Abstract

3D terahertz computed tomography has been performed using a monochromatic millimeter wave imaging system coupled with an infrared temperature sensor. Three different reconstruction methods (standard back-projection algorithm and two iterative analysis) have been compared in order to reconstruct large size 3D objects. The quality (intensity, contrast and geometric preservation) of reconstructed cross-sectional images has been discussed together with the optimization of the number of projections. Final demonstration to real-life 3D objects has been processed to illustrate the potential of the reconstruction methods for applied terahertz tomography.

© 2011 Optical Society of America

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  1. W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007).
    [CrossRef]
  2. K. Kawase, Y. Ogawa, Y. Watanabe, and H. Inoue, “Non-destructive terahertz imaging of illicit drugs using spectral fingerprints,” Opt. Express 11, 2549–2554 (2003).
    [CrossRef] [PubMed]
  3. Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
    [CrossRef]
  4. K. Fukunaga and M. Picollo, “Terahertz spectroscopy applied to the analysis of artists materials,” Appl. Phys., A Mater. Sci. Process. 100, 591–597 (2010).
    [CrossRef]
  5. E. Abraham, A. Younus, J.-C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys., A Mater. Sci. Process. 100, 585–590 (2010).
    [CrossRef]
  6. S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
    [CrossRef]
  7. J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express 17, 7549–7555 (2009).
    [CrossRef] [PubMed]
  8. K. Iwaszczuk, H. Heiselberg, and P. U. Jepsen, “Terahertz radar cross section measurements,” Opt. Express 18, 26399–26408 (2010).
    [CrossRef] [PubMed]
  9. B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002).
    [CrossRef]
  10. E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
    [CrossRef]
  11. S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, “T-ray imaging and tomography,” J. Biol. Phys. 29, 247–256 (2003).
    [CrossRef]
  12. S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37, R1–R36 (2004).
    [CrossRef]
  13. M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86, 221107 (2005).
    [CrossRef]
  14. X. Yin, B. W. H. Ng, B. Ferguson, and D. Abbott, “Wavelet based local tomographic image using terahertz techniques,” Digit. Signal Process. 19, 750–763 (2009).
    [CrossRef]
  15. A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
    [CrossRef]
  16. K. L. Nguyen, M. L. Johns, L. F. Gladden, C. H. Worral, P. Alexander, H. E. Beere, M. Pepper, D. A. Ritchie, J. Alton, S. Barbieri, and E. H. Linfield, “Three-dimensional imaging with a terahertz quantum cascade laser,” Opt. Express 14, 2123–2129 (2006).
    [CrossRef] [PubMed]
  17. A. Younus, S. Salort, B. Recur, P. Desbarats, P. Mounaix, J.-P. Caumes, and E. Abraham, “3D millimeter wave tomographic scanner for large size opaque object inspection with different refractive index contrasts,” in Millimetre Wave and Terahertz Sensors and Technology III, K.A. Krapels and N.A. Salmon, eds., Proc. SPIE 7837, 783709 (2010).
  18. N. Sunaguchi, Y. Sasaki, N. Maikusa, M. Kawai, T. Yuasa, and C. Otani, “Depth-resolving terahertz imaging with tomosynthesis,” Opt. Express 17, 9558–9570 (2009).
    [CrossRef] [PubMed]
  19. T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
    [CrossRef]
  20. T. Yasui, K. Sawanaka, A. Ihara, E. Abraham, M. Hashimoto, and T. Araki, “Real-time terahertz color scanner for moving objects,” Opt. Express 16, 1208–1221 (2008).
    [CrossRef] [PubMed]
  21. G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography (Academic Press Inc., 1980).
  22. A. H. Andersen, and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imaging 6, 81–94 (1984).
    [CrossRef] [PubMed]
  23. L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
    [CrossRef] [PubMed]
  24. H. M. Hudson, and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
    [CrossRef] [PubMed]
  25. C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
    [CrossRef]
  26. P. Toft, “The Radon Transform: Theory and Implementation,” Ph.D. thesis, Department of Mathematical Modelling, Section for Digital Signal Processing, Technical University of Denmark (1996).
  27. J. Radon, “¨Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten,” Ber. Ver. Sachs. Akad.Wiss. Leipzig, Math-Phys. Kl 69, 262–277 (1917). In German. An english translation can be found in S. R. Deans: The Radon Transform and Some of Its Applications.
  28. R. Gordon, R. Bender, and G. T. Herman, “Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography,” J. Theor. Biol. 29, 471–481 (1970).
    [CrossRef] [PubMed]
  29. B. Recur, “Qualité et Précision en Reconstruction Tomographique: Algorithmes et Applications,” Ph.D. thesis, LaBRI, Bordeaux 1 University (2010).
  30. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
    [CrossRef] [PubMed]

2010 (6)

K. Fukunaga and M. Picollo, “Terahertz spectroscopy applied to the analysis of artists materials,” Appl. Phys., A Mater. Sci. Process. 100, 591–597 (2010).
[CrossRef]

E. Abraham, A. Younus, J.-C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys., A Mater. Sci. Process. 100, 585–590 (2010).
[CrossRef]

K. Iwaszczuk, H. Heiselberg, and P. U. Jepsen, “Terahertz radar cross section measurements,” Opt. Express 18, 26399–26408 (2010).
[CrossRef] [PubMed]

E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
[CrossRef]

A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
[CrossRef]

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

2009 (4)

N. Sunaguchi, Y. Sasaki, N. Maikusa, M. Kawai, T. Yuasa, and C. Otani, “Depth-resolving terahertz imaging with tomosynthesis,” Opt. Express 17, 9558–9570 (2009).
[CrossRef] [PubMed]

X. Yin, B. W. H. Ng, B. Ferguson, and D. Abbott, “Wavelet based local tomographic image using terahertz techniques,” Digit. Signal Process. 19, 750–763 (2009).
[CrossRef]

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

J. Takayanagi, H. Jinno, S. Ichino, K. Suizu, M. Yamashita, T. Ouchi, S. Kasai, H. Ohtake, H. Uchida, N. Nishizawa, and K. Kawase, “High-resolution time-of-flight terahertz tomography using a femtosecond fiber laser,” Opt. Express 17, 7549–7555 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007).
[CrossRef]

2006 (2)

2005 (2)

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86, 221107 (2005).
[CrossRef]

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

2004 (2)

S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37, R1–R36 (2004).
[CrossRef]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

1994 (1)

H. M. Hudson, and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef] [PubMed]

1984 (1)

A. H. Andersen, and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imaging 6, 81–94 (1984).
[CrossRef] [PubMed]

1982 (1)

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef] [PubMed]

1970 (1)

R. Gordon, R. Bender, and G. T. Herman, “Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Abbot, D.

Abbott, D.

X. Yin, B. W. H. Ng, B. Ferguson, and D. Abbott, “Wavelet based local tomographic image using terahertz techniques,” Digit. Signal Process. 19, 750–763 (2009).
[CrossRef]

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, “T-ray imaging and tomography,” J. Biol. Phys. 29, 247–256 (2003).
[CrossRef]

Abraham, E.

E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
[CrossRef]

E. Abraham, A. Younus, J.-C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys., A Mater. Sci. Process. 100, 585–590 (2010).
[CrossRef]

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

T. Yasui, K. Sawanaka, A. Ihara, E. Abraham, M. Hashimoto, and T. Araki, “Real-time terahertz color scanner for moving objects,” Opt. Express 16, 1208–1221 (2008).
[CrossRef] [PubMed]

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

Aguerre, C.

E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
[CrossRef]

Ahuja, A. T.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Alexander, P.

Alton, J.

Andersen, A. H.

A. H. Andersen, and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imaging 6, 81–94 (1984).
[CrossRef] [PubMed]

Araki, T.

T. Yasui, K. Sawanaka, A. Ihara, E. Abraham, M. Hashimoto, and T. Araki, “Real-time terahertz color scanner for moving objects,” Opt. Express 16, 1208–1221 (2008).
[CrossRef] [PubMed]

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

Awad, M. M.

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86, 221107 (2005).
[CrossRef]

Balageas, D.

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

Barbieri, S.

Batsale, J.-C.

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

Beere, H. E.

Bender, R.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Brahm, A.

A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
[CrossRef]

Caumes, J.-P.

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

Chan, W. L.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007).
[CrossRef]

Chassagne, B.

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

Cheville, R. A.

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86, 221107 (2005).
[CrossRef]

Cole, B. E.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Deibel, J.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007).
[CrossRef]

Delagnes, J.-C.

E. Abraham, A. Younus, J.-C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys., A Mater. Sci. Process. 100, 585–590 (2010).
[CrossRef]

Desbarats, P.

E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
[CrossRef]

Ferguson, B.

X. Yin, B. W. H. Ng, B. Ferguson, and D. Abbott, “Wavelet based local tomographic image using terahertz techniques,” Digit. Signal Process. 19, 750–763 (2009).
[CrossRef]

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, “T-ray imaging and tomography,” J. Biol. Phys. 29, 247–256 (2003).
[CrossRef]

B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002).
[CrossRef]

Fukunaga, K.

K. Fukunaga and M. Picollo, “Terahertz spectroscopy applied to the analysis of artists materials,” Appl. Phys., A Mater. Sci. Process. 100, 591–597 (2010).
[CrossRef]

Gladden, L. F.

Gordon, R.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Gray, D.

Hashimoto, M.

Heiselberg, H.

Herman, G. T.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Huang, S. Y.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Hudson, H. M.

H. M. Hudson, and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef] [PubMed]

Ichino, S.

Ihara, A.

Inoue, H.

Iwaszczuk, K.

Jepsen, P. U.

Jinno, H.

Johns, M. L.

Kak, A. C.

A. H. Andersen, and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imaging 6, 81–94 (1984).
[CrossRef] [PubMed]

Kasai, S.

Kawai, M.

Kawase, K.

Kemp, M. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Kunz, M.

A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
[CrossRef]

Larkin, R. S.

H. M. Hudson, and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef] [PubMed]

Linfield, E. H.

Lo, T.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Maikusa, N.

Mittleman, D. M.

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007).
[CrossRef]

Mounaix, P.

E. Abraham, A. Younus, J.-C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys., A Mater. Sci. Process. 100, 585–590 (2010).
[CrossRef]

E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
[CrossRef]

Ng, B. W. H.

X. Yin, B. W. H. Ng, B. Ferguson, and D. Abbott, “Wavelet based local tomographic image using terahertz techniques,” Digit. Signal Process. 19, 750–763 (2009).
[CrossRef]

Nguyen, K. L.

Nishizawa, N.

Notni, G.

A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
[CrossRef]

Ogawa, Y.

Ohtake, H.

Otani, C.

Ouchi, T.

Pepper, M.

Pickwell-MacPherson, E.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Picollo, M.

K. Fukunaga and M. Picollo, “Terahertz spectroscopy applied to the analysis of artists materials,” Appl. Phys., A Mater. Sci. Process. 100, 591–597 (2010).
[CrossRef]

Pradere, C.

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

Riehemann, S.

A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
[CrossRef]

Ritchie, D. A.

Salort, S.

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

Sasaki, Y.

Sawanaka, K.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Shen, Y. C.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Shepp, L. A.

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef] [PubMed]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Suizu, K.

Sunaguchi, N.

Taday, P. F.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Takayanagi, J.

Tribe, W. R.

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Tünnermann, A.

A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
[CrossRef]

Uchida, H.

Vardi, Y.

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef] [PubMed]

Wang, S.

S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37, R1–R36 (2004).
[CrossRef]

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, “T-ray imaging and tomography,” J. Biol. Phys. 29, 247–256 (2003).
[CrossRef]

B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002).
[CrossRef]

Wang, Y. X. J.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

Watanabe, Y.

Worral, C. H.

Yamashita, M.

Yasuda, T.

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

Yasui, T.

T. Yasui, K. Sawanaka, A. Ihara, E. Abraham, M. Hashimoto, and T. Araki, “Real-time terahertz color scanner for moving objects,” Opt. Express 16, 1208–1221 (2008).
[CrossRef] [PubMed]

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

Yeung, D. K. W.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Yin, X.

X. Yin, B. W. H. Ng, B. Ferguson, and D. Abbott, “Wavelet based local tomographic image using terahertz techniques,” Digit. Signal Process. 19, 750–763 (2009).
[CrossRef]

Younus, A.

E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
[CrossRef]

E. Abraham, A. Younus, J.-C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys., A Mater. Sci. Process. 100, 585–590 (2010).
[CrossRef]

Yuasa, T.

Zhang, X. C.

S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37, R1–R36 (2004).
[CrossRef]

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, “T-ray imaging and tomography,” J. Biol. Phys. 29, 247–256 (2003).
[CrossRef]

B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. C. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002).
[CrossRef]

Zhang, Y. T.

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Appl. Phys. B (1)

A. Brahm, M. Kunz, S. Riehemann, G. Notni, and A. Tünnermann, “Volumetric spectral analysis of materials using terahertz-tomography techniques,” Appl. Phys. B 100, 151–158 (2010).
[CrossRef]

Appl. Phys. Lett. (2)

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86, 221107 (2005).
[CrossRef]

Y. C. Shen, T. Lo, P. F. Taday, B. E. Cole, W. R. Tribe, and M. C. Kemp, “Detection and identification of explosives using terahertz pulsed spectroscopic imaging,” Appl. Phys. Lett. 86, 241116 (2005).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (2)

K. Fukunaga and M. Picollo, “Terahertz spectroscopy applied to the analysis of artists materials,” Appl. Phys., A Mater. Sci. Process. 100, 591–597 (2010).
[CrossRef]

E. Abraham, A. Younus, J.-C. Delagnes, and P. Mounaix, “Non-invasive investigation of art paintings by terahertz imaging,” Appl. Phys., A Mater. Sci. Process. 100, 585–590 (2010).
[CrossRef]

Digit. Signal Process. (1)

X. Yin, B. W. H. Ng, B. Ferguson, and D. Abbott, “Wavelet based local tomographic image using terahertz techniques,” Digit. Signal Process. 19, 750–763 (2009).
[CrossRef]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (2)

L. A. Shepp, and Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef] [PubMed]

H. M. Hudson, and R. S. Larkin, “Accelerated image reconstruction using ordered subsets of projection data,” IEEE Trans. Med. Imaging 13, 601–609 (1994).
[CrossRef] [PubMed]

J. Biol. Phys. (1)

S. Wang, B. Ferguson, D. Abbott, and X. C. Zhang, “T-ray imaging and tomography,” J. Biol. Phys. 29, 247–256 (2003).
[CrossRef]

J. Phys. D Appl. Phys. (1)

S. Wang and X. C. Zhang, “Pulsed terahertz tomography,” J. Phys. D Appl. Phys. 37, R1–R36 (2004).
[CrossRef]

J. Theor. Biol. (1)

R. Gordon, R. Bender, and G. T. Herman, “Algebraic Reconstruction Techniques (ART) for Three-dimensional Electron Microscopy and X-ray Photography,” J. Theor. Biol. 29, 471–481 (1970).
[CrossRef] [PubMed]

Opt. Commun. (2)

T. Yasuda, T. Yasui, T. Araki, and E. Abraham, “Real-time two-dimensional terahertz tomography of moving objects,” Opt. Commun. 267, 128–136 (2006).
[CrossRef]

E. Abraham, A. Younus, C. Aguerre, P. Desbarats, and P. Mounaix, “Refraction losses in terahertz computed tomography,” Opt. Commun. 283, 2050–2055 (2010).
[CrossRef]

Opt. Express (6)

Opt. Lett. (1)

Phys. Med. Biol. (1)

S. Y. Huang, Y. X. J. Wang, D. K. W. Yeung, A. T. Ahuja, Y. T. Zhang, and E. Pickwell-MacPherson, “Tissue characterization using terahertz pulsed imaging in reflection geometry,” Phys. Med. Biol. 54, 149–160 (2009).
[CrossRef]

Quant. Infrared Thermog. (1)

C. Pradere, J.-P. Caumes, D. Balageas, S. Salort, E. Abraham, B. Chassagne, and J.-C. Batsale, “Photothermal converters for quantitative 2D and 3D real-time terahertz imaging,” Quant. Infrared Thermog. 7, 217–235 (2010).
[CrossRef]

Rep. Prog. Phys. (1)

W. L. Chan, J. Deibel, and D. M. Mittleman, “Imaging with terahertz radiation,” Rep. Prog. Phys. 70, 1325–1379 (2007).
[CrossRef]

Ultrason. Imaging (1)

A. H. Andersen, and A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imaging 6, 81–94 (1984).
[CrossRef] [PubMed]

Other (5)

P. Toft, “The Radon Transform: Theory and Implementation,” Ph.D. thesis, Department of Mathematical Modelling, Section for Digital Signal Processing, Technical University of Denmark (1996).

J. Radon, “¨Uber die Bestimmung von Funktionen durch ihre Integralwerte langs gewisser Mannigfaltigkeiten,” Ber. Ver. Sachs. Akad.Wiss. Leipzig, Math-Phys. Kl 69, 262–277 (1917). In German. An english translation can be found in S. R. Deans: The Radon Transform and Some of Its Applications.

G. T. Herman, Image Reconstruction From Projections: The Fundamentals of Computerized Tomography (Academic Press Inc., 1980).

B. Recur, “Qualité et Précision en Reconstruction Tomographique: Algorithmes et Applications,” Ph.D. thesis, LaBRI, Bordeaux 1 University (2010).

A. Younus, S. Salort, B. Recur, P. Desbarats, P. Mounaix, J.-P. Caumes, and E. Abraham, “3D millimeter wave tomographic scanner for large size opaque object inspection with different refractive index contrasts,” in Millimetre Wave and Terahertz Sensors and Technology III, K.A. Krapels and N.A. Salmon, eds., Proc. SPIE 7837, 783709 (2010).

Supplementary Material (6)

» Media 1: MOV (322 KB)     
» Media 2: MOV (285 KB)     
» Media 3: MOV (215 KB)     
» Media 4: MOV (631 KB)     
» Media 5: MOV (371 KB)     
» Media 6: MOV (354 KB)     

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Figures (9)

Fig. 1
Fig. 1

(a) Experimental setup. C: optical chopper, L: Teflon lens (f′ = 60 mm), M: off-axis parabolic mirror (f′ = 150 mm), S: sample, D: pyroelectric detector. (b) 2D spatial profile of the THz beam waist at the sample position (110 GHz source) visualized with a photothermal THz convertor (Teracam).

Fig. 2
Fig. 2

(a) Photograph of original object: parallelepiped black foam (41 × 49) mm2 with 2 holes, diameter 15 mm (1 hole with air and 1 hole containing a Teflon cylinder with a 6 mm cylindrical air hole inside). (b) Sinogram with Nθ = 72 projections (lines) and Nρ = 128 samples per projection (columns). Acquisition with the 110 GHz source.

Fig. 3
Fig. 3

Sinograms of two metallic bars (12 mm diameter) separated by 50 mm, with a projection number Nθ = 72. (a) Ideal theoretical sinogram calculated by direct Radon transformation of a synthetic model. (b) Acquisition using the millimeter wave tomographic scanner with the 110 GHz source. Same scale and range as in (a).

Fig. 4
Fig. 4

Cross sections of two metallic bars (12 mm diameter) separated by 50 mm. (a) Ideal synthetic cross section of the sample. (b) BFP reconstruction from 3(b). (c) SART reconstruction from 3(b). (d) OSEM reconstruction from 3(b). (b) to (d): same scale as in (a).

Fig. 5
Fig. 5

Intensity profiles along the horizontal line intercepting the center of both metallic bars (from Fig. 4).

Fig. 6
Fig. 6

Manufactured sample presented in Fig. 2. Reconstructions using sinograms with 12, 18, 24, 36, 72 projections and the BFP (a), SART (b) and OSEM (c) methods. Same scale has been used for all cross sections.

Fig. 7
Fig. 7

Manufactured sample presented in Fig. 2. SSIM parameter as a function of the projection number and the reconstruction method.

Fig. 8
Fig. 8

White foam parallelepiped (30 mm cube size) drilled by two oblique metallic bars (6 mm diameter). (a) Photograph of the 3D sample. (b) BFP reconstruction ( Media 1). (c) SART reconstruction ( Media 2). (d) OSEM reconstruction ( Media 3). Acquisition with the 240 GHz source.

Fig. 9
Fig. 9

Wooden Russian doll Matriochka (total height 160 mm). (a) Photograph of the 3D sample. (b) BFP reconstruction ( Media 4). (c) SART reconstruction ( Media 5). (d) OSEM reconstruction ( Media 6). Acquisition with the 110 GHz source.

Tables (1)

Tables Icon

Table 1 Details of the SSIM parameter for BFP (a), SART (b) and OSEM (c). l(I,It): intensity, c(I,It): contrast, r(I,It): geometric equivalence rates. Red color indicates significant results.

Equations (5)

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θ ( ρ ) = f ( x , y ) δ ( ρ x cos θ y sin θ ) d x d y
I ( i , j ) = i θ = 0 N θ 1 ρ = N ρ 2 N ρ 2 W θ ( i θ ) ( ρ ) A ( θ , ρ ) , ( i , j )
I k , s ( i , j ) = I k , s 1 ( i , j ) + λ ρ = 0 N ρ 1 A ( θ s , p ) , ( i , j ) [ θ s ( ρ ) R θ s k ( ρ ) D θ s ( ρ ) ] ρ = 0 N ρ 1 A ( θ s , ρ ) , ( i , j )
I k + 1 ( i , j ) = I ( i , j ) i θ = 0 N θ 1 ρ = 0 N ρ 1 A ( θ , ρ ) , ( i , j ) θ ( ρ ) R θ k ( ρ ) i θ = 0 N θ 1 ρ = 0 N ρ 1 A ( θ , ρ ) , ( i , j )
S S I M ( I , I t ) = l ( I , I t ) c ( I , I t ) r ( I , I t )

Metrics