Abstract

We use reflection terahertz spectroscopy to locate and produce three-dimensional images of air gaps between stones that resemble fractures, even of subwavelength thicknesses. This technique is found to be promising tool for sculpture and building damage evaluation as well as structural quality control in other dielectric materials.

© 2013 Optical Society of America

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References

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  1. G. Demortier and J. Ruvalcaba-Sil, “Quantitative ion beam analysis of complex gold-based artefacts,” Nucl. Instr. Methods B 239, 1–15 (2005).
    [CrossRef]
  2. P. Vandenabeele, F. Verpoort, and L. Moens, “Non-destructive analysis of paintings using fourier transform raman spectroscopy with fibre optics,” J. Raman Spectrosc. 32, 263–269 (2001).
    [CrossRef]
  3. P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
    [CrossRef]
  4. J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
    [CrossRef]
  5. K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Exp. 4, 258–263 (2007).
    [CrossRef]
  6. A. Adam, P. Planken, S. Meloni, and J. Dik, “Terahertz imaging of hidden paint layers on canvas,” Opt. Express 17, 3407–3416 (2009).
    [CrossRef]
  7. K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Application of terahertz spectroscopy for character recognition in a medieval manuscript,” IEICE Electron. Exp. 5, 223–228 (2008).
    [CrossRef]
  8. E. Castro-Camus and M. B. Johnston, “Extraction of the anisotropic dielectric properties of materials from polarization-resolved terahertz time-domain spectra,” J. Opt. A 11, 105206 (2009).
    [CrossRef]
  9. S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
    [CrossRef]
  10. R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
    [CrossRef]
  11. D. Mittleman, S. Hunsche, L. Boivin, and M. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997).
    [CrossRef]
  12. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, “T-ray imaging,” IEEE J. Sel. Top. Quantum Electron. 2, 679–692 (1996).
    [CrossRef]
  13. O. Peters, S. Wietzke, C. Jansen, M. Scheller, and M. Koch, “Nondestructive detection of delaminations in plastic weld joints,” in 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010), pp. 1–2.
  14. G. Fowles, Introduction to Modern Optics (Dover, 1989).

2011

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[CrossRef]

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

2009

A. Adam, P. Planken, S. Meloni, and J. Dik, “Terahertz imaging of hidden paint layers on canvas,” Opt. Express 17, 3407–3416 (2009).
[CrossRef]

E. Castro-Camus and M. B. Johnston, “Extraction of the anisotropic dielectric properties of materials from polarization-resolved terahertz time-domain spectra,” J. Opt. A 11, 105206 (2009).
[CrossRef]

2008

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Application of terahertz spectroscopy for character recognition in a medieval manuscript,” IEICE Electron. Exp. 5, 223–228 (2008).
[CrossRef]

2007

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Exp. 4, 258–263 (2007).
[CrossRef]

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

2006

S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
[CrossRef]

2005

G. Demortier and J. Ruvalcaba-Sil, “Quantitative ion beam analysis of complex gold-based artefacts,” Nucl. Instr. Methods B 239, 1–15 (2005).
[CrossRef]

2001

P. Vandenabeele, F. Verpoort, and L. Moens, “Non-destructive analysis of paintings using fourier transform raman spectroscopy with fibre optics,” J. Raman Spectrosc. 32, 263–269 (2001).
[CrossRef]

1997

1996

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

Adam, A.

Boivin, L.

Bowen, J.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

Castro-Camus, E.

E. Castro-Camus and M. B. Johnston, “Extraction of the anisotropic dielectric properties of materials from polarization-resolved terahertz time-domain spectra,” J. Opt. A 11, 105206 (2009).
[CrossRef]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[CrossRef]

Demortier, G.

G. Demortier and J. Ruvalcaba-Sil, “Quantitative ion beam analysis of complex gold-based artefacts,” Nucl. Instr. Methods B 239, 1–15 (2005).
[CrossRef]

Dik, J.

Elliott, S.

S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
[CrossRef]

Fowles, G.

G. Fowles, Introduction to Modern Optics (Dover, 1989).

Fukunaga, K.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Application of terahertz spectroscopy for character recognition in a medieval manuscript,” IEICE Electron. Exp. 5, 223–228 (2008).
[CrossRef]

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Exp. 4, 258–263 (2007).
[CrossRef]

Hayashi, S.

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Application of terahertz spectroscopy for character recognition in a medieval manuscript,” IEICE Electron. Exp. 5, 223–228 (2008).
[CrossRef]

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Exp. 4, 258–263 (2007).
[CrossRef]

Hosako, I.

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Application of terahertz spectroscopy for character recognition in a medieval manuscript,” IEICE Electron. Exp. 5, 223–228 (2008).
[CrossRef]

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Exp. 4, 258–263 (2007).
[CrossRef]

Hunsche, S.

Jackson, J.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

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]

Jansen, C.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

O. Peters, S. Wietzke, C. Jansen, M. Scheller, and M. Koch, “Nondestructive detection of delaminations in plastic weld joints,” in 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010), pp. 1–2.

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[CrossRef]

Johnston, M. B.

E. Castro-Camus and M. B. Johnston, “Extraction of the anisotropic dielectric properties of materials from polarization-resolved terahertz time-domain spectra,” J. Opt. A 11, 105206 (2009).
[CrossRef]

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[CrossRef]

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

O. Peters, S. Wietzke, C. Jansen, M. Scheller, and M. Koch, “Nondestructive detection of delaminations in plastic weld joints,” in 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010), pp. 1–2.

Kürner, T.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

Labaune, J.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

Lo, T.

S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
[CrossRef]

Meloni, S.

Menu, M.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

Mittleman, D.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

D. Mittleman, S. Hunsche, L. Boivin, and M. Nuss, “T-ray tomography,” Opt. Lett. 22, 904–906 (1997).
[CrossRef]

Mittleman, D. M.

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

Moens, L.

P. Vandenabeele, F. Verpoort, and L. Moens, “Non-destructive analysis of paintings using fourier transform raman spectroscopy with fibre optics,” J. Raman Spectrosc. 32, 263–269 (2001).
[CrossRef]

Mourou, G.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

Neilson, J.

S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
[CrossRef]

Nuss, M.

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]

Ogawa, Y.

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Application of terahertz spectroscopy for character recognition in a medieval manuscript,” IEICE Electron. Exp. 5, 223–228 (2008).
[CrossRef]

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Exp. 4, 258–263 (2007).
[CrossRef]

Peters, O.

O. Peters, S. Wietzke, C. Jansen, M. Scheller, and M. Koch, “Nondestructive detection of delaminations in plastic weld joints,” in 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010), pp. 1–2.

Piesiewicz, R.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

Planken, P.

Ruvalcaba-Sil, J.

G. Demortier and J. Ruvalcaba-Sil, “Quantitative ion beam analysis of complex gold-based artefacts,” Nucl. Instr. Methods B 239, 1–15 (2005).
[CrossRef]

Scheller, M.

O. Peters, S. Wietzke, C. Jansen, M. Scheller, and M. Koch, “Nondestructive detection of delaminations in plastic weld joints,” in 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010), pp. 1–2.

Simdyankin, S.

S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
[CrossRef]

Taraskin, S.

S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
[CrossRef]

Vandenabeele, P.

P. Vandenabeele, F. Verpoort, and L. Moens, “Non-destructive analysis of paintings using fourier transform raman spectroscopy with fibre optics,” J. Raman Spectrosc. 32, 263–269 (2001).
[CrossRef]

Verpoort, F.

P. Vandenabeele, F. Verpoort, and L. Moens, “Non-destructive analysis of paintings using fourier transform raman spectroscopy with fibre optics,” J. Raman Spectrosc. 32, 263–269 (2001).
[CrossRef]

Walker, G.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

Wietzke, S.

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

O. Peters, S. Wietzke, C. Jansen, M. Scheller, and M. Koch, “Nondestructive detection of delaminations in plastic weld joints,” in 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010), pp. 1–2.

IEEE J. Sel. Top. Quantum Electron.

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. THz Sci. Technol.

J. Jackson, J. Bowen, G. Walker, J. Labaune, G. Mourou, M. Menu, and K. Fukunaga, “A survey of terahertz applications in cultural heritage conservation science,” IEEE Trans. THz Sci. Technol. 1, 220–231 (2011).
[CrossRef]

IEICE Electron. Exp.

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Terahertz spectroscopy for art conservation,” IEICE Electron. Exp. 4, 258–263 (2007).
[CrossRef]

K. Fukunaga, Y. Ogawa, S. Hayashi, and I. Hosako, “Application of terahertz spectroscopy for character recognition in a medieval manuscript,” IEICE Electron. Exp. 5, 223–228 (2008).
[CrossRef]

Int. J. Infrared Millim. Waves

R. Piesiewicz, C. Jansen, S. Wietzke, D. Mittleman, M. Koch, and T. Kürner, “Properties of building and plastic materials in the THz range,” Int. J. Infrared Millim. Waves 28, 363–371 (2007).
[CrossRef]

J. Opt. A

E. Castro-Camus and M. B. Johnston, “Extraction of the anisotropic dielectric properties of materials from polarization-resolved terahertz time-domain spectra,” J. Opt. A 11, 105206 (2009).
[CrossRef]

J. Raman Spectrosc.

P. Vandenabeele, F. Verpoort, and L. Moens, “Non-destructive analysis of paintings using fourier transform raman spectroscopy with fibre optics,” J. Raman Spectrosc. 32, 263–269 (2001).
[CrossRef]

Laser Photon. Rev.

P. U. Jepsen, D. G. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser Photon. Rev. 5, 124–166 (2011).
[CrossRef]

Nucl. Instr. Methods B

G. Demortier and J. Ruvalcaba-Sil, “Quantitative ion beam analysis of complex gold-based artefacts,” Nucl. Instr. Methods B 239, 1–15 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

S. Taraskin, S. Simdyankin, S. Elliott, J. Neilson, and T. Lo, “Universal features of terahertz absorption in disordered materials,” Phys. Rev. Lett. 97, 55504 (2006).
[CrossRef]

Other

O. Peters, S. Wietzke, C. Jansen, M. Scheller, and M. Koch, “Nondestructive detection of delaminations in plastic weld joints,” in 35th International Conference on Infrared Millimeter and Terahertz Waves (IRMMW-THz) (IEEE, 2010), pp. 1–2.

G. Fowles, Introduction to Modern Optics (Dover, 1989).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Refractive index and (b) absorption coefficient of various stones used in artwork. The short names of the stones are indicated on the plot; the full names are listed in Table 1.

Fig. 2.
Fig. 2.

Two curves showing the reflected waveform of a single slab of stone as well as one slab followed by an air gap and a second piece of stone. The insets show illustrations to clarify the process.

Fig. 3.
Fig. 3.

(a) Calculated THz time-domain pulses reflected at air gaps of different thicknesses. (b) Fourier transform of the data shown in (a); the arrows indicate the positions where the lowest frequency Fabry–Perot dips are expected for the air gap thickness modeled. (c) Experimental THz time-domain measurement of reflected pulses at an air gap between stones for various gap thicknesses. (d) Fourier transform of the data shown in (c); the arrows indicate the positions where the lowest frequency Fabry–Perot dips are expected for the nominal thickness of the air gaps.

Fig. 4.
Fig. 4.

(a) Reflected time-domain waveforms for small air gaps. The amplitude of the reflection caused by the gap has a strong dependence with gap size in this regime. The integration windows [a1,a2] and [b1,b2] used to calculate the parameter AR are indicated. (b) The parameter AR as function of gap thickness.

Fig. 5.
Fig. 5.

Three-dimensional reconstruction of a subwavelength wedged air gap between two pieces of stone. The inset on the left hand side illustrates the wedge gap geometry. The inset on the right hand side presents the thickness extracted from the THz measurement (circles) at the central position in the y direction. The thickness of a perfect plane is indicated for comparison by a dashed line.

Tables (1)

Tables Icon

Table 1. Average Refractive Indices of Some Stones

Equations (5)

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

d=cΔt2n,
E(t)=Ad2dt2e(t)2/τ2,
ETHz(t)=rasE(td0c)+[tasrsatsaE(td0+nsd1c)+tas2tsa2rasE(td0+nsd1+d2c)]e2αd1,
νFP=c2d2,
AR=a1a2|ETHz(t)|dtb1b2|ETHz(t)|dt.

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