Abstract

The terahertz absorption spectrum has a complex nonlinear relationship with sample thickness, which is normally measured mechanically with limited accuracy. As a result, the terahertz absorption spectrum is usually determined incorrectly. In this paper, an iterative algorithm is proposed to accurately determine sample thickness. This algorithm is independent of the initial value used and results in convergent calculations. Precision in sample thickness can be improved up to 0.1 μm. A more precise absorption spectrum can then be extracted. By comparing the proposed method with the traditional method based on mechanical thickness measurements, quantitative analysis experiments on a three-component amino acid mixture shows that the global error decreased from 0.0338 to 0.0301.

© 2012 Optical Society of America

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References

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  1. Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
    [CrossRef]
  2. W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
    [CrossRef]
  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]
  4. L. Duvillaret, F. Garet, and J. 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]
  5. B. Spangenberg, C. F. Poole, and C. Weins, Quantitative Thin-Layer Chromatography: a Practical Survey (Springer, 2011).
  6. L. Duvillaret, F. Garet, and J. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38, 409–415 (1999).
    [CrossRef]
  7. 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]
  8. J. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15, 4335–4350 (2007).
    [CrossRef]
  9. M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100 μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282, 1304–1306 (2009).
    [CrossRef]
  10. M. Exter, Ch. Fattinger, and D. Grischkowsky, “Terahertz time-domain spectroscopy of water vapor,” Opt. Lett. 14, 1128–1130 (1989).
    [CrossRef]
  11. M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D 42, 065415 (2009).
    [CrossRef]

2009 (2)

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100 μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282, 1304–1306 (2009).
[CrossRef]

M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D 42, 065415 (2009).
[CrossRef]

2007 (1)

2005 (3)

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
[CrossRef]

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]

2001 (1)

1999 (1)

1996 (1)

L. Duvillaret, F. Garet, and J. 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]

1989 (1)

Baraniuk, R. G.

Cole, B. E.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Coutaz, J.

L. Duvillaret, F. Garet, and J. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38, 409–415 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J. 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]

Dorney, T. D.

Duvillaret, L.

L. Duvillaret, F. Garet, and J. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38, 409–415 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J. 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]

Exter, M.

Fattinger, Ch.

Garet, F.

L. Duvillaret, F. Garet, and J. Coutaz, “Highly precise determination of optical constants and sample thickness in terahertz time-domain spectroscopy,” Appl. Opt. 38, 409–415 (1999).
[CrossRef]

L. Duvillaret, F. Garet, and J. 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]

Grischkowsky, D.

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]

Jansen, C.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100 μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282, 1304–1306 (2009).
[CrossRef]

M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D 42, 065415 (2009).
[CrossRef]

Kemp, M. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Koch, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100 μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282, 1304–1306 (2009).
[CrossRef]

M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D 42, 065415 (2009).
[CrossRef]

J. Pupeza, R. Wilk, and M. Koch, “Highly accurate optical material parameter determination with THz time-domain spectroscopy,” Opt. Express 15, 4335–4350 (2007).
[CrossRef]

Lo, T.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (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]

Poole, C. F.

B. Spangenberg, C. F. Poole, and C. Weins, Quantitative Thin-Layer Chromatography: a Practical Survey (Springer, 2011).

Pupeza, J.

Scheller, M.

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100 μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282, 1304–1306 (2009).
[CrossRef]

M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D 42, 065415 (2009).
[CrossRef]

Shen, Y. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Spangenberg, B.

B. Spangenberg, C. F. Poole, and C. Weins, Quantitative Thin-Layer Chromatography: a Practical Survey (Springer, 2011).

Taday, P. F.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

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]

Tribe, W. R.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Wang, W.-N.

W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
[CrossRef]

Weins, C.

B. Spangenberg, C. F. Poole, and C. Weins, Quantitative Thin-Layer Chromatography: a Practical Survey (Springer, 2011).

Wietzke, S.

M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D 42, 065415 (2009).
[CrossRef]

Wilk, R.

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]

Yan, H.-T.

W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
[CrossRef]

Yue, W.-W.

W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
[CrossRef]

Zhang, C.-L.

W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
[CrossRef]

Zhao, G.-Z.

W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
[CrossRef]

Acta Phys. Sin. (1)

W.-W. Yue, W.-N. Wang, G.-Z. Zhao, C.-L. Zhang, and H.-T. Yan, “THz spectrum of aromatic amino acid,” Acta Phys. Sin. 54, 3094–3099 (2005).
[CrossRef]

Appl. Opt. (1)

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]

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

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

L. Duvillaret, F. Garet, and J. 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]

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

J. Phys. D (1)

M. Scheller, S. Wietzke, C. Jansen, and M. Koch, “Modelling heterogeneous dielectric mixtures in the terahertz regime: a quasi-static effective medium theory,” J. Phys. D 42, 065415 (2009).
[CrossRef]

Opt. Commun. (1)

M. Scheller, C. Jansen, and M. Koch, “Analyzing sub-100 μm samples with transmission terahertz time domain spectroscopy,” Opt. Commun. 282, 1304–1306 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

B. Spangenberg, C. F. Poole, and C. Weins, Quantitative Thin-Layer Chromatography: a Practical Survey (Springer, 2011).

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Figures (4)

Fig. 1.
Fig. 1.

Time domain electric field signal of a relatively thick glutamine sample.

Fig. 2.
Fig. 2.

Difference between ns and ns_echo of a histidine sample versus the thicknesses used in the calculation process.

Fig. 3.
Fig. 3.

Absorption spectra of Gln, His, Thr, and GHT.

Fig. 4.
Fig. 4.

Comparison of concentration percentages of each amino acid of sample GHT (black) and quantitative measurement results, obtained from the traditional method (oblique line) and the present method (gray).

Tables (3)

Tables Icon

Table 1. Calculation Results of Sample Histidine

Tables Icon

Table 2. Components of Samples

Tables Icon

Table 3. Comparison between the Calculated and Mechanically Measured Thickness

Equations (17)

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Eecho0(ω)Eref(ω)=4n˜s(1+n˜s)2·exp[i(n˜s1)ωdc],
n˜s(ω)=ns(ω)iks(ω),
Eecho0(ω)Eref(ω)=4n˜s(1+n˜s)2·exp[i(n˜s1)ωdc]=4(nsiks)(1+nsiks)2·exp[i(nsiks1)ωdc]4ns(1+ns)2·exp[i(nsiαc2ω1)ωdc]=4ns(1+ns)2·exp[αd2]·exp[i(ns1)ωdc]=|Eecho0(ω)||Eref(ω)|exp[iϕ(ω)],
α(ω)=2dln{|Eecho0(ω)||Eref(ω)|·[ns(ω)+1]24ns(ω)},
ns(ω)=1+cωd·ϕ(ω).
Δns|1ωd0/c|Δϕ(ω)+|ns01|Δdd0,
Δα(ω)|2ln{|Eecho0(ω)||Eref(ω)|·[ns0(ω)+1]24ns0(ω)}|Δdd0+|2d|ln{14[Δns(ω)+Δns(ω)ns0(ω)]}.
Techo1(ω)=Eecho1(ω)Eref(ω)=4n˜s(n˜s1)2(n˜s+1)4·exp[jωd(3n˜s1)c]4ns(ns1)2(ns+1)4·exp(32αd)·exp[jωd(3ns1)c]=|Eecho1(ω)||Eref(ω)|·exp[jϕ1(ω)],
ns_echo(ω)=13[1+cωdϕ1(ω)].
Δn=1mi=1m[ns(ωi)ns_echo(ωi)].
αGHT(ωi)=Cg·αg(ωi)+Ch·αh(ωi)+Ct·αt(ωi)i=1,2,,n,
αmolar=αaaCaa,
Caa=maaMaa·Vpellet,
A=[αg(ω1)αh(ω1)αt(ω1)αg(ω2)αh(ω2)αt(ω2)αg(ωn)αh(ωn)αt(ωn)],C=[CgChCt],
αGHT=A·C.
C=(A·A)1·A·αGHT.
error_g=13i=13(Pi_calPi_real)2,

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