Abstract

Terahertz (THz) imaging is emerging as a potentially powerful method of detecting explosive devices, even in the presence of occluding materials. However, the characteristic spectral signatures of pure explosive materials may be altered or obscured by electromagnetic scattering caused by their granular nature. This paper presents THz transmission measurements of granular systems representative of explosives and presents results from dense media theory that accurately explain the observed scattering response.

© 2007 Optical Society of America

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References

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  1. L. M. Hayden, A. M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Tweig, and M. He, "New materials for optical rectification and electrooptic sampling of ultrashort pulses in the terahertz regime," J. Polym. Sci., Part B: Polym. Phys. 41, 2492-2500 (2003).
    [CrossRef]
  2. A. M. Sinyukov and L. M. Hayden, "Efficient electrooptic polymers for THz applications," J. Phys. Chem. B 108, 8515-8522 (2004).
    [CrossRef]
  3. X. Zheng, A. Sinyukov, and L. M. Hayden, "Broadband and gap-free response of a terahertz system based on a poled polymer emitter-sensor pair," Appl. Phys. Lett. 87, 081115 (2005).
    [CrossRef]
  4. M. Tonouchi, "Cutting-edge terahertz technology," Nat. Photonics V1, 97-105 (2007).
    [CrossRef]
  5. M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, "Security applications of terahertz technology," Proc. SPIE 5070, 44-52 (2003).
    [CrossRef]
  6. K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, T. Ikeda, A. Masushita, K. Koide, M. Tatsuno, and Y. Minami, "Noninvasive inspection of C-4 explosive in mails by terahertz time-domain spectroscopy," Jpn. J. Appl. Phys., Part 2 43, L414-L417 (2004).
    [CrossRef]
  7. F. Huang, B. Schulkin, H. Altan, J. F. Federici, D. Gary, R. Barat, D. Zimdars, M. Chen, and D. B. Tanner, "Terahertz study of 1,3,5-trinitro-s-triazine by time-domain and Fourier transform infrared spectroscopy," Appl. Phys. Lett. 85, 5535-5537 (2004).
    [CrossRef]
  8. J. Barber, D. E. Hooks, D. J. Funk, R. D. Averitt, A. J. Taylor, and D. Babikov, "Temperature-dependent far-infrared spectra of single crystals of high explosives using terahertz time-domain spectroscopy," J. Phys. Chem. A 109, 3501-3505 (2005).
    [CrossRef]
  9. M. R. Leahy-Hoppa, M. J. Fitch, X. Zhang, L. M. Hayden, R. Osiander, "Wideband terahertz spectroscopy of explosives," Chem. Phys. Lett. 434, 227-230 (2007).
    [CrossRef]
  10. W. R. Tribe, D. A. Newham, P. F. Taday, and M. C. Kemp, "Hidden object detection: Security applications of THz technology," Proc. SPIE 5354168-176 (2004).
    [CrossRef]
  11. J. E. Reagh, "Checking out the hot spots," Science and Technology Review (Lawrence Livermore National Laboratory, 2003).
  12. J. E. Reagh, "Grain-scale dynamics in explosives," Technical Report No. ID-150388 (Lawrence Livermore National Laboratory 2002).
  13. L. Borne and A. Beaucamp, "Effects of crystal internal defects on projectile impact initiation," French-German Research Institute of Saint-Louis (ISL), P.O. Box 34 - F 68301 Saint-Louis Cedex.
  14. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Theories, and Applications (Wiley, 2000).
    [CrossRef]
  15. L. M. Zurk, L. Tsang, K. H. Ding, and D. P. Winebrenner, "Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries," J. Opt. Soc. Am. 12, 1772-1781 (1995).
    [CrossRef]
  16. L. M. Zurk, L. Tsang, J. Shi, and R. Davis, "Electromagnetic scattering calculated from pair distribution functions retreived from planar snow sections," IEEE Trans. Geosci. Remote Sens. 35, 1419-1428 (1997).
    [CrossRef]
  17. L. Tsang, C. Chen, A. Change, J. Guo, and K. Ding, "Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow," Radio Sci. 35, 731-749 (2000).
    [CrossRef]
  18. A. Ponavina, S. Kachan, and N. Silvanovich, "Statistical theory of multiple scattering of waves applied to three-dimensional layered photonic crystals," J. Opt. Soc. Am. B 21, 1866-1875 (2004).
    [CrossRef]
  19. Y. Kuga, D. Rice, and R. D. West, "Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium," IEEE Trans. Antennas Propag. 44, 326-332 (1996).
    [CrossRef]
  20. X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, P. D. Phelps, K. R. Stewart, and C. P. Yakymyshyn, "Terahertz optical rectification from a nonlinear organic crystal," Appl. Phys. Lett. 61, 3080-3082 (1992).
    [CrossRef]
  21. F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing (Addison-Wesley, 1982).
  22. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  23. F. Jackson and E. W. Weisstein, "Tetrahedron," http://mathworld.wolfram.com/tetrahedron.html.

2007 (2)

M. Tonouchi, "Cutting-edge terahertz technology," Nat. Photonics V1, 97-105 (2007).
[CrossRef]

M. R. Leahy-Hoppa, M. J. Fitch, X. Zhang, L. M. Hayden, R. Osiander, "Wideband terahertz spectroscopy of explosives," Chem. Phys. Lett. 434, 227-230 (2007).
[CrossRef]

2005 (2)

X. Zheng, A. Sinyukov, and L. M. Hayden, "Broadband and gap-free response of a terahertz system based on a poled polymer emitter-sensor pair," Appl. Phys. Lett. 87, 081115 (2005).
[CrossRef]

J. Barber, D. E. Hooks, D. J. Funk, R. D. Averitt, A. J. Taylor, and D. Babikov, "Temperature-dependent far-infrared spectra of single crystals of high explosives using terahertz time-domain spectroscopy," J. Phys. Chem. A 109, 3501-3505 (2005).
[CrossRef]

2004 (5)

K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, T. Ikeda, A. Masushita, K. Koide, M. Tatsuno, and Y. Minami, "Noninvasive inspection of C-4 explosive in mails by terahertz time-domain spectroscopy," Jpn. J. Appl. Phys., Part 2 43, L414-L417 (2004).
[CrossRef]

F. Huang, B. Schulkin, H. Altan, J. F. Federici, D. Gary, R. Barat, D. Zimdars, M. Chen, and D. B. Tanner, "Terahertz study of 1,3,5-trinitro-s-triazine by time-domain and Fourier transform infrared spectroscopy," Appl. Phys. Lett. 85, 5535-5537 (2004).
[CrossRef]

A. M. Sinyukov and L. M. Hayden, "Efficient electrooptic polymers for THz applications," J. Phys. Chem. B 108, 8515-8522 (2004).
[CrossRef]

W. R. Tribe, D. A. Newham, P. F. Taday, and M. C. Kemp, "Hidden object detection: Security applications of THz technology," Proc. SPIE 5354168-176 (2004).
[CrossRef]

A. Ponavina, S. Kachan, and N. Silvanovich, "Statistical theory of multiple scattering of waves applied to three-dimensional layered photonic crystals," J. Opt. Soc. Am. B 21, 1866-1875 (2004).
[CrossRef]

2003 (2)

L. M. Hayden, A. M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Tweig, and M. He, "New materials for optical rectification and electrooptic sampling of ultrashort pulses in the terahertz regime," J. Polym. Sci., Part B: Polym. Phys. 41, 2492-2500 (2003).
[CrossRef]

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, "Security applications of terahertz technology," Proc. SPIE 5070, 44-52 (2003).
[CrossRef]

2000 (1)

L. Tsang, C. Chen, A. Change, J. Guo, and K. Ding, "Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow," Radio Sci. 35, 731-749 (2000).
[CrossRef]

1997 (1)

L. M. Zurk, L. Tsang, J. Shi, and R. Davis, "Electromagnetic scattering calculated from pair distribution functions retreived from planar snow sections," IEEE Trans. Geosci. Remote Sens. 35, 1419-1428 (1997).
[CrossRef]

1996 (1)

Y. Kuga, D. Rice, and R. D. West, "Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium," IEEE Trans. Antennas Propag. 44, 326-332 (1996).
[CrossRef]

1995 (1)

L. M. Zurk, L. Tsang, K. H. Ding, and D. P. Winebrenner, "Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries," J. Opt. Soc. Am. 12, 1772-1781 (1995).
[CrossRef]

1992 (1)

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, P. D. Phelps, K. R. Stewart, and C. P. Yakymyshyn, "Terahertz optical rectification from a nonlinear organic crystal," Appl. Phys. Lett. 61, 3080-3082 (1992).
[CrossRef]

Appl. Phys. Lett. (3)

X. Zheng, A. Sinyukov, and L. M. Hayden, "Broadband and gap-free response of a terahertz system based on a poled polymer emitter-sensor pair," Appl. Phys. Lett. 87, 081115 (2005).
[CrossRef]

F. Huang, B. Schulkin, H. Altan, J. F. Federici, D. Gary, R. Barat, D. Zimdars, M. Chen, and D. B. Tanner, "Terahertz study of 1,3,5-trinitro-s-triazine by time-domain and Fourier transform infrared spectroscopy," Appl. Phys. Lett. 85, 5535-5537 (2004).
[CrossRef]

X.-C. Zhang, X. F. Ma, Y. Jin, T.-M. Lu, E. P. Boden, P. D. Phelps, K. R. Stewart, and C. P. Yakymyshyn, "Terahertz optical rectification from a nonlinear organic crystal," Appl. Phys. Lett. 61, 3080-3082 (1992).
[CrossRef]

Chem. Phys. Lett. (1)

M. R. Leahy-Hoppa, M. J. Fitch, X. Zhang, L. M. Hayden, R. Osiander, "Wideband terahertz spectroscopy of explosives," Chem. Phys. Lett. 434, 227-230 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

Y. Kuga, D. Rice, and R. D. West, "Propagation constant and the velocity of the coherent wave in a dense strongly scattering medium," IEEE Trans. Antennas Propag. 44, 326-332 (1996).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

L. M. Zurk, L. Tsang, J. Shi, and R. Davis, "Electromagnetic scattering calculated from pair distribution functions retreived from planar snow sections," IEEE Trans. Geosci. Remote Sens. 35, 1419-1428 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

L. M. Zurk, L. Tsang, K. H. Ding, and D. P. Winebrenner, "Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and nonclustered geometries," J. Opt. Soc. Am. 12, 1772-1781 (1995).
[CrossRef]

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

J. Phys. Chem. A (1)

J. Barber, D. E. Hooks, D. J. Funk, R. D. Averitt, A. J. Taylor, and D. Babikov, "Temperature-dependent far-infrared spectra of single crystals of high explosives using terahertz time-domain spectroscopy," J. Phys. Chem. A 109, 3501-3505 (2005).
[CrossRef]

J. Phys. Chem. B (1)

A. M. Sinyukov and L. M. Hayden, "Efficient electrooptic polymers for THz applications," J. Phys. Chem. B 108, 8515-8522 (2004).
[CrossRef]

J. Polym. Sci., Part B: Polym. Phys. (1)

L. M. Hayden, A. M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Tweig, and M. He, "New materials for optical rectification and electrooptic sampling of ultrashort pulses in the terahertz regime," J. Polym. Sci., Part B: Polym. Phys. 41, 2492-2500 (2003).
[CrossRef]

Jpn. J. Appl. Phys., Part 2 (1)

K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, T. Ikeda, A. Masushita, K. Koide, M. Tatsuno, and Y. Minami, "Noninvasive inspection of C-4 explosive in mails by terahertz time-domain spectroscopy," Jpn. J. Appl. Phys., Part 2 43, L414-L417 (2004).
[CrossRef]

Nat. Photonics (1)

M. Tonouchi, "Cutting-edge terahertz technology," Nat. Photonics V1, 97-105 (2007).
[CrossRef]

Proc. SPIE (2)

M. C. Kemp, P. F. Taday, B. E. Cole, J. A. Cluff, A. J. Fitzgerald, and W. R. Tribe, "Security applications of terahertz technology," Proc. SPIE 5070, 44-52 (2003).
[CrossRef]

W. R. Tribe, D. A. Newham, P. F. Taday, and M. C. Kemp, "Hidden object detection: Security applications of THz technology," Proc. SPIE 5354168-176 (2004).
[CrossRef]

Radio Sci. (1)

L. Tsang, C. Chen, A. Change, J. Guo, and K. Ding, "Dense media radiative transfer theory based on quasicrystalline approximation with applications to passive microwave remote sensing of snow," Radio Sci. 35, 731-749 (2000).
[CrossRef]

Other (7)

J. E. Reagh, "Checking out the hot spots," Science and Technology Review (Lawrence Livermore National Laboratory, 2003).

J. E. Reagh, "Grain-scale dynamics in explosives," Technical Report No. ID-150388 (Lawrence Livermore National Laboratory 2002).

L. Borne and A. Beaucamp, "Effects of crystal internal defects on projectile impact initiation," French-German Research Institute of Saint-Louis (ISL), P.O. Box 34 - F 68301 Saint-Louis Cedex.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves, Theories, and Applications (Wiley, 2000).
[CrossRef]

F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing (Addison-Wesley, 1982).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

F. Jackson and E. W. Weisstein, "Tetrahedron," http://mathworld.wolfram.com/tetrahedron.html.

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Figures (9)

Fig. 1
Fig. 1

Photomicrograph of a plastic explosive sample showing 150-micron HMX crystals in a plastic filler [11].

Fig. 2
Fig. 2

Experimental setup for THz spectroscopy.

Fig. 3
Fig. 3

Pictomicrographs of two different manufacturer lots of PE samples showing different grain sizes. Sample on left is termed SGPE and right-hand sample is LGPE. The scale in μ m is shown in the far left.

Fig. 4
Fig. 4

Magnitude of the Fourier transform of the measured transmission signal for the PE samples shown in the previous figure. Note significantly greater attenuation for LGPE sample at higher frequencies. Pellet thickness was 0.77 and 1.82 mm for SGPE and LGPE samples, respectively. For this and subsequent plots the data curves are truncated once they reach the estimated noise floor.

Fig. 5
Fig. 5

Random media model used in QCA calculations. Background is modeled as pure PE with a relative permittivity of 2.13. Air voids occupy 20% by volume, and have a radius of either 8 or 24 μ m , for SGPE and LGPE, respectively.

Fig. 6
Fig. 6

Close packing of spheres with tetrahedron center.

Fig. 7
Fig. 7

Magnitude of the Fourier transform of the measured transmission signal for LGPE (solid) and SGPE (dotted). Background is modeled as pure PE with a relative permittivity of 2.13. Air voids occupy 20% by volume, and have a radius of either 8 or 24 μ m , for SGPE and LGPE, respectively. Calculations for QCA shown as open square (LGPE) and open circle (SGPE) markers.

Fig. 8
Fig. 8

Attenuation coefficient for measurements and simulations from QCA theory (shown with markers) for LGPE (solid line) and for SGPE (dotted line).

Fig. 9
Fig. 9

Additional measurements of LGPE samples with pellet thicknesses of 1.42 and 3.22 mm . Calculations with QCA shown with markers.

Equations (14)

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E ¯ i n c ( r ¯ ) = m , n [ a m n ( M ) M ¯ m n ( 1 ) ( k r , θ , ϕ ) + a m n ( N ) N ¯ m n ( 1 ) ( k r , θ , ϕ ) ] ,
E ¯ l e x ( r ¯ ) = m , n [ w m n ( M ) M ¯ m n ( 1 ) ( k r , θ , ϕ ) + w m n ( N ) N ¯ m n ( 1 ) ( k r , θ , ϕ ) ] ,
w ¯ ( l ) = j = 1 , j l N σ ̿ ( k r ¯ l j ) T ̿ w ¯ ( j ) + e i k ¯ i r ¯ l a ¯ i n c ,
a ¯ S ( l ) = T ̿ w ¯ ( l ) .
E l ( w ¯ ( l ) ) = d r ¯ 1 d r ¯ 2 d r ¯ l d r ¯ N w ¯ ( l ) p ( r ¯ 1 , r ¯ 2 r ¯ l r ¯ N r ¯ l ) , = w ¯ ( r ¯ l ) ,
w ¯ ( r ¯ l ) = n 0 d r ¯ j g ( r ¯ j r ¯ l ) σ ̿ ( k r ¯ l j ) T ̿ w ¯ ( r ¯ j ) + e i k ¯ i r ¯ l a ¯ i n c ,
w ¯ ( r ¯ l ) = a ¯ i n c e i K ¯ e f f r l ¯ ,
K e f f k = π i n 0 k 2 n ( T n ( M ) X n M + T n ( N ) X N ( N ) ) ( 2 n + 1 ) ,
V = 2 l 3 12 = 2 2 r 3 3 ,
0 r 0 π 3 0 π 3 ( r ) 2 sin ( θ ) d θ d ϕ d r = π r 3 18 .
r v = [ 1 2 π 1 6 ] 1 3 r .
T 21 = 2 k 0 k 0 + K e f f , T 12 = 2 K e f f k 0 + K e f f ,
R 12 = K e f f k 0 K e f f + k 0 ,
E = T 21 T 12 e α d 1 R 12 2 e 2 α d E R E F ,

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