Abstract

We present a simple technique for simultaneous determination of thickness and refractive index of plane-parallel samples in the terahertz radiation domain. The technique uses time-of-flight measurements of the terahertz pulse. It has been employed on nine different polymers and semiconductor materials, which are transparent for terahertz frequencies. Our results of thickness measurement are in good agreement with micrometer reading. The accuracy in the determination of refractive index is on the order of two decimal points.

© 2012 Optical Society of America

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2011

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

2010

2009

2008

2007

C. C. Homes, G. L. Carr, R. P. S. M. Lobo, J. D. Laveigne, and D. B. Tanner, “Silicon beam splitter for far-infrared and terahertz spectroscopy,” Appl. Opt. 46, 7884–7888(2007).
[CrossRef]

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

2005

2004

2002

X. Wang, C. Zhang, L. Zhang, L. Xue, and J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef]

2001

S. Krishnamurthy, M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Characterization of thin polymer films using terahertz time-domain interferometry,” Appl. Phys. Lett. 79, 875–877 (2001).
[CrossRef]

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
[CrossRef]

2000

1999

Araki, T.

Beaumont, A.

Beigang, R.

Breitfeld, F.

Carr, G. L.

Cheville, R. A.

S. Krishnamurthy, M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Characterization of thin polymer films using terahertz time-domain interferometry,” Appl. Phys. Lett. 79, 875–877 (2001).
[CrossRef]

Coutaz, J. L.

Dai, J.

Dodge, J. S.

Donati, S.

Dorney, T. D.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
[CrossRef]

Duvillaret, L.

Evans, M. J.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Fathi, M. T.

Garet, F.

Gillen, G. D.

Gladden, L. F.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Grischkowsky, D.

Groot, P. D.

Guha, S.

Haran, F.

Harmon, S. A.

S. Krishnamurthy, M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Characterization of thin polymer films using terahertz time-domain interferometry,” Appl. Phys. Lett. 79, 875–877 (2001).
[CrossRef]

Hart, C.

Homes, C. C.

Jez, D.

Johnson, J. L.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
[CrossRef]

Kim, M. J.

Kim, S.

Koch, M.

Krishnamurthy, S.

S. Krishnamurthy, M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Characterization of thin polymer films using terahertz time-domain interferometry,” Appl. Phys. Lett. 79, 875–877 (2001).
[CrossRef]

Laveigne, J. D.

Lee, B. H.

Lobo, R. P. S. M.

May, R. K.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Mikulics, M.

Miles, R. E.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

Mittleman, D. M.

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
[CrossRef]

Mousavi, P.

Na, J.

Naftaly, M.

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

Reiten, M. T.

S. Krishnamurthy, M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Characterization of thin polymer films using terahertz time-domain interferometry,” Appl. Phys. Lett. 79, 875–877 (2001).
[CrossRef]

Santosa, F.

Sawanaka, K. I.

Shen, Y.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Tanner, D. B.

Tedaldi, M.

Theuer, M.

Tian, J.

X. Wang, C. Zhang, L. Zhang, L. Xue, and J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef]

Tomlines, P. H.

Wang, X.

X. Wang, C. Zhang, L. Zhang, L. Xue, and J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef]

Warr, I.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Wilk, R.

Wolliams, P.

Xue, L.

X. Wang, C. Zhang, L. Zhang, L. Xue, and J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef]

Yasuda, T.

Yasui, T.

Zeitler, J. A.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Zhang, C.

X. Wang, C. Zhang, L. Zhang, L. Xue, and J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef]

Zhang, J.

Zhang, L.

X. Wang, C. Zhang, L. Zhang, L. Xue, and J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef]

Zhang, W.

Zhong, S.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. Krishnamurthy, M. T. Reiten, S. A. Harmon, and R. A. Cheville, “Characterization of thin polymer films using terahertz time-domain interferometry,” Appl. Phys. Lett. 79, 875–877 (2001).
[CrossRef]

J. L. Johnson, T. D. Dorney, and D. M. Mittleman, “Enhanced depth resolution in terahertz imaging using phase-shift interferometry,” Appl. Phys. Lett. 78, 835–837 (2001).
[CrossRef]

J. Biomed. Opt.

X. Wang, C. Zhang, L. Zhang, L. Xue, and J. Tian, “Simultaneous refractive index and thickness measurements of bio tissue by optical coherence tomography,” J. Biomed. Opt. 7, 628–632 (2002).
[CrossRef]

J. Opt. Soc. Am. B

J. Pharm. Sci.

R. K. May, M. J. Evans, S. Zhong, I. Warr, L. F. Gladden, Y. Shen, and J. A. Zeitler, “Terahertz in-line sensor for direct coating thickness measurement of individual tablets during film coating in real-time,” J. Pharm. Sci. 100, 1535–1544 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. IEEE

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

Schematic showing relative delays in the THz pulse. S: sample. d: thickness of the sample. LS: lateral shift. Δtn: time delay due to sample inserted at normal incidence to the THz radiation beam. Δtθ: time delay due to sample inserted at an angle θ to the THz radiation beam.

Fig. 3.
Fig. 3.

Relative delays of THz pulse for Teflon of thickness 6.15 mm.

Fig. 4.
Fig. 4.

Comparison of experimental and theoretical results of change in OPD versus angle for quartz of thickness 5.7 mm.

Fig. 5.
Fig. 5.

Lateral shift at 40° rotation angle versus refractive index for different values of sample thickness d.

Fig. 6.
Fig. 6.

Change in OPD at 40° rotation angle versus sample thickness for different values of n.

Tables (1)

Tables Icon

Table 1. Experimental Results for Different Materials

Equations (5)

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

ΔPn=(nn0)d,
ΔPθ=dcos(θβ)(nn0cosβ),
β=sin1(n0sinθn).
ΔPθ=dcos(θsin1(dsinθ/(ΔPn+d)))(ΔPn+ddcos(sin1(dsinθΔPn+d))).
LS=dsin(θβ)cosβ.

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