Abstract

A technique which can measure thickness variation of a moving glass plate in real-time with nanometric resolution is proposed. The technique is based on the double-slit interference of light. Owing to the nature of differential measurement scheme, the measurement system is immune to harsh environmental condition of a production line, and the measurement results are not affected by the swaying motion of the panel. With the preliminary experimental setup with scanning speed of 100 mm/s, the measurement repeatability was 3 nm for the waviness component of the thickness profile, filtered with a Gaussian filter with cutoff wavelength of 8 mm.

© 2014 Optical Society of America

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References

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  1. ISO 4287:1997, Geometrical Product Specifications (GPS) – Surface texture: Profile method – Terms, definitions and surface texture parameters (1997).
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    [Crossref]
  7. K. Hibino, B. F. Oreb, P. S. Fairman, and J. Burke, “Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer,” Appl. Opt. 43(6), 1241–1249 (2004).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  9. V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
    [Crossref]
  10. V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
    [Crossref] [PubMed]
  11. C.-H. Liu and Z.-H. Li, “Application of the astigmatic method to the thickness measurement of glass substrates,” Appl. Opt. 47(21), 3968–3972 (2008).
    [Crossref] [PubMed]
  12. Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
    [Crossref]
  13. T. Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philos. Trans. R. Soc. Lond. 94, 1804 (1804).
  14. ISO 16610–21:2011, Geometrical product specifications (GPS)–Filtration–Part 21: Linear profile filters: Gaussian filters (2011).

2013 (1)

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

2008 (2)

2007 (1)

V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
[Crossref] [PubMed]

2006 (1)

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

2004 (1)

2001 (1)

1999 (1)

1997 (1)

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4(4), 507–515 (1997).
[Crossref]

1980 (1)

H. Yamauchi and M. Nakayama, “An automatic measurement of glass thickness,” J. Non-Crystal. Sol. 38, 955–960 (1980).

1976 (1)

1804 (1)

T. Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philos. Trans. R. Soc. Lond. 94, 1804 (1804).

Bodlaj, V.

Burke, J.

Cho, S.

V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
[Crossref] [PubMed]

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

Fairman, P. S.

Fukano, T.

Haruna, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4(4), 507–515 (1997).
[Crossref]

Hibino, K.

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

K. Hibino, B. F. Oreb, P. S. Fairman, and J. Burke, “Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer,” Appl. Opt. 43(6), 1241–1249 (2004).
[Crossref] [PubMed]

Kim, D.

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

Kim, H.

V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
[Crossref] [PubMed]

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

Kim, K.

V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
[Crossref] [PubMed]

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

Kim, M. J.

Kim, S.

Kim, Y.

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

Klement, E.

Lee, B. H.

Lee, S.

V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
[Crossref] [PubMed]

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

Li, Z.-H.

Liu, C.-H.

Mitsuishi, M.

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

Na, J.

Nakayama, M.

H. Yamauchi and M. Nakayama, “An automatic measurement of glass thickness,” J. Non-Crystal. Sol. 38, 955–960 (1980).

Ohmi, M.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4(4), 507–515 (1997).
[Crossref]

Oreb, B. F.

Peiponen, K. E.

Protopopov, V.

V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
[Crossref] [PubMed]

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

Räsänen, J.

Shiraishi, T.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4(4), 507–515 (1997).
[Crossref]

Sugita, N.

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

Tajiri, H.

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4(4), 507–515 (1997).
[Crossref]

Yamaguchi, I.

Yamauchi, H.

H. Yamauchi and M. Nakayama, “An automatic measurement of glass thickness,” J. Non-Crystal. Sol. 38, 955–960 (1980).

Young, T.

T. Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philos. Trans. R. Soc. Lond. 94, 1804 (1804).

Appl. Opt. (5)

J. Non-Crystal. Sol. (1)

H. Yamauchi and M. Nakayama, “An automatic measurement of glass thickness,” J. Non-Crystal. Sol. 38, 955–960 (1980).

Opt. Express (1)

Opt. Lasers Eng. (1)

Y. Kim, K. Hibino, N. Sugita, and M. Mitsuishi, “Optical thickness measurement of mask blank glass plate by the excess fraction method using a wavelength-tuning interferometer,” Opt. Lasers Eng. 51(10), 1173–1178 (2013).
[Crossref]

Opt. Rev. (1)

M. Ohmi, T. Shiraishi, H. Tajiri, and M. Haruna, “Simultaneous measurement of refractive index and thickness of transparent plates by low coherence interferometry,” Opt. Rev. 4(4), 507–515 (1997).
[Crossref]

Philos. Trans. R. Soc. Lond. (1)

T. Young, “Experimental Demonstration of the General Law of the Interference of Light,” Philos. Trans. R. Soc. Lond. 94, 1804 (1804).

Rev. Sci. Instrum. (2)

V. Protopopov, S. Cho, K. Kim, S. Lee, H. Kim, and D. Kim, “Heterodyne double-channel polarimeter for mapping birefringence and thickness of flat glass panels,” Rev. Sci. Instrum. 77(5), 053107 (2006).
[Crossref]

V. Protopopov, S. Cho, K. Kim, S. Lee, and H. Kim, “Differential heterodyne interferometer for measuring thickness of glass panels,” Rev. Sci. Instrum. 78(7), 076101 (2007).
[Crossref] [PubMed]

Other (2)

ISO 16610–21:2011, Geometrical product specifications (GPS)–Filtration–Part 21: Linear profile filters: Gaussian filters (2011).

ISO 4287:1997, Geometrical Product Specifications (GPS) – Surface texture: Profile method – Terms, definitions and surface texture parameters (1997).

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of the double-slit interferometer. G: glass panel; DS: double-slit; L: lens; D: detector plane

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Fig. 2
Fig. 2 Schematic diagram of the experimental setup. SLD: super luminance diode; OF: optical fiber; L1: collimation lens; GP: glass panel; MS: motorized stage; DS: double-slit; L2: lens; CCD: charge coupled device camera; PC: personal computer.

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Fig. 3
Fig. 3 Example of measurement profiles. (a) Raw data which is the position of central peak of the interference pattern. (b) Thickness profile. (c) Filtered profile (waviness component of (b) with cutoff wavelength of 8 mm).

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Fig. 4
Fig. 4 Comparison of thickness profiles and filtered profiles obtained before and after flipping the glass plate horizontally. (a) Thickness profiles and difference. (b) Filtered profiles and difference.

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Fig. 5
Fig. 5 Comparison of the thickness profiles and filtered profiles measured with and without vibration. (a) Thickness profiles. (b) Filtered profiles.

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Fig. 6
Fig. 6 Parameters used to evaluate the amount of shift occurring between object points and the slit centers due to refraction of light.

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Fig. 7
Fig. 7 An optical 4-f system to minimize the shift between object points and slit centers. GP: glass panel; L1, L2: lenses; IGP: image of glass panel; DS: double-slit.

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Equations (12)

Equations on this page are rendered with MathJax. Learn more.

I ( θ ) = I 0 ( sin β β ) 2 cos 2 α ,
β = k b sin θ 2 ,
α = k a sin θ 2 ,
I(θ)= I 0 ( sin( β− bϕ 2a ) β− bϕ 2a ) 2 cos 2 ( α− ϕ 2 ).
θ cp = sin −1 ϕ ka .
θ i = sin −1 (nsin θ w )− θ w .
ϕ=kasin θ i ,
θ cp = θ i .
z=ftan θ i      =ftan[ sin −1 { nsin( tan −1 δt a ) }− tan −1 δt a ] ​​​​    ≈f(n−1) δt a ,
δt= az (n−1)f .
g(t)= 1 α λ c exp [ -π ( t α λ c ) 2 ] ,
( tan 2 θ w − 1 tan 2 θ i ) Δ 2 +( 2ltan θ w +a tan 2 θ w )Δ+( l 2 +altan θ w + a 2 4 tan 2 θ w )=0.

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