Abstract

We propose a novel terahertz material analysis approach that provides highly accurate material parameters and can be used for industrial quality control. The method treats the inspected material within its environment locally as a stratified system and describes the light–matter interaction of each layer in a realistic way. The approach is illustrated in the time-domain and frequency-domain for two potential fields of implementation of terahertz technology: quality control of (coated) paper sheets and car paint multilayers, both measured in humid air.

© 2014 Optical Society of America

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References

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  1. J. White, J. Morgan, J. Riccardi, M. Friese, and I. Duling, in Paper Conference and Trade Show (2011), Vol. 1, pp. 266–280.
  2. M. Tonouchi, Nat. Photonics 1, 97 (2007).
    [CrossRef]
  3. T. Yasui, T. Yasuda, K. Sawanaka, and T. Araki, Appl. Opt. 44, 6849 (2005).
    [CrossRef]
  4. L. Duvillaret, F. Garet, and J. Coutaz, Appl. Opt. 38, 409 (1999).
    [CrossRef]
  5. T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, J. Opt. Soc. Am. A 18, 1562 (2001).
    [CrossRef]
  6. S. Krimi, J. Klier, M. Herrmann, J. Jonuscheit, and R. Beigang, in 38th International Conference on Infrared, Millimeter, and Terahertz Waves (2013), pp. 1–2.
  7. H. Anders, Thin Films in Optics (Focal, 1967).
  8. M. Mizuno, K. Fukunaga, S. Saito, and I. Hosako, J. Eur. Opt. Soc. 4, 09044 (2009).
    [CrossRef]

2009 (1)

M. Mizuno, K. Fukunaga, S. Saito, and I. Hosako, J. Eur. Opt. Soc. 4, 09044 (2009).
[CrossRef]

2007 (1)

M. Tonouchi, Nat. Photonics 1, 97 (2007).
[CrossRef]

2005 (1)

2001 (1)

1999 (1)

Anders, H.

H. Anders, Thin Films in Optics (Focal, 1967).

Araki, T.

Baraniuk, R. G.

Beigang, R.

S. Krimi, J. Klier, M. Herrmann, J. Jonuscheit, and R. Beigang, in 38th International Conference on Infrared, Millimeter, and Terahertz Waves (2013), pp. 1–2.

Coutaz, J.

Dorney, T. D.

Duling, I.

J. White, J. Morgan, J. Riccardi, M. Friese, and I. Duling, in Paper Conference and Trade Show (2011), Vol. 1, pp. 266–280.

Duvillaret, L.

Friese, M.

J. White, J. Morgan, J. Riccardi, M. Friese, and I. Duling, in Paper Conference and Trade Show (2011), Vol. 1, pp. 266–280.

Fukunaga, K.

M. Mizuno, K. Fukunaga, S. Saito, and I. Hosako, J. Eur. Opt. Soc. 4, 09044 (2009).
[CrossRef]

Garet, F.

Herrmann, M.

S. Krimi, J. Klier, M. Herrmann, J. Jonuscheit, and R. Beigang, in 38th International Conference on Infrared, Millimeter, and Terahertz Waves (2013), pp. 1–2.

Hosako, I.

M. Mizuno, K. Fukunaga, S. Saito, and I. Hosako, J. Eur. Opt. Soc. 4, 09044 (2009).
[CrossRef]

Jonuscheit, J.

S. Krimi, J. Klier, M. Herrmann, J. Jonuscheit, and R. Beigang, in 38th International Conference on Infrared, Millimeter, and Terahertz Waves (2013), pp. 1–2.

Klier, J.

S. Krimi, J. Klier, M. Herrmann, J. Jonuscheit, and R. Beigang, in 38th International Conference on Infrared, Millimeter, and Terahertz Waves (2013), pp. 1–2.

Krimi, S.

S. Krimi, J. Klier, M. Herrmann, J. Jonuscheit, and R. Beigang, in 38th International Conference on Infrared, Millimeter, and Terahertz Waves (2013), pp. 1–2.

Mittleman, D. M.

Mizuno, M.

M. Mizuno, K. Fukunaga, S. Saito, and I. Hosako, J. Eur. Opt. Soc. 4, 09044 (2009).
[CrossRef]

Morgan, J.

J. White, J. Morgan, J. Riccardi, M. Friese, and I. Duling, in Paper Conference and Trade Show (2011), Vol. 1, pp. 266–280.

Riccardi, J.

J. White, J. Morgan, J. Riccardi, M. Friese, and I. Duling, in Paper Conference and Trade Show (2011), Vol. 1, pp. 266–280.

Saito, S.

M. Mizuno, K. Fukunaga, S. Saito, and I. Hosako, J. Eur. Opt. Soc. 4, 09044 (2009).
[CrossRef]

Sawanaka, K.

Tonouchi, M.

M. Tonouchi, Nat. Photonics 1, 97 (2007).
[CrossRef]

White, J.

J. White, J. Morgan, J. Riccardi, M. Friese, and I. Duling, in Paper Conference and Trade Show (2011), Vol. 1, pp. 266–280.

Yasuda, T.

Yasui, T.

Appl. Opt. (2)

J. Eur. Opt. Soc. (1)

M. Mizuno, K. Fukunaga, S. Saito, and I. Hosako, J. Eur. Opt. Soc. 4, 09044 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

M. Tonouchi, Nat. Photonics 1, 97 (2007).
[CrossRef]

Other (3)

J. White, J. Morgan, J. Riccardi, M. Friese, and I. Duling, in Paper Conference and Trade Show (2011), Vol. 1, pp. 266–280.

S. Krimi, J. Klier, M. Herrmann, J. Jonuscheit, and R. Beigang, in 38th International Conference on Infrared, Millimeter, and Terahertz Waves (2013), pp. 1–2.

H. Anders, Thin Films in Optics (Focal, 1967).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic representation of a light ray incident at angle θi interacting with a double-layer structure (a) on a reflector and (b) suspended above a reflector, in ambient air.

Fig. 2.
Fig. 2.

Erexp(t) of (a)–(c) uncoated and (d) coated paper sheets, Er,0exp(t) of a copper reflector, and fits Er(t), using s-polarized incident radiation, θi=13°, 26±2°C, and 22±2% relative humidity. (a) Tissue paper, (b) 100g/m2 copy paper, (c) 200g/m2 copy paper, (d) coated board. The inset shows the total thickness of samples (a)–(d) obtained from the fitting procedure as compared to mechanical caliper values.

Fig. 3.
Fig. 3.

Real and imaginary part of n(ω) of tissue paper (a), copy paper (b) and (c), and magazine paper (d). The inset shows ωp2 versus the rated CaCO3 content. The error bar gives the spread in ωp2 of five sheets of different basis weights of the same grade. Note that as compared to samples (c) and (d), copy paper (b) requires an additional oscillator around 1.8 THz.

Fig. 4.
Fig. 4.

(a) Erexp(t) and Er,0exp(t), (b) Etexp(t) and Et,0exp(t), (c) the corresponding |rexp(ω)|2, and (d) |texp(ω)|2 of a triple paint layer on (a), (c) steel and (b), (d) silicon, recorded using 200 averages at 30 Hz, at 26±1°C and 55±1% relative humidity, and the best fit results based on the method. The inset of (c) shows, for a larger set of samples, the determined total paint layer thickness as compared to values from rated techniques.

Tables (2)

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Table 1. Terahertz Thickness Values of Various Paper Sheets as Compared to Values from Rated Mechanical Techniques (in μm)

Tables Icon

Table 2. Terahertz Thickness Values of a Triple Paint Layer on Steel and Silicon Compared to Rated Techniques (in μm)

Equations (3)

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

Er(ω)=T(ω)Er,0(ω),T(ω)=r12+t12r23t21ei2β2+t12r23r21r23t21ei4β2+t12t23r34t32t21ei2(β2+β3)+,
tij=2nini+nj,rij=ninjni+nj.
ϵ(ω)=ϵ+=1mωp,2ω0,2ω2iγω,

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