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Uncertainty in Terahertz Time-Domain Spectroscopy Measurement of Liquids

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Abstract

Terahertz time-domain spectroscopy (THz-TDS) is a significant technique for characterizing materials as it allows fast and broadband measurement of optical constants in the THz regime. The measurement precision of the constants is highly influenced by the complicated measurement procedure and data processing. Taking THz transmission measurement of liquids into account, the sources of error existing in THz-TDS process are identified. The contributions of each source to the uncertainty of optical constants in THz-TDS process are formulated, with particular emphasis on the effect of multilayer reflections and plane wave assumption. As a consequence, an analytical model is proposed for uncertainty evaluation in a THz-TDS measurement of liquids. An actual experiment with a Di 2-Ethyl Hexyl Phthalate (DEHP) sample is carried out to show that the proposed model could be a basis to evaluate the measurement precision of optical constants of liquids.

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References

  1. Timothy D. Dorney, Richard G. Baraniuk, and Daniel M. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A, Vol. 18, No. 7, pp. 1562–1571, 2001.

  2. Fischer B M, Helm H, Jepsen P U. “Chemical Recognition with Broadband THz Spectroscopy,” Proceedings of the IEEE, 2007, 95(8):1592-1604.

    Article  Google Scholar 

  3. P Kužel and H Němec. “Terahertz conductivity in nanoscaled systems: effective medium theory aspects,” J. Phys. D: Appl. Phys. 47 (2014) 374005 (14pp).

  4. Jeon T-I, and D. Grischkowsky. “Characterization of optically dense, doped semiconductors by reflection THz time domain spectroscopy,” Applied Physics Letters 72.23(1998):3032-3034.

    Article  Google Scholar 

  5. Seigo O, Katsuhiko M, Hiroaki M, et al. “New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region,” Optics Express, 2010, 18(16):17306-17312.

    Article  Google Scholar 

  6. M. Walther, B. Fischer, M. Schall, H. Helm, P.U. Jepsen, Chem. Phys. Lett. 332(3–4), 389 (2000)

    Article  Google Scholar 

  7. Naftaly, M. “Metrology Issues and Solutions in THz Time-Domain Spectroscopy: Noise, Errors, Calibration.” IEEE Sensors Journal 13.1(2013):8-17.

    Article  Google Scholar 

  8. H.-W. Hübers, M. F. Kimmitt, N. Hiromoto, and E. Bründermann, Terahertz spectroscopy: System and sensitivity considerations,” IEEE Trans. Terahertz Sci. Technol., vol. 1, no. 1, pp. 321–331, 2011.

    Article  Google Scholar 

  9. N. Hiromoto, S. R. Tripathi, M. Takeda, and M. Aoki, “Study on random errors in THz signal and optical constants observed with THz time-domain spectroscopy,” in Proc. 35th Int. Conf. Infrared Millim. Terahertz Waves, 2010, pp. 1–2.

    Chapter  Google Scholar 

  10. L. Duvillaret, F. Garet, and J.-L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Amer. B, vol. 17, no. 3, pp. 452–461, 2000.

    Article  Google Scholar 

  11. W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Amer. B, vol. 25, no. 6, pp. 1059–1072, 2008.

    Article  Google Scholar 

  12. W. Withayachumnankul, H. Lin, S. P. Mickan, B. M. Fischer, and D. Abbott, “Analysis of measurement uncertainty in THz-TDS,” Proc. SPIE, vol. 6593, p. 659326, 2007.

    Article  Google Scholar 

  13. A. B. Ruffin, J. V. Rudd, J. F. Whitaker, S. Feng, and H. G. Winful, Direct Observation of the Gouy Phase Shift with Single-Cycle Terahertz Pulses, Phys. Rev. Lett. Vol. 83, no. 17, pp. 3410–3413, 1999.

  14. P.U. Jepsen, U. Moller, H. Merbold, Investigation of aqueous alcohol and sugar solutions with reflection terahertz time-domain spectroscopy. Opt. Express 15(22), 14717–14737 (2007).

    Article  Google Scholar 

  15. A. Oka, K. Tominaga, Terahertz spectroscopy of polar solute molecules in non-polar solvents. J. Non Cryst. Solids 352(42–49), 4606–4609 (2006).

    Article  Google Scholar 

  16. H. A. Haus and A. Mecozzi, “Noise of mode-locked lasers,” IEEE J. Quantum Electron. 29, 983–996 (1993).

    Article  Google Scholar 

  17. M. van Exter and D. R. Grischkowsky, “Characterization of an optoelectronic terahertz beam system,” IEEE Trans. Microwave Theory Tech. 38, 1684–1691 (1990).

    Article  Google Scholar 

  18. Amin Soltani, David Jahn, Lennart Duschek et al. “Attenuated Total Reflection Terahertz Time-Domain Spectroscopy: Uncertainty Analysis and Reduction Scheme,” IEEE Transactions on Terahertz Science and Technology, 2016, 6(1):32–39.

  19. J. Letosa, M. García-Gracia, J. M. Forniés-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).

    Article  Google Scholar 

  20. N. Cohen, J. W. Handley, R. D. Boyle, S. L. Braunstein, and E. Berry, “Experimental signature of registration noise in pulsed terahertz systems,” Fluct. Noise Lett. 6, L77–L84 (2006).

    Article  Google Scholar 

  21. P. U. Jepsen, D. G. Cooke, M. Koch, “Terahertz spectroscopy and imaging – Modern techniques and applications,” Laser Photon. Rev., Vol. 5, No. 1,124-166 (2011)

    Article  Google Scholar 

  22. W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Material thickness optimization for terahertz time-domain spectroscopy,” Opt. Express 16, 7382–7396 (2008).

    Article  Google Scholar 

  23. I. H. Lira and W. Wöger, “The evaluation of standard uncertainty in the presence of limited resolution of indicating devices,” Meas. Sci. Technol. 8, 441–443 (1997).

    Article  Google Scholar 

  24. T. Dorney, R. Baraniuk, and D. Mittleman, “Material parameter estimation with terahertz time-domain spectroscopy,” J. Opt. Soc. Am. A 18, 1562–1571 (2001).

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. R. Wilk, I. Pupeza, R. Cernat, M. Koch, “Highly accurate THz time-domain spectroscopy of multilayers structures,” IEEE Journal of Selected Topics In Quantum Electronics 14, 392–398 (2008).

  27. P. Kužel, M. A. Khazan, and J. Kroupa, “Spatio-temporal transformations of ultrashort terahertz pulses,” J. Opt. Soc. Am. B 16(10), 1795–1800 (1999).

    Article  Google Scholar 

  28. P. Juzel, H. Nemec, F. Kadlec, C. Kadlec, “Gouy shift correction for highly accurate refractive index retrieval in time-domain terahertz spectroscopy”, Optics Express, 18, 15 (2010): 15338–15348.

  29. Rossi G B. The Evaluation of Measurement Uncertainty [M]//Measurement and Probability. Springer Netherlands, 2014:205–221.

  30. Raul R Cordero, G. Seckmeryer and F. Labbe, “Effect of the resolution on the uncertainty evaluation,” Metroloiga, 43, L33–L38 (2006).

    Article  Google Scholar 

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Authors and Affiliations

  1. Guizhou Institute of Metrology, Guiyang, 550003, China

    Fei Yang, Liping Liu, Maojiang Song, Feng Han, Li Shen & Pengfei Hu

  2. Guiyang Vocational and Technical College, Guiyang, 550023, China

    Fang Zhang

Authors
  1. Fei Yang
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  2. Liping Liu
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  3. Maojiang Song
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  4. Feng Han
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  5. Li Shen
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  6. Pengfei Hu
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  7. Fang Zhang
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Correspondence to Fei Yang or Fang Zhang.

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Funding Information

This study was funded by the National Natural Science Foundation of China (NSFC) (21503045, 61540038); Guizhou Science and Technology Department (J20142107, SY20143065); and General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China (2014QK063).

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Yang, F., Liu, L., Song, M. et al. Uncertainty in Terahertz Time-Domain Spectroscopy Measurement of Liquids. J Infrared Milli Terahz Waves 38, 229–247 (2017). https://doi.org/10.1007/s10762-016-0318-1

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  • DOI: https://doi.org/10.1007/s10762-016-0318-1

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