Abstract

Time-domain terahertz spectroscopy typically uses mechanical delay stages that inherently suffer from non-uniform sampling positions. We review, simulate, and experimentally test, as a proof of principle, the ability of corrective cubic spline and Shannon re-gridding algorithms to mitigate the inherent sampling position noise. We experimentally confirm that sampling position uncertainty is not a leading source error in a modern time-domain terahertz spectrometer. Though modern systems are presently limited by other noise sources, our simulations and data suggest that re-gridding is an effective technique to improve the signal-to-noise ratio of a system limited by sampling position within the frequency range of 100 GHz to 2 THz. We also predict that re-gridding corrections will become increasingly important to both spectroscopy and imaging as THz technology continues to improve and higher frequencies become experimentally accessible.

© 2019 Optical Society of America

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References

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2017 (2)

B. K. Russell, B. K. Ofori-Okai, Z. Chen, M. C. Hoffmann, Y. Y. Tsui, and S. H. Glenzer, “Self-referenced single-shot THz detection,” Opt. Express 25, 16140–16150 (2017).
[Crossref]

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

2016 (2)

2015 (1)

D. M. Slocum, R. H. Giles, and T. M. Goyette, “High-resolution water vapor spectrum and line shape analysis in the Terahertz region,” J. Quant. Spectrosc. Radiat. Transfer 159, 69–79 (2015).
[Crossref]

2014 (5)

D. M. Slocum, T. M. Goyette, and R. H. Giles, “High-resolution terahertz atmospheric water vapor continuum measurements,” Proc. SPIE 9102, 91020E (2014).
[Crossref]

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

S. Proppert, S. Wolter, T. Holm, T. Klein, S. van de Linde, and M. Sauer, “Cubic B-spline calibration for 3D super-resolution measurements using astigmatic imaging,” Opt. Express 22, 10304–10316 (2014).
[Crossref]

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 610–637 (2014).
[Crossref]

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

2011 (1)

D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).
[Crossref]

2009 (2)

2008 (2)

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
[Crossref]

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. A 464, 2435–2456 (2008).
[Crossref]

2007 (1)

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

2004 (2)

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52, 2438–2447 (2004).
[Crossref]

D. A. Zimdars and J. S. White, “Terahertz reflection imaging for package and personnel inspection,” Proc. SPIE 5411, 562216 (2004).
[Crossref]

2002 (2)

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

X. C. Zhang, “Terahertz wave imaging: horizons and hurdles.,” Phys. Med. Biol. 47, 3667–3677 (2002).
[Crossref]

2000 (2)

1999 (2)

D. Strauch and B. Dorner, “Phonon dispersion in GaAs,” J. Phys. Condens. Matter 2, 1457–1474 (1999).
[Crossref]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

1996 (2)

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[Crossref]

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

1989 (1)

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[Crossref]

Abbott, D.

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. A 464, 2435–2456 (2008).
[Crossref]

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
[Crossref]

S. Mickan, D. Abbott, J. Munch, X.-C. Zhang, and T. van Doorn, “Analysis of system trade-offs for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Alfaro-Gomez, M.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Allred, J. J.

Arnone, D. D.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

Artacho, J. M.

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

Ashworth, P. C.

Averitt, R. D.

D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).
[Crossref]

Balzer, J. C.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in THz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37, 605–613 (2016).
[Crossref]

Baraniuk, R. G.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

Bartels, A.

Bartels, L.

Basov, D. N.

D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).
[Crossref]

Bilbro, L.

L. Bilbro, “Fluctuations of superconductivity in La2-xSrxCuO4 measured with terahertz time-domain spectroscopy,” Ph.D. thesis (The Johns Hopkins University, 2012).

Bisi, M.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in THz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37, 605–613 (2016).
[Crossref]

Bonn, M.

Brown, R. G.

R. G. Brown and P. Hwang, Introduction to Random Signals and Applied Kalman Filtering, 2nd ed. (John Wiley & Sons, 1992).

Busch, S. F.

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

Castillo-Guzman, A.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Castro-Camus, E.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

Chen, Y.

Chen, Z.

Cole, B. E.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

de Boor, C. R.

C. R. de Boor, A Practical Guide to Splines,” Vol. 27 of Applied Mathematical Sciences (Springer, 1978).

Dekorsy, T.

Deninger, A.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

Dexheimer, S. L.

S. L. Dexheimer, Terahertz Spectroscopy: Principles and Applications (CRC Press, 2007).

Dietz, R.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

Dorner, B.

D. Strauch and B. Dorner, “Phonon dispersion in GaAs,” J. Phys. Condens. Matter 2, 1457–1474 (1999).
[Crossref]

Dressel, M.

D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).
[Crossref]

Fattinger, C.

Fischer, B. M.

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
[Crossref]

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. A 464, 2435–2456 (2008).
[Crossref]

Fornies-Marquina, J.

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

Garcia-Gracia, M.

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

Gebs, R.

Giles, R. H.

D. M. Slocum, R. H. Giles, and T. M. Goyette, “High-resolution water vapor spectrum and line shape analysis in the Terahertz region,” J. Quant. Spectrosc. Radiat. Transfer 159, 69–79 (2015).
[Crossref]

D. M. Slocum, T. M. Goyette, and R. H. Giles, “High-resolution terahertz atmospheric water vapor continuum measurements,” Proc. SPIE 9102, 91020E (2014).
[Crossref]

Glenzer, S. H.

Göbel, T.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

Goyette, T. M.

D. M. Slocum, R. H. Giles, and T. M. Goyette, “High-resolution water vapor spectrum and line shape analysis in the Terahertz region,” J. Quant. Spectrosc. Radiat. Transfer 159, 69–79 (2015).
[Crossref]

D. M. Slocum, T. M. Goyette, and R. H. Giles, “High-resolution terahertz atmospheric water vapor continuum measurements,” Proc. SPIE 9102, 91020E (2014).
[Crossref]

Grant, P.

B. Mulgrew, P. Grant, and J. Thompson, Digital Signal Processing: Concepts and Applications, 2nd ed. (2002).

Grischkowsky, D.

Gupta, M.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

Haule, K.

D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).
[Crossref]

Heinz, T. F.

Hernandez-Cardoso, G.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Hernandez-Serrano, A.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Hoffmann, M. C.

Holm, T.

Horowitz, J. A.

Huang, S.

Hwang, P.

R. G. Brown and P. Hwang, Introduction to Random Signals and Applied Kalman Filtering, 2nd ed. (John Wiley & Sons, 1992).

Jacobsen, R. H.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[Crossref]

Jahn, D.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in THz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37, 605–613 (2016).
[Crossref]

Janke, C.

Kan, K. W.

Katayama, I.

Katsutani, F.

Klatt, G.

Klein, T.

Knoesel, E.

Koch, M.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in THz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37, 605–613 (2016).
[Crossref]

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

Kono, J.

Lee, Y.-S.

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).

Lemus-Bedolla, E.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Letosa, J.

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

Lin, H.

Linfield, E. H.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

Lippert, S.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in THz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37, 605–613 (2016).
[Crossref]

Lopez-Lemus, H.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Mickan, S.

S. Mickan, D. Abbott, J. Munch, X.-C. Zhang, and T. van Doorn, “Analysis of system trade-offs for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

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.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[Crossref]

Mohlenkamp, M. J.

T. Young and M. J. Mohlenkamp, Introduction to Numerical Methods and Matlab Programming for Engineers, 7th ed. (Ohio University, 2017).

Mulgrew, B.

B. Mulgrew, P. Grant, and J. Thompson, Digital Signal Processing: Concepts and Applications, 2nd ed. (2002).

Munch, J.

S. Mickan, D. Abbott, J. Munch, X.-C. Zhang, and T. van Doorn, “Analysis of system trade-offs for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Naftaly, M.

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 610–637 (2014).
[Crossref]

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

Nahata, A.

Neelamani, R.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

Noe, G. T.

Nojiri, H.

Nuss, M. C.

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[Crossref]

Oberto, L.

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in THz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37, 605–613 (2016).
[Crossref]

Ofori-Okai, B. K.

Pepper, M.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

Pickwell-MacPherson, E.

Probst, T.

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

Proppert, S.

Pye, R. J.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

Reider, G. A.

Rettich, F.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

Roehle, H.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

Rojas-Landeros, S.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Rudd, J. V.

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

Russell, B. K.

Salas-Gutierrez, I.

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Sauer, M.

Schell, M.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

Schwerdtfeger, M.

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

Sekiguchi, F.

Shan, J.

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[Crossref]

Siegel, P. H.

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52, 2438–2447 (2004).
[Crossref]

Slocum, D. M.

D. M. Slocum, R. H. Giles, and T. M. Goyette, “High-resolution water vapor spectrum and line shape analysis in the Terahertz region,” J. Quant. Spectrosc. Radiat. Transfer 159, 69–79 (2015).
[Crossref]

D. M. Slocum, T. M. Goyette, and R. H. Giles, “High-resolution terahertz atmospheric water vapor continuum measurements,” Proc. SPIE 9102, 91020E (2014).
[Crossref]

Soltani, A.

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

Strauch, D.

D. Strauch and B. Dorner, “Phonon dispersion in GaAs,” J. Phys. Condens. Matter 2, 1457–1474 (1999).
[Crossref]

Sullivan, D. M.

Takeda, J.

Thompson, J.

B. Mulgrew, P. Grant, and J. Thompson, Digital Signal Processing: Concepts and Applications, 2nd ed. (2002).

Tsui, Y. Y.

van de Linde, S.

Van Der Marel, D.

D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).
[Crossref]

van Doorn, T.

S. Mickan, D. Abbott, J. Munch, X.-C. Zhang, and T. van Doorn, “Analysis of system trade-offs for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

van Exter, M.

Vieweg, N.

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

Wallace, V. P.

S. Huang, P. C. Ashworth, K. W. Kan, Y. Chen, V. P. Wallace, Y.-T. Zhang, and E. Pickwell-MacPherson, “Improved sample characterization in terahertz reflection imaging and spectroscopy,” Opt. Express 17, 3848–3854 (2009).
[Crossref]

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

Weling, A. S.

White, J. S.

D. A. Zimdars and J. S. White, “Terahertz reflection imaging for package and personnel inspection,” Proc. SPIE 5411, 562216 (2004).
[Crossref]

Withayachumnankul, W.

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 610–637 (2014).
[Crossref]

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. A 464, 2435–2456 (2008).
[Crossref]

W. Withayachumnankul, B. M. Fischer, H. Lin, and D. Abbott, “Uncertainty in terahertz time-domain spectroscopy measurement,” J. Opt. Soc. Am. B 25, 1059–1072 (2008).
[Crossref]

Wolter, S.

Woods, G. L.

Woodward, R. M.

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

Young, T.

T. Young and M. J. Mohlenkamp, Introduction to Numerical Methods and Matlab Programming for Engineers, 7th ed. (Ohio University, 2017).

Zhang, Q.

Zhang, X. C.

X. C. Zhang, “Terahertz wave imaging: horizons and hurdles.,” Phys. Med. Biol. 47, 3667–3677 (2002).
[Crossref]

Zhang, X.-C.

S. Mickan, D. Abbott, J. Munch, X.-C. Zhang, and T. van Doorn, “Analysis of system trade-offs for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Zhang, Y.-T.

Zimdars, D. A.

D. A. Zimdars and J. S. White, “Terahertz reflection imaging for package and personnel inspection,” Proc. SPIE 5411, 562216 (2004).
[Crossref]

Appl. Phys. B (1)

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Koch, “Recent advances in terahertz imaging,” Appl. Phys. B 68, 1085–1094 (1999).
[Crossref]

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

D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
[Crossref]

IEEE Trans. Magn. (1)

J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, J. M. Artacho, J. Letosa, M. Garcia-Gracia, J. Fornies-Marquina, and J. M. Artacho, “Performance limits in TDR technique by Monte Carlo simulation,” IEEE Trans. Magn. 32, 958–961 (1996).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

P. H. Siegel, “Terahertz technology in biology and medicine,” IEEE Trans. Microw. Theory Tech. 52, 2438–2447 (2004).
[Crossref]

J. Infrared Millim. Terahertz Waves (4)

W. Withayachumnankul and M. Naftaly, “Fundamentals of measurement in terahertz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 610–637 (2014).
[Crossref]

N. Vieweg, F. Rettich, A. Deninger, H. Roehle, R. Dietz, T. Göbel, and M. Schell, “Terahertz-time domain spectrometer with 90  dB peak dynamic range,” J. Infrared Millim. Terahertz Waves 35, 823–832 (2014).
[Crossref]

D. Jahn, S. Lippert, M. Bisi, L. Oberto, J. C. Balzer, and M. Koch, “On the influence of delay line uncertainty in THz time-domain spectroscopy,” J. Infrared Millim. Terahertz Waves 37, 605–613 (2016).
[Crossref]

A. Soltani, T. Probst, S. F. Busch, M. Schwerdtfeger, E. Castro-Camus, and M. Koch, “Error from delay drift in terahertz attenuated total reflection spectroscopy,” J. Infrared Millim. Terahertz Waves 35, 468–477 (2014).
[Crossref]

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

J. Phys. Condens. Matter (1)

D. Strauch and B. Dorner, “Phonon dispersion in GaAs,” J. Phys. Condens. Matter 2, 1457–1474 (1999).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

D. M. Slocum, R. H. Giles, and T. M. Goyette, “High-resolution water vapor spectrum and line shape analysis in the Terahertz region,” J. Quant. Spectrosc. Radiat. Transfer 159, 69–79 (2015).
[Crossref]

Microelectron. J. (1)

S. Mickan, D. Abbott, J. Munch, X.-C. Zhang, and T. van Doorn, “Analysis of system trade-offs for terahertz imaging,” Microelectron. J. 31, 503–514 (2000).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Phys. Med. Biol. (2)

X. C. Zhang, “Terahertz wave imaging: horizons and hurdles.,” Phys. Med. Biol. 47, 3667–3677 (2002).
[Crossref]

R. M. Woodward, B. E. Cole, V. P. Wallace, R. J. Pye, D. D. Arnone, E. H. Linfield, and M. Pepper, “Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue,” Phys. Med. Biol. 47, 3853–3863 (2002).
[Crossref]

Proc. IEEE (1)

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

Proc. IRE (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[Crossref]

Proc. R. Soc. A (1)

W. Withayachumnankul, B. M. Fischer, and D. Abbott, “Numerical removal of water vapour effects from terahertz time-domain spectroscopy measurements,” Proc. R. Soc. A 464, 2435–2456 (2008).
[Crossref]

Proc. SPIE (2)

D. M. Slocum, T. M. Goyette, and R. H. Giles, “High-resolution terahertz atmospheric water vapor continuum measurements,” Proc. SPIE 9102, 91020E (2014).
[Crossref]

D. A. Zimdars and J. S. White, “Terahertz reflection imaging for package and personnel inspection,” Proc. SPIE 5411, 562216 (2004).
[Crossref]

Rev. Mod. Phys. (1)

D. N. Basov, R. D. Averitt, D. Van Der Marel, M. Dressel, and K. Haule, “Electrodynamics of correlated electron materials,” Rev. Mod. Phys. 83, 471–541 (2011).
[Crossref]

Sci. Rep. (1)

G. Hernandez-Cardoso, S. Rojas-Landeros, M. Alfaro-Gomez, A. Hernandez-Serrano, I. Salas-Gutierrez, E. Lemus-Bedolla, A. Castillo-Guzman, H. Lopez-Lemus, and E. Castro-Camus, “Terahertz imaging for early screening of diabetic foot syndrome: a proof of concept,” Sci. Rep. 7, 42124 (2017).
[Crossref]

Other (7)

R. G. Brown and P. Hwang, Introduction to Random Signals and Applied Kalman Filtering, 2nd ed. (John Wiley & Sons, 1992).

B. Mulgrew, P. Grant, and J. Thompson, Digital Signal Processing: Concepts and Applications, 2nd ed. (2002).

S. L. Dexheimer, Terahertz Spectroscopy: Principles and Applications (CRC Press, 2007).

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009).

L. Bilbro, “Fluctuations of superconductivity in La2-xSrxCuO4 measured with terahertz time-domain spectroscopy,” Ph.D. thesis (The Johns Hopkins University, 2012).

C. R. de Boor, A Practical Guide to Splines,” Vol. 27 of Applied Mathematical Sciences (Springer, 1978).

T. Young and M. J. Mohlenkamp, Introduction to Numerical Methods and Matlab Programming for Engineers, 7th ed. (Ohio University, 2017).

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Figures (3)

Fig. 1.
Fig. 1. Illustration of the re-gridding process of the main peak for a real THz pulse. This process takes irregularly sampled data points (red) and produces a regularly sampled estimate of the pulse (black). The line is a guide to the eye.
Fig. 2.
Fig. 2. Simulated re-gridding error as a function of frequency for varying dynamic range (DR) and different percent RMS sampling errors averaged over 100 simulated scans; lower is better. Re-gridding becomes increasingly effective with increasingly high dynamic range and increasingly large sampling position deviations. Note that the Shannon and cubic spline terms produce errors indistinguishable from each other on this scale when the dynamic range is 40.0, which is somewhat typical of a TDTS system.
Fig. 3.
Fig. 3. Improvement versus frequency (for experimental data) by re-gridding process for Shannon (panel A), and cubic spline re-gridding (panel B) with various artificially generated sampling position error distributions with the RMS error quoted in panel C. Delay-stage measurement steps of 10 micrometers at a dynamic range of approximately 40 dB were used. The improvement in the standard deviation by re-gridding averaged from 100 GHz to 2.0 THz versus RMS sampling deviations (panel D) and shows ratios greater than unity, indicating improvement. Cubic spline re-gridding is consistently more effective than Shannon re-gridding at high sampling position deviations.

Equations (4)

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

Sk(x)=Ak+Bkx+Ckx2+Dkx3.
(y(x1)y(x2)y(xn))=(sinc(x1XX)sinc(x12XX)sinc(x1nXX)sinc(x2XX)sinc(x22XX)sinc(x2nXX)sinc(xnXX)sinc(xn2XX)sinc(xnnXX))(Y(X)Y(2X)Y(nX)).
y=R¯Y.
Y=R¯1y.

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