Abstract

In many industrial fields, like automotive and painting industry, the thickness of thin layers is a crucial parameter for quality control. Hence, the demand for thickness measurement techniques continuously grows. In particular, non-destructive and contact-free terahertz techniques access a wide range of thickness determination applications. However, terahertz time-domain spectroscopy based systems perform the measurement in a sampling manner, requiring fixed distances between measurement head and sample. In harsh industrial environments vibrations of sample and measurement head distort the time-base and decrease measurement accuracy. We present an interferometer-based vibration correction for terahertz time-domain measurements, able to reduce thickness distortion by one order of magnitude for vibrations with frequencies up to 100 Hz and amplitudes up to 100 µm. We further verify the experimental results by numerical calculations and find very good agreement.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. Ch. Fattinger and D. Grischkowsky, “Terahertz beams,” Appl. Phys. Lett. 54(6), 490–492 (1989).
    [Crossref]
  2. F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
    [Crossref] [PubMed]
  3. S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
    [Crossref]
  4. S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).
  5. J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).
  6. J. L. M. van Mechelen, D. J. H. C. Maas, and H. Merbold, “Paper sheet parameter determination using terahertz spectroscopy,” in the 41st International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (2016).
  7. F. Ellrich, J. Klier, S. Weber, J. Jonuscheit, and G. von Freymann, “Terahertz time-domain technology for thickness determination of industrial relevant multi-layer coatings,” in the 41st International Conference on Infrared, Millimeter, and Terahertz aves (IRMMW-THz) (2016).
  8. H. Merbold, D. J. H. C. Maas, and J. L. M. van Mechelen, “Multiparameter sensing of paper sheets using terahertz time-domain spectroscopy: Caliper, fiber orientation, moisture, and the role of spatial inhomogeneity,” SENSORS, 2016 IEEE, 1–3 (2016).
  9. S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).
  10. S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-Based Terahertz Approach for In-Line Multilayer Thickness Measurements,” IEEE J. Sel. Top. Quantum Electron.  23 (4), 1–12, (2017).
    [Crossref]
  11. T. Yasui, T. Yasuda, K.-i. Sawanaka, and T. Araki, “Terahertz paintmeter for noncontact monitoring of thickness and drying progress in paint film,” Appl. Opt. 44, 6849–6856 (2005).
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    [Crossref]
  13. D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25 (7), 7547–7558 (2017).
    [Crossref] [PubMed]
  14. P. Uhd. Jepsen, R. H. Jacobsen, and SR. Keiding, “ Generation and detection of terahertz pulses from biased semiconductor antennas,” JOSA B 13 (11), 2424–2436 (1996).
    [Crossref]
  15. S. Pullteap and HC. Seat, “Dynamic displacement measurements with a dual-cavity fiber Fabry-Perot interferometer,” Proc. SPIE 6793, 67930A (2008).
    [Crossref]
  16. IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
    [Crossref]
  17. G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
    [Crossref]

2017 (3)

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-Based Terahertz Approach for In-Line Multilayer Thickness Measurements,” IEEE J. Sel. Top. Quantum Electron.  23 (4), 1–12, (2017).
[Crossref]

D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25 (7), 7547–7558 (2017).
[Crossref] [PubMed]

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

2016 (1)

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

2011 (2)

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
[Crossref] [PubMed]

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

2008 (1)

S. Pullteap and HC. Seat, “Dynamic displacement measurements with a dual-cavity fiber Fabry-Perot interferometer,” Proc. SPIE 6793, 67930A (2008).
[Crossref]

2005 (1)

1996 (1)

P. Uhd. Jepsen, R. H. Jacobsen, and SR. Keiding, “ Generation and detection of terahertz pulses from biased semiconductor antennas,” JOSA B 13 (11), 2424–2436 (1996).
[Crossref]

1990 (1)

1989 (1)

Ch. Fattinger and D. Grischkowsky, “Terahertz beams,” Appl. Phys. Lett. 54(6), 490–492 (1989).
[Crossref]

Araki, T.

Bartels, A.

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

Beigang, R.

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-Based Terahertz Approach for In-Line Multilayer Thickness Measurements,” IEEE J. Sel. Top. Quantum Electron.  23 (4), 1–12, (2017).
[Crossref]

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
[Crossref] [PubMed]

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

Bernath, PF.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Birk, M.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Boudon, V.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Campargue, A.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Chance, KV.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Dekorsy, T.

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

Ellrich, F.

D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25 (7), 7547–7558 (2017).
[Crossref] [PubMed]

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
[Crossref] [PubMed]

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

F. Ellrich, J. Klier, S. Weber, J. Jonuscheit, and G. von Freymann, “Terahertz time-domain technology for thickness determination of industrial relevant multi-layer coatings,” in the 41st International Conference on Infrared, Millimeter, and Terahertz aves (IRMMW-THz) (2016).

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

Fattinger, Ch.

Gebs, R.

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

Gordon, IE.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Grischkowsky, D.

Guettler, N.

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

Hill, C.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Jacobsen, R. H.

P. Uhd. Jepsen, R. H. Jacobsen, and SR. Keiding, “ Generation and detection of terahertz pulses from biased semiconductor antennas,” JOSA B 13 (11), 2424–2436 (1996).
[Crossref]

Janke, C.

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

Jepsen, P. Uhd.

P. Uhd. Jepsen, R. H. Jacobsen, and SR. Keiding, “ Generation and detection of terahertz pulses from biased semiconductor antennas,” JOSA B 13 (11), 2424–2436 (1996).
[Crossref]

Jonuscheit, J.

D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25 (7), 7547–7558 (2017).
[Crossref] [PubMed]

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
[Crossref] [PubMed]

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

F. Ellrich, J. Klier, S. Weber, J. Jonuscheit, and G. von Freymann, “Terahertz time-domain technology for thickness determination of industrial relevant multi-layer coatings,” in the 41st International Conference on Infrared, Millimeter, and Terahertz aves (IRMMW-THz) (2016).

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

Keiding, S.

Keiding, SR.

P. Uhd. Jepsen, R. H. Jacobsen, and SR. Keiding, “ Generation and detection of terahertz pulses from biased semiconductor antennas,” JOSA B 13 (11), 2424–2436 (1996).
[Crossref]

Klatt, G.

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

Klier, J.

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

F. Ellrich, J. Klier, S. Weber, J. Jonuscheit, and G. von Freymann, “Terahertz time-domain technology for thickness determination of industrial relevant multi-layer coatings,” in the 41st International Conference on Infrared, Millimeter, and Terahertz aves (IRMMW-THz) (2016).

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

Kochanov, RV.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Krimi, S.

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-Based Terahertz Approach for In-Line Multilayer Thickness Measurements,” IEEE J. Sel. Top. Quantum Electron.  23 (4), 1–12, (2017).
[Crossref]

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

Maas, D. J. H. C.

J. L. M. van Mechelen, D. J. H. C. Maas, and H. Merbold, “Paper sheet parameter determination using terahertz spectroscopy,” in the 41st International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (2016).

H. Merbold, D. J. H. C. Maas, and J. L. M. van Mechelen, “Multiparameter sensing of paper sheets using terahertz time-domain spectroscopy: Caliper, fiber orientation, moisture, and the role of spatial inhomogeneity,” SENSORS, 2016 IEEE, 1–3 (2016).

Matheis, C.

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

Merbold, H.

J. L. M. van Mechelen, D. J. H. C. Maas, and H. Merbold, “Paper sheet parameter determination using terahertz spectroscopy,” in the 41st International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (2016).

H. Merbold, D. J. H. C. Maas, and J. L. M. van Mechelen, “Multiparameter sensing of paper sheets using terahertz time-domain spectroscopy: Caliper, fiber orientation, moisture, and the role of spatial inhomogeneity,” SENSORS, 2016 IEEE, 1–3 (2016).

Molter, D.

D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25 (7), 7547–7558 (2017).
[Crossref] [PubMed]

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
[Crossref] [PubMed]

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

Nagel, M.

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

Paustian, S.

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

Pullteap, S.

S. Pullteap and HC. Seat, “Dynamic displacement measurements with a dual-cavity fiber Fabry-Perot interferometer,” Proc. SPIE 6793, 67930A (2008).
[Crossref]

Rothman, LS.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Sawanaka, K.-i.

Schäfer, H.

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
[Crossref]

Seat, HC.

S. Pullteap and HC. Seat, “Dynamic displacement measurements with a dual-cavity fiber Fabry-Perot interferometer,” Proc. SPIE 6793, 67930A (2008).
[Crossref]

Tan, Y.

IE. Gordon, LS. Rothman, C. Hill, RV. Kochanov, Y. Tan, PF. Bernath, M. Birk, V. Boudon, A. Campargue, and KV. Chance,“The HITRAN 2016 molecular spectroscopic database,” J. Quant. Spectrosc. Rad. Trans. ( 203), 3–69 (2017).
[Crossref]

Theuer, M.

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

Tiedje, O.

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

Torosyan, G.

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-Based Terahertz Approach for In-Line Multilayer Thickness Measurements,” IEEE J. Sel. Top. Quantum Electron.  23 (4), 1–12, (2017).
[Crossref]

Trierweiler, M.

Urbansky, R.

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

van Exter, M.

van Mechelen, J. L. M.

J. L. M. van Mechelen, D. J. H. C. Maas, and H. Merbold, “Paper sheet parameter determination using terahertz spectroscopy,” in the 41st International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (2016).

H. Merbold, D. J. H. C. Maas, and J. L. M. van Mechelen, “Multiparameter sensing of paper sheets using terahertz time-domain spectroscopy: Caliper, fiber orientation, moisture, and the role of spatial inhomogeneity,” SENSORS, 2016 IEEE, 1–3 (2016).

von Freymann, G.

D. Molter, M. Trierweiler, F. Ellrich, J. Jonuscheit, and G. von Freymann, “Interferometry-aided terahertz time-domain spectroscopy,” Opt. Express 25 (7), 7547–7558 (2017).
[Crossref] [PubMed]

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

F. Ellrich, J. Klier, S. Weber, J. Jonuscheit, and G. von Freymann, “Terahertz time-domain technology for thickness determination of industrial relevant multi-layer coatings,” in the 41st International Conference on Infrared, Millimeter, and Terahertz aves (IRMMW-THz) (2016).

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

Weber, S.

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

F. Ellrich, J. Klier, S. Weber, J. Jonuscheit, and G. von Freymann, “Terahertz time-domain technology for thickness determination of industrial relevant multi-layer coatings,” in the 41st International Conference on Infrared, Millimeter, and Terahertz aves (IRMMW-THz) (2016).

Weinland, T.

F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
[Crossref] [PubMed]

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Yasui, T.

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[Crossref]

S. Krimi, J. Klier, J. Jonuscheit, G. von Freymann, R. Urbansky, and R. Beigang, “Highly accurate thickness measurement of multi-layered automotive paints using terahertz technology,” Appl. Phys. Lett. 109, 021105 (2016).
[Crossref]

IEEE J. Sel. Top. Quantum Electron (2)

S. Krimi, G. Torosyan, and R. Beigang, “Advanced GPU-Based Terahertz Approach for In-Line Multilayer Thickness Measurements,” IEEE J. Sel. Top. Quantum Electron.  23 (4), 1–12, (2017).
[Crossref]

G. Klatt, R. Gebs, H. Schäfer, M. Nagel, C. Janke, A. Bartels, and T. Dekorsy, “High-resolution terahertz spectrometer,” IEEE J. Sel. Top. Quantum Electron 17 (1), 159–168 (2011).
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F. Ellrich, T. Weinland, D. Molter, J. Jonuscheit, and R. Beigang, “Compact fiber-coupled terahertz spectroscopy system pumped at 800 nm wavelength,” Rev. Sci. Instrum. 82, 053102 (2011).
[Crossref] [PubMed]

Other (6)

S. Krimi, J. Klier, F. Ellrich, J. Jonuscheit, R. Urbansky, R. Beigang, and G. von Freymann, ”An evolutionary algorithm based approach to improve the limits of minimum thickness measurements of multilayered automotive paints,” in the 40th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2 (2015).

J. Jonuscheit, R. Beigang, F. Ellrich, J. Klier, C. Matheis, D. Molter, and M. Theuer, ”Terahertz imaging for non-destructive testing,” in the Second International Symposium on NDT in Aerospace (2010).

J. L. M. van Mechelen, D. J. H. C. Maas, and H. Merbold, “Paper sheet parameter determination using terahertz spectroscopy,” in the 41st International Conference on Infrared, Millimeter, and Terahertz waves (IRMMW-THz) (2016).

F. Ellrich, J. Klier, S. Weber, J. Jonuscheit, and G. von Freymann, “Terahertz time-domain technology for thickness determination of industrial relevant multi-layer coatings,” in the 41st International Conference on Infrared, Millimeter, and Terahertz aves (IRMMW-THz) (2016).

H. Merbold, D. J. H. C. Maas, and J. L. M. van Mechelen, “Multiparameter sensing of paper sheets using terahertz time-domain spectroscopy: Caliper, fiber orientation, moisture, and the role of spatial inhomogeneity,” SENSORS, 2016 IEEE, 1–3 (2016).

S. Weber, J. Klier, F. Ellrich, S. Paustian, N. Guettler, O. Tiedje, J. Jonuscheit, and G. von Freymann, “Thickness determination of wet coatings using self-calibration method,” in the 42nd International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) (2017).

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Figures (9)

Fig. 1
Fig. 1 (left) Time-domain spectroscopy principle with a terahertz emitter and detector. To perform pump-probe experiments, a delay-line is placed in the detector arm. (right) An incident terahertz pulse is partly reflected and partly transmitted at the interfaces, defined by the Fresnel equations.
Fig. 2
Fig. 2 Influence of vibrating sample. Depending on the sample movement direction (in propagation direction of the terahertz pulse (green) and in opposite direction (blue)) the pulse is stretched or compressed compared to a resting sample (red).
Fig. 3
Fig. 3 Left hand side: terahertz time-domain spectrometer with external transceiver module. The transceiver consists of a terahertz emitter and detector module with 5 m long umbilicals including all electrical and optical connections. Right hand side: scheme of the sample mount with a piezo driven linear stage to induce vibrations with amplitudes of up to 100 µm and frequencies up to 100 Hz.
Fig. 4
Fig. 4 Top: Spectra of a terahertz pulse reflected by an uncoated metal plate. With vibration (νvib = 99 Hz, Avib = 100 µm) the absorption lines of the water vapor are distorted (red) compared to the original water absorption (black) for averaged and unaveraged measurements, respectively. Bottom: After vibration correction the spectra do not show any distorted absorption lines (red) and are very similar to the spectra of the resting sample (black), for averaged and unaveraged measurements, respectively. The averaged and unaveraged signals are vertically shifted for better visibility.
Fig. 5
Fig. 5 Schematic functionality of the used fiber-based interferometer. The end of the fiber and the object act as the two interferometer mirrors.
Fig. 6
Fig. 6 With the correction method (right) the thickness determination can be improved compared to the uncorrected results (left) for both single-layer samples, thin (above) and thick (below). In addition, the resonance effects are completely removed by the correction algorithm.
Fig. 7
Fig. 7 The results confirm the behavior of the correction method. The full-range deviation can be improved (right) compared to the uncorrected values (left). The vibration correction of the automotive four-layer sample reduces the distortion from maximal 10.1 µm to 0.8 µm and the full-range deviation from 3.0 µm to 0.3 µm.
Fig. 8
Fig. 8 Layers with dominant influence on the thickness deviation of the investigated four-layer sample. In the investigated four-layer sample, the most sensitive layers are layer 1 and layer 2.
Fig. 9
Fig. 9 The numerically calculated results agree well with the measured values, although the absolute distortions are higher for experimental investigation. For both samples Single01(a) and Quad01(b) the influence of vibrations increases with increasing amplitude and frequency. To be compared with Fig. 6 and Fig. 8, respectively.

Tables (2)

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Table 1 Overview of the investigated samples: two single-layer samples with the same coating but different thicknesses and an automotive four-layer coating system

Tables Icon

Table 2 Overview of the results after vibration correction. With the presented vibration correction, for all samples and settings the full-range deviation could be improved by about one order of magnitude.

Equations (4)

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r 1 , 2 = n 1 n 2 n 1 + n 2 .
E ( d ) = E 0 exp ( 2 π κ d λ 0 )
d n ( t ) d t = n τ c + G ,
α ( ν ) = S ρ H 2 O 1 π γ γ 2 + ( ν ( ν 0 + δ a i r p ) ) 2 ,

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