Abstract

We present a noncontact method for quantitative composition and thickness monitoring of flat sheet products using terahertz time-domain spectroscopy. We apply the method to obtain simultaneous measurement of thickness and moisture content of paper sheets. The paper is modeled as an effective medium of water mixed with fibers, and model parameters are estimated from fits to the measured transmission amplitude. We demonstrate the method on two different paper samples and obtain uncertainties that are comparable with existing sensor technology. Monte Carlo simulations indicate that these uncertainties can be reduced further by at least an order of magnitude.

© 2009 Optical Society of America

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  1. D. Mittleman, ed., Sensing with Terahertz Radiation (Springer, 2004).
  2. G. Grüner, ed., Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, 1998).
    [CrossRef]
  3. R. E. Miles, X. C. Zhang, H. Eisele, and A. Krotkus, eds., Proceedings of the NATO Advanced Research Workshop on Terahertz Frequency Detection and Identification of Materials and Objects (Springer, 2007).
    [CrossRef] [PubMed]
  4. A. G. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett. 320, 42-48 (2000).
    [CrossRef]
  5. M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
    [CrossRef]
  6. K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
    [CrossRef] [PubMed]
  7. K. Kogermann, J. A. Zeitler, J. Rantanen, T. Rades, P. F. Taday, M. Pepper, J. Heinämäki, and C. J. Strachan, “Investigating dehydration from compacts using terahertz pulsed, Raman, and near-infrared spectroscopy,” Appl. Spectrosc. 61, 1265-1274 (2007).
    [CrossRef]
  8. M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
    [CrossRef]
  9. C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
    [CrossRef] [PubMed]
  10. M. Naftaly, A. P. Foulds, R. E. Miles, and A. G. Davies, “Terahertz transmission spectroscopy of nonpolar materials and relationship with composition and properties,” Int. J. Infrared Millim. Waves 26, 55-64 (2005).
    [CrossRef]
  11. K. Cutshall, “Cross-directional control,” in Paper Machine Operations, 3rd ed., Pulp and Paper Manufacture Series, B. A. Thorp and M. J. Kocurek, eds. (TAPPI Press, 1991), Vol. 7, pp. 472-506.
  12. D. Banerjee, W. von Spiegel, M. D. Thomson, S. Schabel, and H. G. Roskos, “Diagnosing water content in paper by terahertz radiation,” Opt. Express 16, 9060-9066 (2008).
    [CrossRef] [PubMed]
  13. F. Huang, J. F. Federici, and D. Gary, “Determining thickness independently from optical constants by use of ultrafast light,” Opt. Lett. 29, 2435-2437 (2004).
    [CrossRef] [PubMed]
  14. T. D. Dorney, R. G. Baraniuk, and D. M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18, 1562-1571 (2001).
    [CrossRef]
  15. T. C. Choy, Effective Medium Theory: Principles and Applications, International Series of Monographs on Physics (Oxford, 1999).
  16. J. K. Vij, D. R. J. Simpson, and O. E. Panarina, “Far infrared spectroscopy of water at different temperatures: GHz to THz dielectric spectroscopy of water,” J. Mol. Liq. 112, 125-135(2004).
    [CrossRef]
  17. C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
    [CrossRef]
  18. E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, 1964), pp. 51-63.
  20. L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739-746 (1996).
    [CrossRef]
  21. P. C. Gregory, Bayesian Logical Data Analysis for the Physical Sciences (Cambridge, 2005).
    [CrossRef]

2008 (1)

2007 (2)

K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
[CrossRef] [PubMed]

K. Kogermann, J. A. Zeitler, J. Rantanen, T. Rades, P. F. Taday, M. Pepper, J. Heinämäki, and C. J. Strachan, “Investigating dehydration from compacts using terahertz pulsed, Raman, and near-infrared spectroscopy,” Appl. Spectrosc. 61, 1265-1274 (2007).
[CrossRef]

2005 (3)

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
[CrossRef]

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

M. Naftaly, A. P. Foulds, R. E. Miles, and A. G. Davies, “Terahertz transmission spectroscopy of nonpolar materials and relationship with composition and properties,” Int. J. Infrared Millim. Waves 26, 55-64 (2005).
[CrossRef]

2004 (3)

F. Huang, J. F. Federici, and D. Gary, “Determining thickness independently from optical constants by use of ultrafast light,” Opt. Lett. 29, 2435-2437 (2004).
[CrossRef] [PubMed]

J. K. Vij, D. R. J. Simpson, and O. E. Panarina, “Far infrared spectroscopy of water at different temperatures: GHz to THz dielectric spectroscopy of water,” J. Mol. Liq. 112, 125-135(2004).
[CrossRef]

E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
[CrossRef]

2001 (1)

2000 (2)

A. G. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett. 320, 42-48 (2000).
[CrossRef]

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

1997 (1)

C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
[CrossRef]

1996 (1)

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739-746 (1996).
[CrossRef]

Astrand, P. O.

C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
[CrossRef]

Banerjee, D.

Baraniuk, R. G.

Born, M.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, 1964), pp. 51-63.

Choy, T. C.

T. C. Choy, Effective Medium Theory: Principles and Applications, International Series of Monographs on Physics (Oxford, 1999).

Cole, B. E.

E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
[CrossRef]

Coutaz, J. L.

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739-746 (1996).
[CrossRef]

Cutshall, K.

K. Cutshall, “Cross-directional control,” in Paper Machine Operations, 3rd ed., Pulp and Paper Manufacture Series, B. A. Thorp and M. J. Kocurek, eds. (TAPPI Press, 1991), Vol. 7, pp. 472-506.

Davies, A. G.

M. Naftaly, A. P. Foulds, R. E. Miles, and A. G. Davies, “Terahertz transmission spectroscopy of nonpolar materials and relationship with composition and properties,” Int. J. Infrared Millim. Waves 26, 55-64 (2005).
[CrossRef]

Day, G. M.

K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
[CrossRef] [PubMed]

Dorney, T. D.

Duvillaret, L.

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739-746 (1996).
[CrossRef]

Federici, J. F.

Fischer, B.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

Fitzgerald, A. J.

E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
[CrossRef]

Foulds, A. P.

M. Naftaly, A. P. Foulds, R. E. Miles, and A. G. Davies, “Terahertz transmission spectroscopy of nonpolar materials and relationship with composition and properties,” Int. J. Infrared Millim. Waves 26, 55-64 (2005).
[CrossRef]

Frišcic, T.

K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
[CrossRef] [PubMed]

Garet, F.

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739-746 (1996).
[CrossRef]

Gary, D.

Gladden, L. F.

K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
[CrossRef] [PubMed]

Gordon, K. C.

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

Gregory, P. C.

P. C. Gregory, Bayesian Logical Data Analysis for the Physical Sciences (Cambridge, 2005).
[CrossRef]

Hangyo, M.

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
[CrossRef]

Heilweil, E. J.

A. G. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett. 320, 42-48 (2000).
[CrossRef]

Heinämäki, J.

Helm, H.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

Huang, F.

Jepsen, P. U.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

Jones, W.

K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
[CrossRef] [PubMed]

Keiding, S. R.

C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
[CrossRef]

Kogermann, K.

Markelz, A. G.

A. G. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett. 320, 42-48 (2000).
[CrossRef]

Mikkelsen, K. V.

C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
[CrossRef]

Miles, R. E.

M. Naftaly, A. P. Foulds, R. E. Miles, and A. G. Davies, “Terahertz transmission spectroscopy of nonpolar materials and relationship with composition and properties,” Int. J. Infrared Millim. Waves 26, 55-64 (2005).
[CrossRef]

Mittleman, D. M.

Miyamaru, F.

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
[CrossRef]

Naftaly, M.

M. Naftaly, A. P. Foulds, R. E. Miles, and A. G. Davies, “Terahertz transmission spectroscopy of nonpolar materials and relationship with composition and properties,” Int. J. Infrared Millim. Waves 26, 55-64 (2005).
[CrossRef]

Newnham, D. A.

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

Nguyen, K. L.

K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
[CrossRef] [PubMed]

Panarina, O. E.

J. K. Vij, D. R. J. Simpson, and O. E. Panarina, “Far infrared spectroscopy of water at different temperatures: GHz to THz dielectric spectroscopy of water,” J. Mol. Liq. 112, 125-135(2004).
[CrossRef]

Pepper, M.

K. Kogermann, J. A. Zeitler, J. Rantanen, T. Rades, P. F. Taday, M. Pepper, J. Heinämäki, and C. J. Strachan, “Investigating dehydration from compacts using terahertz pulsed, Raman, and near-infrared spectroscopy,” Appl. Spectrosc. 61, 1265-1274 (2007).
[CrossRef]

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
[CrossRef]

Pickwell, E.

E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
[CrossRef]

Rades, T.

K. Kogermann, J. A. Zeitler, J. Rantanen, T. Rades, P. F. Taday, M. Pepper, J. Heinämäki, and C. J. Strachan, “Investigating dehydration from compacts using terahertz pulsed, Raman, and near-infrared spectroscopy,” Appl. Spectrosc. 61, 1265-1274 (2007).
[CrossRef]

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

Rantanen, J.

Roitberg, A.

A. G. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett. 320, 42-48 (2000).
[CrossRef]

Roskos, H. G.

Schabel, S.

Schall, M.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

Simpson, D. R. J.

J. K. Vij, D. R. J. Simpson, and O. E. Panarina, “Far infrared spectroscopy of water at different temperatures: GHz to THz dielectric spectroscopy of water,” J. Mol. Liq. 112, 125-135(2004).
[CrossRef]

Strachan, C. J.

K. Kogermann, J. A. Zeitler, J. Rantanen, T. Rades, P. F. Taday, M. Pepper, J. Heinämäki, and C. J. Strachan, “Investigating dehydration from compacts using terahertz pulsed, Raman, and near-infrared spectroscopy,” Appl. Spectrosc. 61, 1265-1274 (2007).
[CrossRef]

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

Taday, P. F.

K. Kogermann, J. A. Zeitler, J. Rantanen, T. Rades, P. F. Taday, M. Pepper, J. Heinämäki, and C. J. Strachan, “Investigating dehydration from compacts using terahertz pulsed, Raman, and near-infrared spectroscopy,” Appl. Spectrosc. 61, 1265-1274 (2007).
[CrossRef]

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

Tani, M.

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
[CrossRef]

Thomson, M. D.

Thrane, C. N.

C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
[CrossRef]

Vij, J. K.

J. K. Vij, D. R. J. Simpson, and O. E. Panarina, “Far infrared spectroscopy of water at different temperatures: GHz to THz dielectric spectroscopy of water,” J. Mol. Liq. 112, 125-135(2004).
[CrossRef]

von Spiegel, W.

Wallace, V. P.

E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
[CrossRef]

Wallqvist, A.

C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
[CrossRef]

Walther, M.

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, 1964), pp. 51-63.

Yamaguchi, M.

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
[CrossRef]

Yamamoto, K.

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
[CrossRef]

Zeitler, J. A.

K. Kogermann, J. A. Zeitler, J. Rantanen, T. Rades, P. F. Taday, M. Pepper, J. Heinämäki, and C. J. Strachan, “Investigating dehydration from compacts using terahertz pulsed, Raman, and near-infrared spectroscopy,” Appl. Spectrosc. 61, 1265-1274 (2007).
[CrossRef]

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani, and M. Hangyo, “Terahertz absorption spectra of L-, D-, and DL-alanine and their application to determination of enantiometric composition,” Appl. Phys. Lett. 86, 053903 (2005).
[CrossRef]

E. Pickwell, B. E. Cole, A. J. Fitzgerald, V. P. Wallace, and M. Pepper, “Simulation of terahertz pulse propagation in biological systems,” Appl. Phys. Lett. 84, 2190-2192 (2004).
[CrossRef]

Appl. Spectrosc. (1)

Chem. Phys. Lett. (2)

A. G. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett. 320, 42-48 (2000).
[CrossRef]

M. Walther, B. Fischer, M. Schall, H. Helm, and P. U. Jepsen, “Far-infrared vibrational spectra of all-trans, 9-cis, and 13-cis retinal measured by THz time-domain spectroscopy,” Chem. Phys. Lett. 332, 389-395 (2000).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739-746 (1996).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

M. Naftaly, A. P. Foulds, R. E. Miles, and A. G. Davies, “Terahertz transmission spectroscopy of nonpolar materials and relationship with composition and properties,” Int. J. Infrared Millim. Waves 26, 55-64 (2005).
[CrossRef]

J. Chem. Phys. (1)

C. N. Thrane, P. O. Astrand, A. Wallqvist, K. V. Mikkelsen, and S. R. Keiding, “Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation,” J. Chem. Phys. 107, 5319-5331 (1997).
[CrossRef]

J. Mol. Liq. (1)

J. K. Vij, D. R. J. Simpson, and O. E. Panarina, “Far infrared spectroscopy of water at different temperatures: GHz to THz dielectric spectroscopy of water,” J. Mol. Liq. 112, 125-135(2004).
[CrossRef]

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

J. Pharm. Sci. (1)

C. J. Strachan, P. F. Taday, D. A. Newnham, K. C. Gordon, J. A. Zeitler, M. Pepper, and T. Rades, “Using terahertz pulsed spectroscopy to quantify pharmaceutical polymorphism and crystallinity,” J. Pharm. Sci. 94, 837-846 (2005).
[CrossRef] [PubMed]

Nat. Mater. (1)

K. L. Nguyen, T. Friščić, G. M. Day, L. F. Gladden, and W. Jones, “Terahertz time-domain spectroscopy and the quantitative monitoring of mechanochemical cocrystal formation,” Nat. Mater. 6, 206-209 (2007).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Other (7)

T. C. Choy, Effective Medium Theory: Principles and Applications, International Series of Monographs on Physics (Oxford, 1999).

M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon, 1964), pp. 51-63.

D. Mittleman, ed., Sensing with Terahertz Radiation (Springer, 2004).

G. Grüner, ed., Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, 1998).
[CrossRef]

R. E. Miles, X. C. Zhang, H. Eisele, and A. Krotkus, eds., Proceedings of the NATO Advanced Research Workshop on Terahertz Frequency Detection and Identification of Materials and Objects (Springer, 2007).
[CrossRef] [PubMed]

K. Cutshall, “Cross-directional control,” in Paper Machine Operations, 3rd ed., Pulp and Paper Manufacture Series, B. A. Thorp and M. J. Kocurek, eds. (TAPPI Press, 1991), Vol. 7, pp. 472-506.

P. C. Gregory, Bayesian Logical Data Analysis for the Physical Sciences (Cambridge, 2005).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Typical set of reference (dashed line) and sample (solid line) pulses and their corresponding spectra. The residual of a typical fit is shown in the bottom figure.

Fig. 2
Fig. 2

Calibration of ρ d / ρ w . Measurements of moisture fraction M determined by weight are plotted against ν d / ( 1 ν d ) determined from THz measurements (•), together with the fit to Eq. (6) with ρ d / ρ w = 0.87 (dashed line).

Fig. 3
Fig. 3

Experimental scatter plots or ν d and h resulting from repeated THz measurements on the same spot on a sample for (a) photocopy paper and (b) fine paper.

Fig. 4
Fig. 4

Measured and simulated noise in the time domain. Solid lines show the standard deviations of a set of 100 pulses generated by Monte Carlo simulation (top) and by the experimental apparatus (bottom). For clarity the simulation noise curve is offset upward from the experimental curve. For comparison the dotted line shows a typical signal curve, scaled down by a factor of 60.

Fig. 5
Fig. 5

Monte Carlo simulation of the parameter estimates. An ideal input signal pulse y i , shown at the left, is used to generate two simulated transmitted pulses, y and y ˜ . The pulse y ˜ is the convolution of y i with the transmittance function with estimated parameters θ ˜ and no noise added, and y is the convolution of y i with the transmittance function using ideal parameters θ i d , with noise added according to Eq. (7). The best fit parameters are estimated by minimizing the sum of the squared differences between two transmitted pulses, as shown on the right.

Fig. 6
Fig. 6

Monte Carlo simulation of h and ν d estimates for fine paper, with (a)  a 1 = 0.0024 , a 5 = 2.027 mV , a 3 = 1.95 fs , and a 2 = a 4 = 0 , and with (b)  a 5 = 1.5 mV and a 1 = a 2 = a 3 = a 4 = 0 . In (b), the true value of the parameters is shown at the center in red (⧫), and the elliptical contours represent 99%, 95%, 90%, and 68% confidence regions. Note the scale difference between (a) and (b).

Tables (4)

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Table 1 Calibration Parameters Used for Photocopy and Fine Paper Samples

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Table 2 Paper Parameters Measured Using THz and by Independent Methods a

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Table 3 Noise Simulation and Uncertainties:—(J) Jitter Noise, (M) Multiplicative Noise, (W) White Noise

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Table 4 Simulated Uncertainties and Correlation Coefficients Assuming Only White Gaussian Noise

Equations (7)

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ε p = 1 4 ( β + β 2 + 8 ε d ε w ) ,
ε w ( ω ) = ε + ε s ε 2 1 i ω τ 1 + ε 2 ε 1 i ω τ 2 ,
T ( ω ; θ ) E t ( ω ) E i ( ω ) = t ( ω ; θ ) t ( ω ; θ ) e i β ( ω ; θ ) 1 + r ( ω ; θ ) r ( ω ; θ ) e 2 i β ( ω ; θ ) ,
f ( θ ; y r ) = F 1 ( { T ( ω k ; θ ) exp ( i h ω k / c ) F ( y r ) k } ) .
C ( θ ; y s , y r ) = k | y k s f k ( θ ; y r ) | 2 .
1 ν d ν d = ρ d ρ w M 1 M .
y k [ 1 + a 1 X ( 1 ) + a 2 X k ( 2 ) ] y ( t k + a 3 X ( 3 ) + a 4 X k ( 4 ) ) + a 5 X k ( 5 ) .

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