Abstract

We use terahertz transmission through limestone sedimentary rock samples to assess the macro and micro porosity. We exploit the notable water absorption in the terahertz spectrum to interact with the pores that are two orders of magnitude smaller (<1μm) than the terahertz wavelength. Terahertz water sensitivity provides us with the dehydration profile of the rock samples. The results show that there is a linear correlation between such a profile and the ratio of micro to macro porosity of the rock. Furthermore, this study estimates the absolute value of total porosity based on optical diffusion theory. We compare our results with that of mercury injection capillary pressure as a benchmark to confirm our analytic framework. The porosimetry method presented here sets a foundation for a new generation of less invasive porosimetry methods with higher penetration depth based on lower frequency (f<10THz) scattering and absorption. The technique has applications in geological studies and in other industries without the need for hazardous mercury or ionizing radiation.

© 2017 Optical Society of America

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References

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2017 (2)

D. Markl, P. Wang, C. Ridgway, A.-P. Karttunen, M. Chakraborty, P. Bawuah, P. Pääkkönen, P. Gane, J. Ketolainen, K.-E. Peiponen, and J. A. Zeitler, “characterization of the pore structure of functionalized calcium carbonate tablets by terahertz time-domain spectroscopy and x-ray computed microtomography,” J. Pharm. Sci. 106(6), 1586–1595 (2017).
[PubMed]

D. Markl, J. Sauerwein, D. J. Goodwin, S. van den Ban, and J. A. Zeitler, “non-destructive determination of disintegration time and dissolution in immediate release tablets by terahertz transmission measurements,” Pharm. Res. 34(5), 1012–1022 (2017).
[PubMed]

2016 (5)

P. Bawuah, T. Ervasti, N. Tan, J. A. Zeitler, J. Ketolainen, and K.-E. Peiponen, “noninvasive porosity measurement of biconvex tablets using terahertz pulses,” Int. J. Pharm. 509(1-2), 439–443 (2016).
[PubMed]

A. Aghasi, B. Heshmat, A. Redo-Sanchez, J. Romberg, and R. Raskar, “Sweep distortion removal from terahertz images via blind demodulation,” Optica 3(7), 754 (2016).

A. Redo-Sanchez, B. Heshmat, A. Aghasi, S. Naqvi, M. Zhang, J. Romberg, and R. Raskar, “Terahertz time-gated spectral imaging for content extraction through layered structures,” Nat. Commun. 7, 12665 (2016).
[PubMed]

H. Zhan, S. Wu, K. Zhao, R. Bao, and L. Xiao, “CaCO3, its reaction and carbonate rocks: terahertz spectroscopy investigation,” J. Geophys. Eng. 13(5), 768–774 (2016).

B. Groever, B. Heshmat, and R. Raskar, “Tyndall windows: tunable scattering of disordered solid–liquid matching mixtures,” ACS Photonics 3(6), 930–935 (2016).

2015 (1)

K.-E. Peiponen, P. Bawuah, M. Chakraborty, M. Juuti, J. A. Zeitler, and J. Ketolainen, “estimation of young’s modulus of pharmaceutical tablet obtained by terahertz time-delay measurement,” Int. J. Pharm. 489(1-2), 100–105 (2015).
[PubMed]

2014 (1)

P. Bawuah, A. Pierotic Mendia, P. Silfsten, P. Pääkkönen, T. Ervasti, J. Ketolainen, J. A. Zeitler, and K.-E. Peiponen, “Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques,” Int. J. Pharm. 465(1-2), 70–76 (2014).
[PubMed]

2013 (2)

B. Bijeljic, P. Mostaghimi, and M. J. Blunt, “Insights into non-fickian solute transport in carbonates,” Water Resour. Res. 49(5), 2714–2728 (2013).
[PubMed]

E. Castro-Camus, M. Palomar, and A. A. Covarrubias, “Leaf water dynamics of arabidopsis thaliana monitored in-vivo using terahertz time-domain spectroscopy,” Sci. Rep. 3, 2910 (2013).
[PubMed]

2012 (9)

M. Kaushik, B. W. H. Ng, B. M. Fischer, and D. Abbott, “Terahertz scattering by dense media,” Appl. Phys. Lett. 100(24), 241110 (2012).

O. Gharbi and M. J. Blunt, “The impact of wettability and connectivity on relative permeability in carbonates: a pore network modeling analysis,” Water Resour. Res. 48(12), 1–14 (2012).

B. Heshmat, H. Pahlevaninezhad, Y. Pang, M. Masnadi-Shirazi, R. Burton Lewis, T. Tiedje, R. Gordon, and T. E. Darcie, “Nanoplasmonic terahertz photoconductive switch on GaAs,” Nano Lett. 12(12), 6255–6259 (2012).
[PubMed]

B. Heshmat, H. Pahlevaninezhad, and T. E. Darcie, “Carbon nanotube-based photoconductive switches for thz detection: an assessment of capabilities and limitations,” IEEE Photon. J. 4(3), 970–985 (2012).

K. M. Nam, L. M. Zurk, and S. Schecklman, “Modeling terahertz diffuse scattering from granular media using radiative transfer theory,” Prog. Electromagn. Res. B 38, 205–223 (2012).

C. R. Clarkson, M. Freeman, L. He, M. Agamalian, Y. B. Melnichenko, M. Mastalerz, R. M. Bustin, A. P. Radliński, and T. P. Blach, “Characterization of tight gas reservoir pore structure using usans/sans and gas adsorption analysis,” Fuel 95, 371–385 (2012).

O. K. Farha, I. Eryazici, N. C. Jeong, B. G. Hauser, C. E. Wilmer, A. A. Sarjeant, R. Q. Snurr, S. T. Nguyen, A. Ö. Yazaydın, and J. T. Hupp, “Metal-organic framework materials with ultrahigh surface areas: is the sky the limit?” J. Am. Chem. Soc. 134(36), 15016–15021 (2012).
[PubMed]

A. Samanta, A. Zhao, G. K. H. Shimizu, P. Sarkar, and R. Gupta, “Post-combustion co2 capture using solid sorbents: a review,” Ind. Eng. Chem. Res. 51(4), 1438–1463 (2012).

L. Mei, S. Svanberg, and G. Somesfalean, “Combined optical porosimetry and gas absorption spectroscopy in gas-filled porous media using diode-laser-based frequency domain photon migration,” Opt. Express 20(15), 16942 (2012).

2011 (2)

F. Zhou, Y. Bao, W. Cao, C. T. Stuart, J. Gu, W. Zhang, and C. Sun, “Hiding a realistic object using a broadband terahertz invisibility cloak,” Sci. Rep. 1, 78 (2011).
[PubMed]

H. Pahlevaninezhad, B. Heshmat, and T. E. Darcie, “Advances in terahertz waveguides and sources,” IEEE Photon. J. 3(2), 307–310 (2011).

2010 (1)

2009 (1)

E. A. Clerke, “Permeability, relative permeability, microscopic displacement efficiency and pore geometry of m_1 bimodal pore systems in arab-d limestone,” SPE J. 14(3), 524–531 (2009).

2008 (1)

C. C. Egger, C. du Fresne, V. I. Raman, V. Schädler, T. Frechen, S. V. Roth, and P. Müller-Buschbaum, “Characterization of highly porous polymeric materials with pore diameters larger than 100 nm by mercury porosimetry and x-ray scattering methods,” Langmuir 24(11), 5877–5887 (2008).
[PubMed]

2007 (4)

F. Porcheron, M. Thommes, R. Ahmad, and P. A. Monson, “Mercury porosimetry in mesoporous glasses: a comparison of experiments with results from a molecular model,” Langmuir 23(6), 3372–3380 (2007).
[PubMed]

S. Eslava, M. R. Baklanov, C. E. Kirschhock, F. Iacopi, S. Aldea, K. Maex, and J. A. Martens, “Characterization of a molecular sieve coating using ellipsometric porosimetry,” Langmuir 23(26), 12811–12816 (2007).
[PubMed]

T. Metzger, A. Irawan, and E. Tsotsas, “Influence of pore structure on drying kinetics: a pore network study,” AIChE J. 53(12), 3029–3041 (2007).

L. M. Zurk, B. Orlowski, D. P. Winebrenner, E. I. Thorsos, M. R. Leahy-Hoppa, and L. M. Hayden, “Terahertz scattering from granular material,” J. Opt. Soc. Am. B 24(9), 2238 (2007).

2005 (2)

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913–4930 (2005).
[PubMed]

B. D. Vogt, R. A. Pai, H. J. Lee, R. C. Hedden, C. L. Soles, W. Wu, E. K. Lin, B. J. Bauer, and J. J. Watkins, “Characterization of ordered mesoporous silica films using small-angle neutron scattering and x-ray porosimetry,” Chem. Mater. 17(6), 1398–1408 (2005).

2004 (2)

F. Porcheron, P. A. Monson, and M. Thommes, “Modeling mercury porosimetry using statistical mechanics,” Langmuir 20(15), 6482–6489 (2004).
[PubMed]

H. K. Chae, D. Y. Siberio-Pérez, J. Kim, Y. Go, M. Eddaoudi, A. J. Matzger, M. O’Keeffe, and O. M. Yaghi, “A route to high surface area, porosity and inclusion of large molecules in crystals,” Nature 427(6974), 523–527 (2004).
[PubMed]

2002 (2)

A. J. Cox, A. J. DeWeerd, and J. Linden, “An experiment to measure mie and rayleigh total scattering cross sections,” Am. J. Phys. 70(6), 620 (2002).

M. Hartmann and A. Vinu, “Mechanical stability and porosity analysis of large-pore sba-15 mesoporous molecular sieves by mercury porosimetry and organics adsorption,” Langmuir 18, 8010–8016 (2002).

2000 (2)

S. H. Kim and C.-C. Chu, “Pore structure analysis of swollen dextran-methacrylate hydrogels by SEM and mercury intrusion porosimetry,” J. Biomed. Mater. Res. 53(3), 258–266 (2000).
[PubMed]

L. Tsang, C. Te Chen, A. T. C. Chang, J. Guo, and K. H. Ding, “Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow,” Radio Sci. 35(3), 731–749 (2000).

1999 (1)

D. L. Cantrell and R. M. Hagerty, “Microporosity in arab formation carbonates, saudi arabia,” GeoArabia 4(2), 129–154 (1999).

1998 (1)

A. Fischer, J. Jindra, and H. Wendt, “Porosity and catalyst utilization of thin layer cathodes in air operated pem-fuel cells,” J. Appl. Electrochem. 28(3), 277–282 (1998).

1993 (1)

M. Prat, “Percolation model of drying under isothermal conditions in porous media,” Int. J. Multiph. Flow 19(4), 691–704 (1993).

1991 (1)

H. J. Liebe, G. A. Hufford, and T. Manabe, “A model for the complex permittivity of water at frequencies below 1 thz,” Int. J. Infrared Millim. Waves 12(7), 659–675 (1991).

1989 (1)

1986 (1)

W. C. Conner, J. F. Cevallos-Candau, E. L. Weist, J. Pajares, S. Mendioroz, and A. Cortes, “Characterization of pore structure: porosimetry and sorption,” Langmuir 2(2), 151–154 (1986).

1985 (1)

V. V. Varadan and V. K. Varadan, “The quasicrystalline approximation and multiple scattering of waves in random media,” J. Acoust. Soc. Am. 77, S3 (1985).

1982 (1)

R. Chandler, J. Koplik, K. Lerman, and J. F. Willemsen, “Capillary displacement and percolation in porous media,” J. Fluid Mech. 119(1), 249 (1982).

1975 (1)

J. Van Brakel, “Pore space models for transport phenomena in porous media review and evaluation with special emphasis on capillary liquid transport,” Powder Technol. 11(3), 205–236 (1975).

1974 (1)

J. C. Melrose, “Role of capillary forces in detennining microscopic displacement efficiency for oil recovery by waterflooding,” J. Can. Pet. Technol. 13(4), 9 (1974).

1951 (1)

E. P. Barrett, L. G. Joyner, and P. P. Halenda, “The determination of pore volume and area distributions in porous substances; computations from nitrogen isotherms,” J. Am. Chem. Soc. 73(1), 373–380 (1951).

1938 (1)

S. Brunauer, P. H. Emmett, and E. Teller, “Adsorption of gases in multimolecular layers,” J. Am. Chem. Soc. 60(1), 309–319 (1938).

Abbott, D.

M. Kaushik, B. W. H. Ng, B. M. Fischer, and D. Abbott, “Terahertz scattering by dense media,” Appl. Phys. Lett. 100(24), 241110 (2012).

Agamalian, M.

C. R. Clarkson, M. Freeman, L. He, M. Agamalian, Y. B. Melnichenko, M. Mastalerz, R. M. Bustin, A. P. Radliński, and T. P. Blach, “Characterization of tight gas reservoir pore structure using usans/sans and gas adsorption analysis,” Fuel 95, 371–385 (2012).

Aghasi, A.

A. Aghasi, B. Heshmat, A. Redo-Sanchez, J. Romberg, and R. Raskar, “Sweep distortion removal from terahertz images via blind demodulation,” Optica 3(7), 754 (2016).

A. Redo-Sanchez, B. Heshmat, A. Aghasi, S. Naqvi, M. Zhang, J. Romberg, and R. Raskar, “Terahertz time-gated spectral imaging for content extraction through layered structures,” Nat. Commun. 7, 12665 (2016).
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R. Stanley, S. Guidry, and H. Al-Ansi, “Microporosity spatial modeling in a giant carbonate reservoir,” in International Petroleum Technology Conference (2015).

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S. Eslava, M. R. Baklanov, C. E. Kirschhock, F. Iacopi, S. Aldea, K. Maex, and J. A. Martens, “Characterization of a molecular sieve coating using ellipsometric porosimetry,” Langmuir 23(26), 12811–12816 (2007).
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Bao, Y.

F. Zhou, Y. Bao, W. Cao, C. T. Stuart, J. Gu, W. Zhang, and C. Sun, “Hiding a realistic object using a broadband terahertz invisibility cloak,” Sci. Rep. 1, 78 (2011).
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E. P. Barrett, L. G. Joyner, and P. P. Halenda, “The determination of pore volume and area distributions in porous substances; computations from nitrogen isotherms,” J. Am. Chem. Soc. 73(1), 373–380 (1951).

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B. D. Vogt, R. A. Pai, H. J. Lee, R. C. Hedden, C. L. Soles, W. Wu, E. K. Lin, B. J. Bauer, and J. J. Watkins, “Characterization of ordered mesoporous silica films using small-angle neutron scattering and x-ray porosimetry,” Chem. Mater. 17(6), 1398–1408 (2005).

Bawuah, P.

D. Markl, P. Wang, C. Ridgway, A.-P. Karttunen, M. Chakraborty, P. Bawuah, P. Pääkkönen, P. Gane, J. Ketolainen, K.-E. Peiponen, and J. A. Zeitler, “characterization of the pore structure of functionalized calcium carbonate tablets by terahertz time-domain spectroscopy and x-ray computed microtomography,” J. Pharm. Sci. 106(6), 1586–1595 (2017).
[PubMed]

P. Bawuah, T. Ervasti, N. Tan, J. A. Zeitler, J. Ketolainen, and K.-E. Peiponen, “noninvasive porosity measurement of biconvex tablets using terahertz pulses,” Int. J. Pharm. 509(1-2), 439–443 (2016).
[PubMed]

K.-E. Peiponen, P. Bawuah, M. Chakraborty, M. Juuti, J. A. Zeitler, and J. Ketolainen, “estimation of young’s modulus of pharmaceutical tablet obtained by terahertz time-delay measurement,” Int. J. Pharm. 489(1-2), 100–105 (2015).
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P. Bawuah, A. Pierotic Mendia, P. Silfsten, P. Pääkkönen, T. Ervasti, J. Ketolainen, J. A. Zeitler, and K.-E. Peiponen, “Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques,” Int. J. Pharm. 465(1-2), 70–76 (2014).
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Blunt, M. J.

B. Bijeljic, P. Mostaghimi, and M. J. Blunt, “Insights into non-fickian solute transport in carbonates,” Water Resour. Res. 49(5), 2714–2728 (2013).
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S. Brunauer, P. H. Emmett, and E. Teller, “Adsorption of gases in multimolecular layers,” J. Am. Chem. Soc. 60(1), 309–319 (1938).

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B. Heshmat, H. Pahlevaninezhad, Y. Pang, M. Masnadi-Shirazi, R. Burton Lewis, T. Tiedje, R. Gordon, and T. E. Darcie, “Nanoplasmonic terahertz photoconductive switch on GaAs,” Nano Lett. 12(12), 6255–6259 (2012).
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C. R. Clarkson, M. Freeman, L. He, M. Agamalian, Y. B. Melnichenko, M. Mastalerz, R. M. Bustin, A. P. Radliński, and T. P. Blach, “Characterization of tight gas reservoir pore structure using usans/sans and gas adsorption analysis,” Fuel 95, 371–385 (2012).

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D. L. Cantrell and R. M. Hagerty, “Microporosity in arab formation carbonates, saudi arabia,” GeoArabia 4(2), 129–154 (1999).

Cao, W.

F. Zhou, Y. Bao, W. Cao, C. T. Stuart, J. Gu, W. Zhang, and C. Sun, “Hiding a realistic object using a broadband terahertz invisibility cloak,” Sci. Rep. 1, 78 (2011).
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[PubMed]

K.-E. Peiponen, P. Bawuah, M. Chakraborty, M. Juuti, J. A. Zeitler, and J. Ketolainen, “estimation of young’s modulus of pharmaceutical tablet obtained by terahertz time-delay measurement,” Int. J. Pharm. 489(1-2), 100–105 (2015).
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W. C. Conner, J. F. Cevallos-Candau, E. L. Weist, J. Pajares, S. Mendioroz, and A. Cortes, “Characterization of pore structure: porosimetry and sorption,” Langmuir 2(2), 151–154 (1986).

Cortes, A.

W. C. Conner, J. F. Cevallos-Candau, E. L. Weist, J. Pajares, S. Mendioroz, and A. Cortes, “Characterization of pore structure: porosimetry and sorption,” Langmuir 2(2), 151–154 (1986).

Covarrubias, A. A.

E. Castro-Camus, M. Palomar, and A. A. Covarrubias, “Leaf water dynamics of arabidopsis thaliana monitored in-vivo using terahertz time-domain spectroscopy,” Sci. Rep. 3, 2910 (2013).
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B. Heshmat, H. Pahlevaninezhad, Y. Pang, M. Masnadi-Shirazi, R. Burton Lewis, T. Tiedje, R. Gordon, and T. E. Darcie, “Nanoplasmonic terahertz photoconductive switch on GaAs,” Nano Lett. 12(12), 6255–6259 (2012).
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B. Heshmat, H. Pahlevaninezhad, and T. E. Darcie, “Carbon nanotube-based photoconductive switches for thz detection: an assessment of capabilities and limitations,” IEEE Photon. J. 4(3), 970–985 (2012).

H. Pahlevaninezhad, B. Heshmat, and T. E. Darcie, “Advances in terahertz waveguides and sources,” IEEE Photon. J. 3(2), 307–310 (2011).

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A. J. Cox, A. J. DeWeerd, and J. Linden, “An experiment to measure mie and rayleigh total scattering cross sections,” Am. J. Phys. 70(6), 620 (2002).

Ding, K. H.

L. Tsang, C. Te Chen, A. T. C. Chang, J. Guo, and K. H. Ding, “Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow,” Radio Sci. 35(3), 731–749 (2000).

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C. C. Egger, C. du Fresne, V. I. Raman, V. Schädler, T. Frechen, S. V. Roth, and P. Müller-Buschbaum, “Characterization of highly porous polymeric materials with pore diameters larger than 100 nm by mercury porosimetry and x-ray scattering methods,” Langmuir 24(11), 5877–5887 (2008).
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Eddaoudi, M.

H. K. Chae, D. Y. Siberio-Pérez, J. Kim, Y. Go, M. Eddaoudi, A. J. Matzger, M. O’Keeffe, and O. M. Yaghi, “A route to high surface area, porosity and inclusion of large molecules in crystals,” Nature 427(6974), 523–527 (2004).
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Edwards, E.

S. M. Fullmer, S. A. Guidry, J. Gournay, E. Bowlin, G. Ottinger, A. M. Al Neyadi, G. Gupta, B. Gao, and E. Edwards, ” Microporosity: characterization, distribution, and influence on oil recovery,” in International Petroleum Technology Conference (2014).

Egger, C. C.

C. C. Egger, C. du Fresne, V. I. Raman, V. Schädler, T. Frechen, S. V. Roth, and P. Müller-Buschbaum, “Characterization of highly porous polymeric materials with pore diameters larger than 100 nm by mercury porosimetry and x-ray scattering methods,” Langmuir 24(11), 5877–5887 (2008).
[PubMed]

Emmett, P. H.

S. Brunauer, P. H. Emmett, and E. Teller, “Adsorption of gases in multimolecular layers,” J. Am. Chem. Soc. 60(1), 309–319 (1938).

Ervasti, T.

P. Bawuah, T. Ervasti, N. Tan, J. A. Zeitler, J. Ketolainen, and K.-E. Peiponen, “noninvasive porosity measurement of biconvex tablets using terahertz pulses,” Int. J. Pharm. 509(1-2), 439–443 (2016).
[PubMed]

P. Bawuah, A. Pierotic Mendia, P. Silfsten, P. Pääkkönen, T. Ervasti, J. Ketolainen, J. A. Zeitler, and K.-E. Peiponen, “Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques,” Int. J. Pharm. 465(1-2), 70–76 (2014).
[PubMed]

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O. K. Farha, I. Eryazici, N. C. Jeong, B. G. Hauser, C. E. Wilmer, A. A. Sarjeant, R. Q. Snurr, S. T. Nguyen, A. Ö. Yazaydın, and J. T. Hupp, “Metal-organic framework materials with ultrahigh surface areas: is the sky the limit?” J. Am. Chem. Soc. 134(36), 15016–15021 (2012).
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S. Eslava, M. R. Baklanov, C. E. Kirschhock, F. Iacopi, S. Aldea, K. Maex, and J. A. Martens, “Characterization of a molecular sieve coating using ellipsometric porosimetry,” Langmuir 23(26), 12811–12816 (2007).
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Farha, O. K.

O. K. Farha, I. Eryazici, N. C. Jeong, B. G. Hauser, C. E. Wilmer, A. A. Sarjeant, R. Q. Snurr, S. T. Nguyen, A. Ö. Yazaydın, and J. T. Hupp, “Metal-organic framework materials with ultrahigh surface areas: is the sky the limit?” J. Am. Chem. Soc. 134(36), 15016–15021 (2012).
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Fischer, B. M.

M. Kaushik, B. W. H. Ng, B. M. Fischer, and D. Abbott, “Terahertz scattering by dense media,” Appl. Phys. Lett. 100(24), 241110 (2012).

Frechen, T.

C. C. Egger, C. du Fresne, V. I. Raman, V. Schädler, T. Frechen, S. V. Roth, and P. Müller-Buschbaum, “Characterization of highly porous polymeric materials with pore diameters larger than 100 nm by mercury porosimetry and x-ray scattering methods,” Langmuir 24(11), 5877–5887 (2008).
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Freeman, M.

C. R. Clarkson, M. Freeman, L. He, M. Agamalian, Y. B. Melnichenko, M. Mastalerz, R. M. Bustin, A. P. Radliński, and T. P. Blach, “Characterization of tight gas reservoir pore structure using usans/sans and gas adsorption analysis,” Fuel 95, 371–385 (2012).

Fullmer, S. M.

S. M. Fullmer, S. A. Guidry, J. Gournay, E. Bowlin, G. Ottinger, A. M. Al Neyadi, G. Gupta, B. Gao, and E. Edwards, ” Microporosity: characterization, distribution, and influence on oil recovery,” in International Petroleum Technology Conference (2014).

Gane, P.

D. Markl, P. Wang, C. Ridgway, A.-P. Karttunen, M. Chakraborty, P. Bawuah, P. Pääkkönen, P. Gane, J. Ketolainen, K.-E. Peiponen, and J. A. Zeitler, “characterization of the pore structure of functionalized calcium carbonate tablets by terahertz time-domain spectroscopy and x-ray computed microtomography,” J. Pharm. Sci. 106(6), 1586–1595 (2017).
[PubMed]

Gao, B.

S. M. Fullmer, S. A. Guidry, J. Gournay, E. Bowlin, G. Ottinger, A. M. Al Neyadi, G. Gupta, B. Gao, and E. Edwards, ” Microporosity: characterization, distribution, and influence on oil recovery,” in International Petroleum Technology Conference (2014).

Gharbi, O.

O. Gharbi and M. J. Blunt, “The impact of wettability and connectivity on relative permeability in carbonates: a pore network modeling analysis,” Water Resour. Res. 48(12), 1–14 (2012).

Go, Y.

H. K. Chae, D. Y. Siberio-Pérez, J. Kim, Y. Go, M. Eddaoudi, A. J. Matzger, M. O’Keeffe, and O. M. Yaghi, “A route to high surface area, porosity and inclusion of large molecules in crystals,” Nature 427(6974), 523–527 (2004).
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D. Markl, J. Sauerwein, D. J. Goodwin, S. van den Ban, and J. A. Zeitler, “non-destructive determination of disintegration time and dissolution in immediate release tablets by terahertz transmission measurements,” Pharm. Res. 34(5), 1012–1022 (2017).
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B. Heshmat, H. Pahlevaninezhad, Y. Pang, M. Masnadi-Shirazi, R. Burton Lewis, T. Tiedje, R. Gordon, and T. E. Darcie, “Nanoplasmonic terahertz photoconductive switch on GaAs,” Nano Lett. 12(12), 6255–6259 (2012).
[PubMed]

Gournay, J.

S. M. Fullmer, S. A. Guidry, J. Gournay, E. Bowlin, G. Ottinger, A. M. Al Neyadi, G. Gupta, B. Gao, and E. Edwards, ” Microporosity: characterization, distribution, and influence on oil recovery,” in International Petroleum Technology Conference (2014).

Grischkowsky, D.

Groever, B.

B. Groever, B. Heshmat, and R. Raskar, “Tyndall windows: tunable scattering of disordered solid–liquid matching mixtures,” ACS Photonics 3(6), 930–935 (2016).

Gu, J.

F. Zhou, Y. Bao, W. Cao, C. T. Stuart, J. Gu, W. Zhang, and C. Sun, “Hiding a realistic object using a broadband terahertz invisibility cloak,” Sci. Rep. 1, 78 (2011).
[PubMed]

Guidry, S.

R. Stanley, S. Guidry, and H. Al-Ansi, “Microporosity spatial modeling in a giant carbonate reservoir,” in International Petroleum Technology Conference (2015).

Guidry, S. A.

S. M. Fullmer, S. A. Guidry, J. Gournay, E. Bowlin, G. Ottinger, A. M. Al Neyadi, G. Gupta, B. Gao, and E. Edwards, ” Microporosity: characterization, distribution, and influence on oil recovery,” in International Petroleum Technology Conference (2014).

Guo, J.

L. Tsang, C. Te Chen, A. T. C. Chang, J. Guo, and K. H. Ding, “Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow,” Radio Sci. 35(3), 731–749 (2000).

Gupta, G.

S. M. Fullmer, S. A. Guidry, J. Gournay, E. Bowlin, G. Ottinger, A. M. Al Neyadi, G. Gupta, B. Gao, and E. Edwards, ” Microporosity: characterization, distribution, and influence on oil recovery,” in International Petroleum Technology Conference (2014).

Gupta, R.

A. Samanta, A. Zhao, G. K. H. Shimizu, P. Sarkar, and R. Gupta, “Post-combustion co2 capture using solid sorbents: a review,” Ind. Eng. Chem. Res. 51(4), 1438–1463 (2012).

Hagerty, R. M.

D. L. Cantrell and R. M. Hagerty, “Microporosity in arab formation carbonates, saudi arabia,” GeoArabia 4(2), 129–154 (1999).

Halenda, P. P.

E. P. Barrett, L. G. Joyner, and P. P. Halenda, “The determination of pore volume and area distributions in porous substances; computations from nitrogen isotherms,” J. Am. Chem. Soc. 73(1), 373–380 (1951).

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O. K. Farha, I. Eryazici, N. C. Jeong, B. G. Hauser, C. E. Wilmer, A. A. Sarjeant, R. Q. Snurr, S. T. Nguyen, A. Ö. Yazaydın, and J. T. Hupp, “Metal-organic framework materials with ultrahigh surface areas: is the sky the limit?” J. Am. Chem. Soc. 134(36), 15016–15021 (2012).
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He, L.

C. R. Clarkson, M. Freeman, L. He, M. Agamalian, Y. B. Melnichenko, M. Mastalerz, R. M. Bustin, A. P. Radliński, and T. P. Blach, “Characterization of tight gas reservoir pore structure using usans/sans and gas adsorption analysis,” Fuel 95, 371–385 (2012).

Hedden, R. C.

B. D. Vogt, R. A. Pai, H. J. Lee, R. C. Hedden, C. L. Soles, W. Wu, E. K. Lin, B. J. Bauer, and J. J. Watkins, “Characterization of ordered mesoporous silica films using small-angle neutron scattering and x-ray porosimetry,” Chem. Mater. 17(6), 1398–1408 (2005).

Heshmat, B.

A. Redo-Sanchez, B. Heshmat, A. Aghasi, S. Naqvi, M. Zhang, J. Romberg, and R. Raskar, “Terahertz time-gated spectral imaging for content extraction through layered structures,” Nat. Commun. 7, 12665 (2016).
[PubMed]

A. Aghasi, B. Heshmat, A. Redo-Sanchez, J. Romberg, and R. Raskar, “Sweep distortion removal from terahertz images via blind demodulation,” Optica 3(7), 754 (2016).

B. Groever, B. Heshmat, and R. Raskar, “Tyndall windows: tunable scattering of disordered solid–liquid matching mixtures,” ACS Photonics 3(6), 930–935 (2016).

B. Heshmat, H. Pahlevaninezhad, and T. E. Darcie, “Carbon nanotube-based photoconductive switches for thz detection: an assessment of capabilities and limitations,” IEEE Photon. J. 4(3), 970–985 (2012).

B. Heshmat, H. Pahlevaninezhad, Y. Pang, M. Masnadi-Shirazi, R. Burton Lewis, T. Tiedje, R. Gordon, and T. E. Darcie, “Nanoplasmonic terahertz photoconductive switch on GaAs,” Nano Lett. 12(12), 6255–6259 (2012).
[PubMed]

H. Pahlevaninezhad, B. Heshmat, and T. E. Darcie, “Advances in terahertz waveguides and sources,” IEEE Photon. J. 3(2), 307–310 (2011).

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Hupp, J. T.

O. K. Farha, I. Eryazici, N. C. Jeong, B. G. Hauser, C. E. Wilmer, A. A. Sarjeant, R. Q. Snurr, S. T. Nguyen, A. Ö. Yazaydın, and J. T. Hupp, “Metal-organic framework materials with ultrahigh surface areas: is the sky the limit?” J. Am. Chem. Soc. 134(36), 15016–15021 (2012).
[PubMed]

Iacopi, F.

S. Eslava, M. R. Baklanov, C. E. Kirschhock, F. Iacopi, S. Aldea, K. Maex, and J. A. Martens, “Characterization of a molecular sieve coating using ellipsometric porosimetry,” Langmuir 23(26), 12811–12816 (2007).
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T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913–4930 (2005).
[PubMed]

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L. Tsang, C. Te Chen, A. T. C. Chang, J. Guo, and K. H. Ding, “Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow,” Radio Sci. 35(3), 731–749 (2000).

Teller, E.

S. Brunauer, P. H. Emmett, and E. Teller, “Adsorption of gases in multimolecular layers,” J. Am. Chem. Soc. 60(1), 309–319 (1938).

Thommes, M.

F. Porcheron, M. Thommes, R. Ahmad, and P. A. Monson, “Mercury porosimetry in mesoporous glasses: a comparison of experiments with results from a molecular model,” Langmuir 23(6), 3372–3380 (2007).
[PubMed]

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[PubMed]

Thorsos, E. I.

Tiedje, T.

B. Heshmat, H. Pahlevaninezhad, Y. Pang, M. Masnadi-Shirazi, R. Burton Lewis, T. Tiedje, R. Gordon, and T. E. Darcie, “Nanoplasmonic terahertz photoconductive switch on GaAs,” Nano Lett. 12(12), 6255–6259 (2012).
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T. Metzger, A. Irawan, and E. Tsotsas, “Influence of pore structure on drying kinetics: a pore network study,” AIChE J. 53(12), 3029–3041 (2007).

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D. Markl, J. Sauerwein, D. J. Goodwin, S. van den Ban, and J. A. Zeitler, “non-destructive determination of disintegration time and dissolution in immediate release tablets by terahertz transmission measurements,” Pharm. Res. 34(5), 1012–1022 (2017).
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T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913–4930 (2005).
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Vogt, B. D.

B. D. Vogt, R. A. Pai, H. J. Lee, R. C. Hedden, C. L. Soles, W. Wu, E. K. Lin, B. J. Bauer, and J. J. Watkins, “Characterization of ordered mesoporous silica films using small-angle neutron scattering and x-ray porosimetry,” Chem. Mater. 17(6), 1398–1408 (2005).

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M. H. Rahman, B. J. Pierson, and W. I. Wan Yusoff, “Classification of microporosity in carbonates: examples from miocene carbonate reservoirs of central luconia, offshore sarawak, malaysia,”in International Petroleum Technology Conference (2011).

Wang, P.

D. Markl, P. Wang, C. Ridgway, A.-P. Karttunen, M. Chakraborty, P. Bawuah, P. Pääkkönen, P. Gane, J. Ketolainen, K.-E. Peiponen, and J. A. Zeitler, “characterization of the pore structure of functionalized calcium carbonate tablets by terahertz time-domain spectroscopy and x-ray computed microtomography,” J. Pharm. Sci. 106(6), 1586–1595 (2017).
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O. K. Farha, I. Eryazici, N. C. Jeong, B. G. Hauser, C. E. Wilmer, A. A. Sarjeant, R. Q. Snurr, S. T. Nguyen, A. Ö. Yazaydın, and J. T. Hupp, “Metal-organic framework materials with ultrahigh surface areas: is the sky the limit?” J. Am. Chem. Soc. 134(36), 15016–15021 (2012).
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B. D. Vogt, R. A. Pai, H. J. Lee, R. C. Hedden, C. L. Soles, W. Wu, E. K. Lin, B. J. Bauer, and J. J. Watkins, “Characterization of ordered mesoporous silica films using small-angle neutron scattering and x-ray porosimetry,” Chem. Mater. 17(6), 1398–1408 (2005).

Xiao, L.

H. Zhan, S. Wu, K. Zhao, R. Bao, and L. Xiao, “CaCO3, its reaction and carbonate rocks: terahertz spectroscopy investigation,” J. Geophys. Eng. 13(5), 768–774 (2016).

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H. K. Chae, D. Y. Siberio-Pérez, J. Kim, Y. Go, M. Eddaoudi, A. J. Matzger, M. O’Keeffe, and O. M. Yaghi, “A route to high surface area, porosity and inclusion of large molecules in crystals,” Nature 427(6974), 523–527 (2004).
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D. Markl, J. Sauerwein, D. J. Goodwin, S. van den Ban, and J. A. Zeitler, “non-destructive determination of disintegration time and dissolution in immediate release tablets by terahertz transmission measurements,” Pharm. Res. 34(5), 1012–1022 (2017).
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D. Markl, P. Wang, C. Ridgway, A.-P. Karttunen, M. Chakraborty, P. Bawuah, P. Pääkkönen, P. Gane, J. Ketolainen, K.-E. Peiponen, and J. A. Zeitler, “characterization of the pore structure of functionalized calcium carbonate tablets by terahertz time-domain spectroscopy and x-ray computed microtomography,” J. Pharm. Sci. 106(6), 1586–1595 (2017).
[PubMed]

P. Bawuah, T. Ervasti, N. Tan, J. A. Zeitler, J. Ketolainen, and K.-E. Peiponen, “noninvasive porosity measurement of biconvex tablets using terahertz pulses,” Int. J. Pharm. 509(1-2), 439–443 (2016).
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K.-E. Peiponen, P. Bawuah, M. Chakraborty, M. Juuti, J. A. Zeitler, and J. Ketolainen, “estimation of young’s modulus of pharmaceutical tablet obtained by terahertz time-delay measurement,” Int. J. Pharm. 489(1-2), 100–105 (2015).
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P. Bawuah, A. Pierotic Mendia, P. Silfsten, P. Pääkkönen, T. Ervasti, J. Ketolainen, J. A. Zeitler, and K.-E. Peiponen, “Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques,” Int. J. Pharm. 465(1-2), 70–76 (2014).
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Zhang, M.

A. Redo-Sanchez, B. Heshmat, A. Aghasi, S. Naqvi, M. Zhang, J. Romberg, and R. Raskar, “Terahertz time-gated spectral imaging for content extraction through layered structures,” Nat. Commun. 7, 12665 (2016).
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Zhang, W.

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Zhao, K.

H. Zhan, S. Wu, K. Zhao, R. Bao, and L. Xiao, “CaCO3, its reaction and carbonate rocks: terahertz spectroscopy investigation,” J. Geophys. Eng. 13(5), 768–774 (2016).

Zhou, F.

F. Zhou, Y. Bao, W. Cao, C. T. Stuart, J. Gu, W. Zhang, and C. Sun, “Hiding a realistic object using a broadband terahertz invisibility cloak,” Sci. Rep. 1, 78 (2011).
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ACS Photonics (1)

B. Groever, B. Heshmat, and R. Raskar, “Tyndall windows: tunable scattering of disordered solid–liquid matching mixtures,” ACS Photonics 3(6), 930–935 (2016).

AIChE J. (1)

T. Metzger, A. Irawan, and E. Tsotsas, “Influence of pore structure on drying kinetics: a pore network study,” AIChE J. 53(12), 3029–3041 (2007).

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Fuel (1)

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Ind. Eng. Chem. Res. (1)

A. Samanta, A. Zhao, G. K. H. Shimizu, P. Sarkar, and R. Gupta, “Post-combustion co2 capture using solid sorbents: a review,” Ind. Eng. Chem. Res. 51(4), 1438–1463 (2012).

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K.-E. Peiponen, P. Bawuah, M. Chakraborty, M. Juuti, J. A. Zeitler, and J. Ketolainen, “estimation of young’s modulus of pharmaceutical tablet obtained by terahertz time-delay measurement,” Int. J. Pharm. 489(1-2), 100–105 (2015).
[PubMed]

P. Bawuah, A. Pierotic Mendia, P. Silfsten, P. Pääkkönen, T. Ervasti, J. Ketolainen, J. A. Zeitler, and K.-E. Peiponen, “Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques,” Int. J. Pharm. 465(1-2), 70–76 (2014).
[PubMed]

P. Bawuah, T. Ervasti, N. Tan, J. A. Zeitler, J. Ketolainen, and K.-E. Peiponen, “noninvasive porosity measurement of biconvex tablets using terahertz pulses,” Int. J. Pharm. 509(1-2), 439–443 (2016).
[PubMed]

J. Acoust. Soc. Am. (1)

V. V. Varadan and V. K. Varadan, “The quasicrystalline approximation and multiple scattering of waves in random media,” J. Acoust. Soc. Am. 77, S3 (1985).

J. Am. Chem. Soc. (3)

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J. Geophys. Eng. (1)

H. Zhan, S. Wu, K. Zhao, R. Bao, and L. Xiao, “CaCO3, its reaction and carbonate rocks: terahertz spectroscopy investigation,” J. Geophys. Eng. 13(5), 768–774 (2016).

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

J. Pharm. Sci. (1)

D. Markl, P. Wang, C. Ridgway, A.-P. Karttunen, M. Chakraborty, P. Bawuah, P. Pääkkönen, P. Gane, J. Ketolainen, K.-E. Peiponen, and J. A. Zeitler, “characterization of the pore structure of functionalized calcium carbonate tablets by terahertz time-domain spectroscopy and x-ray computed microtomography,” J. Pharm. Sci. 106(6), 1586–1595 (2017).
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Langmuir (6)

C. C. Egger, C. du Fresne, V. I. Raman, V. Schädler, T. Frechen, S. V. Roth, and P. Müller-Buschbaum, “Characterization of highly porous polymeric materials with pore diameters larger than 100 nm by mercury porosimetry and x-ray scattering methods,” Langmuir 24(11), 5877–5887 (2008).
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Nano Lett. (1)

B. Heshmat, H. Pahlevaninezhad, Y. Pang, M. Masnadi-Shirazi, R. Burton Lewis, T. Tiedje, R. Gordon, and T. E. Darcie, “Nanoplasmonic terahertz photoconductive switch on GaAs,” Nano Lett. 12(12), 6255–6259 (2012).
[PubMed]

Nat. Commun. (1)

A. Redo-Sanchez, B. Heshmat, A. Aghasi, S. Naqvi, M. Zhang, J. Romberg, and R. Raskar, “Terahertz time-gated spectral imaging for content extraction through layered structures,” Nat. Commun. 7, 12665 (2016).
[PubMed]

Nature (1)

H. K. Chae, D. Y. Siberio-Pérez, J. Kim, Y. Go, M. Eddaoudi, A. J. Matzger, M. O’Keeffe, and O. M. Yaghi, “A route to high surface area, porosity and inclusion of large molecules in crystals,” Nature 427(6974), 523–527 (2004).
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Opt. Express (1)

Opt. Lett. (2)

Optica (1)

Pharm. Res. (1)

D. Markl, J. Sauerwein, D. J. Goodwin, S. van den Ban, and J. A. Zeitler, “non-destructive determination of disintegration time and dissolution in immediate release tablets by terahertz transmission measurements,” Pharm. Res. 34(5), 1012–1022 (2017).
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Phys. Med. Biol. (1)

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50(20), 4913–4930 (2005).
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Radio Sci. (1)

L. Tsang, C. Te Chen, A. T. C. Chang, J. Guo, and K. H. Ding, “Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow,” Radio Sci. 35(3), 731–749 (2000).

Sci. Rep. (2)

F. Zhou, Y. Bao, W. Cao, C. T. Stuart, J. Gu, W. Zhang, and C. Sun, “Hiding a realistic object using a broadband terahertz invisibility cloak,” Sci. Rep. 1, 78 (2011).
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Figures (7)

Fig. 1
Fig. 1

Beam geometry and specifications. (a) A slice of limestone sedimentary rock with thickness d is illuminated with THz beam. The scattered light (THz pulse) is measured in the THz receiver. (b) Typical THz pulse in time domain and its spectrum (c) in the frequency domain. The green region is where the signal to noise ratio (SNR) is reliable. Between 2 and 2.2 THz the SNR starts to decline rapidly. 2.2-2.5 THz range can be improper for highly absorptive samples. Commonplace commercial THz-TDS systems usually don’t provide reliable SNR above 2.5 THz.

Fig. 2
Fig. 2

Setup and signal specifications. (a) THz setup. Samples are held on top of posts. Inset figure shows the top view of the sample, the Gaussian beam spot has 1.0 mm diameter at FWHM (b) Temporal profile of THz reference pulse before transmitting through the sample in blue and after the transmission through an arbitrary (4.5 mm) dry limestone sample in red. (c) Fourier transform of the THz pulse before the sample (blue) and after the dry sample (red).

Fig. 3
Fig. 3

Volume fraction plots. For each sample the volume fraction function f is a 2D function of the pore radii (0.5a) shown by vertical axis and wavelength or frequency shown by horizontal axis. The color bar indicates the value of the volume fraction between 0 and 1. (a1) Mean volume fraction profile for sample A across varying sample thicknesses between 2.76 and 10.55 mm. The inset figure shows two volume fraction sample curves (the values on 2 vertical lines on the 2D color map) (a2) standard deviation of sample A mean volume fraction (b1) Mean volume fraction profile for sample B averaged across varying sample thicknesses between 2.15 and 6.9 mm (b2) standard deviation of sample B mean volume fraction. Darker blue regions indicate the regions where the standard deviation is lower, and therefore, less oscillations is present in the volume fraction value among all samples. These data points are more probable to be close to the solution of the equation set (or crossing points of the volume fraction curves at different wavelengths) as they are showing less variation across all the sample thicknesses and the nearby frequency ranges. The top left corner flat-yellow regions in (a1) and (b1) are close to the poles of Eq. (3) with f >1 that are then thresholded to 1.

Fig. 4
Fig. 4

(a) Dehydration profiles of sample A. The vertical axis shows the peak-to-peak THz E-field amplitude and the horizontal axis shows the time in minutes. The dashed horizontal lines are the peak-to-peak value measured for the dry sample before the saturation. (b) Dehydration profile for sample B.

Fig. 5
Fig. 5

Mercury intrusion results for CaCO3 samples. (a) Pore volume percent versus pore diameter. (b) Cumulative pore volume percentage versus pore diameter.

Fig. 6
Fig. 6

Fourier transform of the pulses measured during dehydration profile. (a) Sample set A. (b) Sample set B. Dark areas circled by green dashed curve indicate the contribution of water absorption and scattering. Comparing the two samples indicate that A samples have less water compared to B samples which indicates higher porosity for B. Horizontal axis is time in minutes and vertical axis is frequency in THz.

Fig. 7
Fig. 7

N2 adsorption isotherms for a powder of sample A (specific surface area 9.7 m2 g−1) and a powder of sample B (specific surface area 12.8 m2 g−1). (b) BJH incremental pore volume versus average pore width.

Tables (5)

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Table 1 Sample A dehydration profile values.

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Table 2 Sample B dehydration profile values.

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Table 3 Mercury intrusion data summary for our two Indiana limestone samples

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Table 4 Comparison of mercury intrusion with THz scattering and dehydration method.

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Table 5 Overview of experimental methods for porosity determination

Equations (10)

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I( λ ) I 0 ( λ ) = e μ s ' ( k )d .
μ s ' = 3fQ( m,k,a ) 4a ( 1-g( m,k,a ) ).
f( k,a )= 4a μ s ' ( k ) 3Q( m,k,a )( 1g( m,k,a ) ) .
Q s = 2 x 2 l=1 ( 2l+1 )( | a l | 2 + | b l | 2 ),
g= 4 Q s x 2 l=1 [ l ( l+1 ) l+1 Re( a l a l+1 + b l b l+1 * )+ 2l+1 l ( l+1 ) Re( a l b l * ) ],
a l =  ψ l ' ( y ) ψ l ( x ) m ψ l ( y ) ψ l ' ( x ) ψ l ' ( y ) ξ l ( x ) m ψ l ( y ) ξ l ' ( x ) ,
b l =  m ψ l ' ( y ) ψ l ( x )  ψ l ( y ) ψ l ' ( x ) m ψ l ' ( y ) ξ l ( x )  ψ l ( y ) ξ l ' ( x ) ,
ψ l ( z )= z  j l ( z )= ( πz 2 ) 0.5 J l+1 ( z ),
χ l ( z )= z  y l ( z )= ( πz 2 ) 0.5 Y l+0.5 ( z ),
ξ l ( z )= ψ l ( z )+i χ l ( z )=z h l ( 2 ) ( z ).

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