Abstract

Wavelength-tuning interferometry can measure surface shapes with discontinuous steps using a unit of synthetic wavelength that is usually larger than the step height. However, measurement resolution decreases for large step heights since the synthetic wavelength becomes much larger than the source wavelength. The excess fraction method with a piezoelectric transducer phase shifting is applied to two-dimensional surface shape measurements. Systematic errors caused by nonlinearity in source frequency scanning are fully corrected by a correlation analysis between the observed and calculated interference fringes. Experiment results demonstrate that the determination of absolute interference order gives the profile of a surface with a step height of 1mm with an accuracy of 12nm.

© 2011 Optical Society of America

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References

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  1. M. Born and E. Wolf, “Theory of interference and interferometers,” in Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 324–325.
  2. Y. Bitou and K. Seta, “Gauge block measurement using a wavelength scanning interferometer,” Jpn. J. Appl. Phys. 39, 6084–6088 (2000).
    [CrossRef]
  3. A. Pfortner and J. Schwider, “Red-green-blue interferometer for the metrology of discontinuous structures,” Appl. Opt. 42, 667–673 (2003).
    [CrossRef] [PubMed]
  4. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  5. Y. Y. Chen and J. C. Wyant, “Two-wavelength phase-shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef]
  6. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816(1987).
    [CrossRef] [PubMed]
  7. A. F. Fercher, H. Z. Hu, and U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometry,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  8. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode laser,” Appl. Opt. 27, 306–311(1988).
    [CrossRef]
  9. R. Dandliker, R. Thalmann, and D. Prongue, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett. 13, 339–341 (1988).
    [CrossRef] [PubMed]
  10. H. J. Tiziani, A. Rothe, and N. Maier, “Dual-wavelength heterodyne differential interferometer for high-precision measurement of reflective aspherical surfaces and step heights,” Appl. Opt. 35, 3525–3533 (1996).
    [CrossRef] [PubMed]
  11. S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
    [CrossRef]
  12. R. Onodera and Y. Ishii, “Fourier description of the phase-measuring process in wavelength phase-shifting interferometry,” Opt. Commun. 137, 27–30 (1997).
    [CrossRef]
  13. Y. Bitou, “Two wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator,” Appl. Opt. 44, 1577–1581 (2005).
    [CrossRef] [PubMed]
  14. T. Suzuki, T. Yazawa, and O. Sasaki, “Two-wavelength laser diode interferometer with time-sharing sinusoidal phase modulation,” Appl. Opt. 41, 1972–1976 (2002).
    [CrossRef] [PubMed]
  15. P. J. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
    [CrossRef]
  16. Y. Ishii and R. Onodera, “Two-wavelength laser diode interferometry that uses phase-shifting techniques,” Opt. Lett. 16, 1523–1525 (1991).
    [CrossRef] [PubMed]
  17. K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).
  18. K. G. Larkin and B. F. Oreb, “Design and assessment of symmetrical phase-shifting algorithms,” J. Opt. Soc. Am. A 9, 1740–1748 (1992).
    [CrossRef]
  19. P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
    [CrossRef] [PubMed]

2006

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

2005

2003

2002

2000

Y. Bitou and K. Seta, “Gauge block measurement using a wavelength scanning interferometer,” Jpn. J. Appl. Phys. 39, 6084–6088 (2000).
[CrossRef]

1999

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

1997

R. Onodera and Y. Ishii, “Fourier description of the phase-measuring process in wavelength phase-shifting interferometry,” Opt. Commun. 137, 27–30 (1997).
[CrossRef]

1996

1995

P. J. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

1992

1991

1988

1987

1985

1984

1973

Bitou, Y.

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

Y. Bitou, “Two wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator,” Appl. Opt. 44, 1577–1581 (2005).
[CrossRef] [PubMed]

Y. Bitou and K. Seta, “Gauge block measurement using a wavelength scanning interferometer,” Jpn. J. Appl. Phys. 39, 6084–6088 (2000).
[CrossRef]

Born, M.

M. Born and E. Wolf, “Theory of interference and interferometers,” in Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 324–325.

Chen, Y. Y.

Ciddor, P. E.

Creath, K.

Dandliker, R.

de Groot, P. J.

P. J. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

Deck, L. L.

P. J. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

den Boef, A. J.

Fercher, A. F.

Hibino, K.

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

Hu,

Ishii, Y.

R. Onodera and Y. Ishii, “Fourier description of the phase-measuring process in wavelength phase-shifting interferometry,” Opt. Commun. 137, 27–30 (1997).
[CrossRef]

Y. Ishii and R. Onodera, “Two-wavelength laser diode interferometry that uses phase-shifting techniques,” Opt. Lett. 16, 1523–1525 (1991).
[CrossRef] [PubMed]

Iwasaki, S.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

Larkin, K. G.

Maier, N.

Matsumoto, H.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

Mitsuishi, M.

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

Ohnishi, J.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

Onodera, R.

R. Onodera and Y. Ishii, “Fourier description of the phase-measuring process in wavelength phase-shifting interferometry,” Opt. Commun. 137, 27–30 (1997).
[CrossRef]

Y. Ishii and R. Onodera, “Two-wavelength laser diode interferometry that uses phase-shifting techniques,” Opt. Lett. 16, 1523–1525 (1991).
[CrossRef] [PubMed]

Oreb, B. F.

Pfortner, A.

Polhemus, C.

Prongue, D.

Rothe, A.

Sasaki, O.

Schwider, J.

Seta, K.

Y. Bitou and K. Seta, “Gauge block measurement using a wavelength scanning interferometer,” Jpn. J. Appl. Phys. 39, 6084–6088 (2000).
[CrossRef]

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

Suzuki, N.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

Suzuki, T.

Takatsuji, T.

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

Tani, Y.

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

Thalmann, R.

Tiziani, H. J.

Vry, U.

Warisawa, S.

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

Wolf, E.

M. Born and E. Wolf, “Theory of interference and interferometers,” in Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 324–325.

Wyant, J. C.

Yazawa, T.

Yokoyama, S.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

Appl. Opt.

A. Pfortner and J. Schwider, “Red-green-blue interferometer for the metrology of discontinuous structures,” Appl. Opt. 42, 667–673 (2003).
[CrossRef] [PubMed]

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
[CrossRef] [PubMed]

Y. Y. Chen and J. C. Wyant, “Two-wavelength phase-shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
[CrossRef]

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816(1987).
[CrossRef] [PubMed]

A. F. Fercher, H. Z. Hu, and U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometry,” Appl. Opt. 24, 2181–2188 (1985).
[CrossRef] [PubMed]

A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode laser,” Appl. Opt. 27, 306–311(1988).
[CrossRef]

H. J. Tiziani, A. Rothe, and N. Maier, “Dual-wavelength heterodyne differential interferometer for high-precision measurement of reflective aspherical surfaces and step heights,” Appl. Opt. 35, 3525–3533 (1996).
[CrossRef] [PubMed]

Y. Bitou, “Two wavelength phase-shifting interferometry with a superimposed grating displayed on an electrically addressed spatial light modulator,” Appl. Opt. 44, 1577–1581 (2005).
[CrossRef] [PubMed]

T. Suzuki, T. Yazawa, and O. Sasaki, “Two-wavelength laser diode interferometer with time-sharing sinusoidal phase modulation,” Appl. Opt. 41, 1972–1976 (2002).
[CrossRef] [PubMed]

P. E. Ciddor, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt. 35, 1566–1573 (1996).
[CrossRef] [PubMed]

J. Mod. Opt.

P. J. de Groot and L. L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

Y. Bitou and K. Seta, “Gauge block measurement using a wavelength scanning interferometer,” Jpn. J. Appl. Phys. 39, 6084–6088 (2000).
[CrossRef]

Meas. Sci. Technol.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using a two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10, 1233–1239(1999).
[CrossRef]

Opt. Commun.

R. Onodera and Y. Ishii, “Fourier description of the phase-measuring process in wavelength phase-shifting interferometry,” Opt. Commun. 137, 27–30 (1997).
[CrossRef]

Opt. Lett.

Proc. SPIE

K. Hibino, Y. Tani, T. Takatsuji, Y. Bitou, S. Warisawa, and M. Mitsuishi, “Absolute interferometry for surface shapes with large steps by wavelength tuning with a mechanical phase shift,” Proc. SPIE 6292, 62920Q (2006).

Other

M. Born and E. Wolf, “Theory of interference and interferometers,” in Principles of Optics, 7th ed. (Cambridge University, 1999), pp. 324–325.

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Figures (8)

Fig. 1
Fig. 1

Wavelength-tuning Fizeau interferometer for testing a discontinuous surface. PBS, polarization beam splitter; QWP, quarter-wave plate; MO, microscope objective. Physical distance between a point ( x , y ) on the object surface and the reference surface is L ( x , y ) .

Fig. 2
Fig. 2

Temporal variations of the source wavelength and the position of the object along the optical axis controlled by PZTs. The image recording speed is 7 frames / s .

Fig. 3
Fig. 3

Whole view of the test object. Two gauge blocks of 1.001 and 1.005 mm heights are wrung to a fused silica plate 40 mm in diameter.

Fig. 4
Fig. 4

Observed raw interferogram at wavelength 632 nm .

Fig. 5
Fig. 5

Measured fraction ε 1 ( x , y ) at wavelength λ 1 .

Fig. 6
Fig. 6

Measured displacement M ( x , y ) after the correction by the correlation integral.

Fig. 7
Fig. 7

Measured interference order N 1 ( x , y ) at wavelength λ 1 .

Fig. 8
Fig. 8

Measured absolute distance L ( x , y ) between the object and the reference surface. The ordinate units are (from left to right) for the base plate and for 1.001 and 1.005 mm high gauges, respectively.

Equations (17)

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2 L ( x , y ) = ( N 1 + ε 1 ) λ 1 = ( N 2 + ε 2 ) λ 2 ,
L ( x , y ) = λ 1 λ 2 2 ( λ 2 λ 1 ) ( N 1 N 2 + ε 1 ε 2 ) .
φ 1 = arctan 1 2 ( I 1 I 21 ) cot ( 2 π / 20 ) + r = 1 19 I r + 1 sin ( 2 π r / 20 ) 1 2 ( I 1 + I 21 ) r = 1 19 I r + 1 cos ( 2 π r / 20 ) ,
ε 1 = ( φ 1 + π ) / 2 π .
F ( f ) = { ( j = 1 490 I j + 20 w ( j ) cos 2 π f ( j 1 ) / 490 ) 2 + ( j = 1 490 I j + 20 w ( j ) sin 2 π f ( j 1 ) / 490 ) 2 } 1 / 2 , for     f = 1 , 2 , , 245 ,
w ( j ) = ( 2 / 245 ) cos 2 π ( j 245 ) / 490 .
ε 2 = ( φ 2 + π ) / 2 π .
Ψ = 4 π L / λ .
δ Ψ = 4 π n g L δ λ / n λ 2 ,
2 n g L / n = A λ s ( M + ε 1 ε 2 ) ,
I ( t ) s 0 + s 1 cos 2 π [ A λ s ( M + ε 1 ε 2 ) ( λ 1 + d λ d t t ) 2 d λ d t t + ε 1 ] , for     0 t T ,
I M ( t ) = s 0 + s 1 cos 2 π [ λ 2 2 ( M + ε 1 ε 2 ) ( λ 1 + d λ d t t ) 2 t T ε 1 ] .
C ( k ) = i = 21 510 I i I k ( t i ) ,
2 L A = λ s ( k max + ε 1 ε 2 ) .
δ L L = 2 δ λ λ δ ( λ 1 λ 2 ) λ 1 λ 2 + δ ( N 1 N 2 + ε 1 ε 2 ) N 1 N 2 + ε 1 ε 2 , 1 / m ( N 1 N 2 ) ,
m > 2 λ s / λ 1 = 130 .
L ( x , y ) = λ 1 λ 2 2 ( λ 2 λ 1 ) ( N 1 N 2 + ε 1 ε 2 ) λ 1 λ 2 λ 1 τ .

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