optical Shop Testing (Wiley, 1992), pp. 123-172.

J. E. Millerd and N. J. Brock, U.S. patent 6,304,330 (Oct. 16, 2001).

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Figures (3)

Fig. 1
Fig. 1

Vibration-desensitized interferometer implementing the continuous phase-shifting method proposed in this investigation. HWP, half-wave plate; LP, linear polarizer; PBS, polarizing beam splitter; PZT, piezoelectric transducer; QWP, quarter-wave plate.

Fig. 2
Fig. 2

Phase measuring procedure with continuous phase shifting. (a) Time-varying interference intensity signal. (b) Fourier analysis. (c) Phase determination at ν 0 .

Fig. 3
Fig. 3

Phase distortion caused by window function. (a) Fourier transform of Hanning window function. (b) Phase distortion.

Equations (6)

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g ( t ) = Q { 1 + γ cos [ θ + 2 π ν 0 t + r cos ( 2 π ν ν t + α ) ] } ,
G ( ν ) = G 0 ( ν ) + G 1 ( ν ) + G 1 ( ν ) + G 11 ( ν , ν ν ) + G 1 1 ( ν , ν ν ) + G 11 ( ν , ν ν ) + G 1 1 ( ν , ν ν ) ,
G 0 ( ν ) = Q δ ( ν ) , G ± 1 ( ν ) = ( Q γ 2 ) exp ( ± i θ ) δ ( ν ν 0 ) ,
G 1 ± 1 ( ν , ν ν ) = ( i r Q γ 4 ) exp [ i ( θ ± α ) ] δ ( ν ν 0 ν ν ) ,
G 1 ± 1 ( ν , ν ν ) = ( i r Q γ 4 ) exp [ i ( θ ± α ) ] δ ( ν + ν 0 ν ν ) .
Φ = G ( θ , ν 0 ) = tan 1 ( γ 2 sin θ ( W ( 0 ) W ( 2 ν 0 ) ) W ( ν 0 ) + γ 2 cos θ ( W ( 0 ) + W ( 2 ν 0 ) ) ) ,

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