Abstract

An optical method to resolve the non-measurable thickness problem caused by the overlap of optical path differences within a specific thickness range when measuring the physical thickness of a sample using a spectral-domain interferometer is proposed and realized. Optical path differences can be discerned by inserting a correction glass piece into the measurement path, thus increasing the measurement optical path length. To verify the proposed method, 0.2-mm-thick N-BK7 glass was used as a sample, with physical thickness and group refractive index measurements conducted according to three different correction glass elements with corresponding nominal thicknesses of 3.0 mm, 3.5 mm, and 4.0 mm. Through uncertainty evaluations according to the correction glass used, the physical thicknesses of the sample were found to be in good agreement within measurement uncertainties of less than 100 nm, results comparable to those of previous works which did not use any correction glass.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  2. J. Park, J.-A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf. 20(3), 463–477 (2019).
    [Crossref]
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    [Crossref]
  4. J. Kim, C. Kang, T. B. Eom, J. Jin, H. S. Suh, and J. W. Kim, “Quadrature laser interferometer for in-line thickness measurement of glass panels using a current modulation technique,” Appl. Opt. 53(20), 4604–4610 (2014).
    [Crossref]
  5. J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2019 (1)

J. Park, J.-A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf. 20(3), 463–477 (2019).
[Crossref]

2017 (2)

J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref]

H. M. Park and K.-N. Joo, “High-speed combined NIR low-coherence interferometry for wafer metrology,” Appl. Opt. 56(31), 8592–8597 (2017).
[Crossref]

2016 (1)

J. Jin, “Dimensional metrology using the optical comb of a mode-locked laser,” Meas. Sci. Technol. 27(2), 022001 (2016).
[Crossref]

2015 (2)

2014 (2)

2013 (1)

J. Park, J. Jin, J. W. Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305, 170–174 (2013).
[Crossref]

2012 (2)

2010 (1)

2009 (1)

2008 (1)

2007 (1)

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]

2005 (1)

2004 (1)

2003 (1)

2000 (1)

Ahn, H.

J. Park, J.-A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf. 20(3), 463–477 (2019).
[Crossref]

Bae, J.

J. Park, J.-A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf. 20(3), 463–477 (2019).
[Crossref]

J. Park, J. Bae, J. Jin, J.-A. Kim, and J. W. Kim, “Vibration-insensitive measurements of the thickness profile of large glass panels,” Opt. Express 23(26), 32941–32949 (2015).
[Crossref]

Burke, J.

Chen, L.

Cho, S.

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]

Choi, E. S.

Choi, H. Y.

Coppola, G.

De Groot, P.

De. Nicola, S.

Ellis, J. D.

Eom, T. B.

Fairman, P. S.

Ferraro, P.

Gillen, G. D.

Griesmann, U.

Guha, S.

Hibino, K.

Iodice, M.

Jin, J.

J. Park, J.-A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf. 20(3), 463–477 (2019).
[Crossref]

J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref]

J. Jin, “Dimensional metrology using the optical comb of a mode-locked laser,” Meas. Sci. Technol. 27(2), 022001 (2016).
[Crossref]

J. Park, J. Bae, J. Jin, J.-A. Kim, and J. W. Kim, “Vibration-insensitive measurements of the thickness profile of large glass panels,” Opt. Express 23(26), 32941–32949 (2015).
[Crossref]

J. Kim, C. Kang, T. B. Eom, J. Jin, H. S. Suh, and J. W. Kim, “Quadrature laser interferometer for in-line thickness measurement of glass panels using a current modulation technique,” Appl. Opt. 53(20), 4604–4610 (2014).
[Crossref]

J. Park, J. Jin, J. W. Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305, 170–174 (2013).
[Crossref]

S. Maeng, J. Park, B. O, and J. Jin, “Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser,” Opt. Express 20(11), 12184–12190 (2012).
[Crossref]

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010).
[Crossref]

Joo, K.-N.

Kang, C.

J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref]

J. Kim, C. Kang, T. B. Eom, J. Jin, H. S. Suh, and J. W. Kim, “Quadrature laser interferometer for in-line thickness measurement of glass panels using a current modulation technique,” Appl. Opt. 53(20), 4604–4610 (2014).
[Crossref]

Kang, C.-S.

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, 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, J.

J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref]

J. Kim, C. Kang, T. B. Eom, J. Jin, H. S. Suh, and J. W. Kim, “Quadrature laser interferometer for in-line thickness measurement of glass panels using a current modulation technique,” Appl. Opt. 53(20), 4604–4610 (2014).
[Crossref]

Kim, J. W.

J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref]

J. Park, J. Bae, J. Jin, J.-A. Kim, and J. W. Kim, “Vibration-insensitive measurements of the thickness profile of large glass panels,” Opt. Express 23(26), 32941–32949 (2015).
[Crossref]

J. Kim, C. Kang, T. B. Eom, J. Jin, H. S. Suh, and J. W. Kim, “Quadrature laser interferometer for in-line thickness measurement of glass panels using a current modulation technique,” Appl. Opt. 53(20), 4604–4610 (2014).
[Crossref]

J. Park, J. Jin, J. W. Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305, 170–174 (2013).
[Crossref]

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010).
[Crossref]

Kim, J.-A.

J. Park, J.-A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf. 20(3), 463–477 (2019).
[Crossref]

J. Park, J. Bae, J. Jin, J.-A. Kim, and J. W. Kim, “Vibration-insensitive measurements of the thickness profile of large glass panels,” Opt. Express 23(26), 32941–32949 (2015).
[Crossref]

J. Park, J. Jin, J. W. Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305, 170–174 (2013).
[Crossref]

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010).
[Crossref]

Kim, K.

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, S.-W.

Lee, B. H.

Lee, C.

Lee, J. Y.

J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref]

Lee, S.

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]

Maeng, S.

Moore, D. T.

Na, J.

O, B.

Oreb, B. F.

Park, H. M.

Park, J.

Protopopov, V.

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]

Schmidt, G.

Suh, H. S.

Wang, Q.

Zhao, Y.

Zilio, S. C.

Appl. Opt. (8)

P. De Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt. 39(16), 2658–2663 (2000).
[Crossref]

G. Coppola, P. Ferraro, M. Iodice, and S. De. Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003).
[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]

G. D. Gillen and S. Guha, “Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt. 44(3), 344–347 (2005).
[Crossref]

J. Na, H. Y. Choi, E. S. Choi, C. Lee, and B. H. Lee, “Self-referenced spectral interferometry for simultaneous measurements of thickness and refractive index,” Appl. Opt. 48(13), 2461–2467 (2009).
[Crossref]

J. Kim, C. Kang, T. B. Eom, J. Jin, H. S. Suh, and J. W. Kim, “Quadrature laser interferometer for in-line thickness measurement of glass panels using a current modulation technique,” Appl. Opt. 53(20), 4604–4610 (2014).
[Crossref]

Y. Zhao, G. Schmidt, D. T. Moore, and J. D. Ellis, “Absolute thickness metrology with submicrometer accuracy using a low-coherence distance measuring interferometer,” Appl. Opt. 54(25), 7693–7700 (2015).
[Crossref]

H. M. Park and K.-N. Joo, “High-speed combined NIR low-coherence interferometry for wafer metrology,” Appl. Opt. 56(31), 8592–8597 (2017).
[Crossref]

Int. J. Precis. Eng. Manuf. (1)

J. Park, J.-A. Kim, H. Ahn, J. Bae, and J. Jin, “A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry,” Int. J. Precis. Eng. Manuf. 20(3), 463–477 (2019).
[Crossref]

Meas. Sci. Technol. (1)

J. Jin, “Dimensional metrology using the optical comb of a mode-locked laser,” Meas. Sci. Technol. 27(2), 022001 (2016).
[Crossref]

Opt. Commun. (1)

J. Park, J. Jin, J. W. Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305, 170–174 (2013).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

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]

J. Kim, J. W. Kim, C. Kang, J. Jin, and J. Y. Lee, “An interferometric system for measuring thickness of parallel glass plates without 2π ambiguity using phase analysis of quadrature Haidinger fringes,” Rev. Sci. Instrum. 88(5), 055108 (2017).
[Crossref]

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Figures (8)

Fig. 1.
Fig. 1. Schematic diagram of reference and measurement paths in a transmission-type interferometer.
Fig. 2.
Fig. 2. (a) Variations of OPD2 and OPD3 and (b) variation of the difference between OPD2 and OPD3 according to a change in the thickness.
Fig. 3.
Fig. 3. Variation of the difference between OPD2 and OPD3 before and after the insertion of a correction glass into the measurement path.
Fig. 4.
Fig. 4. (a) Optical configuration of the proposed system, (b) drawings of the reference and measurement path brackets, and (c) a photo of the experimental setup (BS1, BS2: beam splitter, M1, M2: mirror).
Fig. 5.
Fig. 5. (a) Interference spectrum and (b) Fourier-transformed amplitude when no correction glass is inserted.
Fig. 6.
Fig. 6. (a) Interference spectrum and (b) Fourier-transformed amplitude when a 4-mm-thick correction glass is inserted.
Fig. 7.
Fig. 7. Comparison of measurable thickness ranges according to the nominal thicknesses of correction glasses with a glass sample and an initial OPD1 value of 0.5 mm.
Fig. 8.
Fig. 8. Thickness comparison in consideration of the measurement uncertainty according to the thickness of the correction glass used.

Tables (4)

Tables Icon

Table 1. Repeatability of physical thickness and group refractive index measurements of the sample according to three correction glasses of different thicknesses

Tables Icon

Table 2. Uncertainty evaluation of the T = 212.459 µm @ 4.0 T correction glass

Tables Icon

Table 3. Uncertainty evaluation of the T = 212.426 µm @ 3.5 T correction glass

Tables Icon

Table 4. Uncertainty evaluation of the T = 212.445 µm @ 3.0 T correction glass

Equations (9)

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

OP D 1 = l m l r
OP D 2 = 2 N T
OP D 3 = l m + N T T l r = T ( N 1 ) + OP D 1
T = OP D 2 2 ( OP D 3 OP D 1 )
N = OP D 2 2 T
T c = OP D 1 N + 1
| OP D 2 OP D 3 | = { OP D 1 T ( N + 1 ) , w h e n 0 T T c T ( N + 1 ) OP D 1 , w h e n T c T
Δ T = ε N + 1
OP D 1 , s = OP D 1 + Δ OP D 1 = l m l r + T s ( N s 1 )

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