Advertisement

Terahertz Differential Computed Tomography: a Relevant Nondestructive Inspection Application

  • Alexandre DuhantEmail author
  • Meriam Triki
  • Olivier Strauss
Article
  • 116 Downloads

Abstract

In recent years, tremendous advances have been made in the choice of materials used in the industry. With weight reduction as the goal, composite and polymer materials are more and more popular but they are almost transparent to X-ray. Because of this, interest has grown in other wavelengths like terahertz (THz). Due to a difference in how X-ray and THz propagate, X-ray CT algorithms cannot be directly used. For example, THz induces refraction making the reconstruction problem nonlinear. In this paper, we present a new algorithm which complies with beam profile intensities, refraction, and reflection. It is based on linearizing the reconstruction process around a computer-aided design (CAD) model of the object to be reconstructed. The method we propose computes the deviation between the object and this model.

Keywords

Terahertz computed tomography Inverse problem Nondestructive testing Refraction Nonlinear problem Modeling Projection simulation Monte Carlo 

References

  1. 1.
    Reiser, M.F., Semmler, W., Hricak, H.: Magnetic Resonance Tomography. Springer Science & Business Media (2007).Google Scholar
  2. 2.
    Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. Society of Industrial and Applied Mathematics (2001).Google Scholar
  3. 3.
    Bailey, D.L., Townsend, D.W., Valk, P.E., Maisey, M.N.: Positron Emission Tomography: Basic Sciences. Springer Science & Business Media (2006).Google Scholar
  4. 4.
    Chiesura, G., Luyckx, G., Voet, E., Lammens, N., van Paepegem, W., Degrieck, J., Dierick, M., van Hoorebeke, L., Vanderniepen, P., Sulejmani, S., Sonnenfeld, C., Geernaert, T., Berghmans, F.: A micro-computed tomography technique to study the quality of fibre optics embedded in composite materials. Sensors 15(5), 10852–10871 (2015).Google Scholar
  5. 5.
    Stock, S.: X-ray microtomography of materials. International Materials Reviews 44(4), 141–64 (2015).Google Scholar
  6. 6.
    Mittleman, D., Hunsche, S., Boivin, L., Nuss, M.C.: T-ray tomography. Optics Letters 22(12), 904–906 (1997).Google Scholar
  7. 7.
    Mukherjee, S., Federici, J., Lopes, P., Cabral, M.: Elimination of fresnel reflection boundary effects and beam steering in pulsed terahertz computed tomography. Journal of Infrared, Millimeter, and Terahertz Waves 34(9), 539–555 (2013).Google Scholar
  8. 8.
    Strauss, O., Lahrech, A., Rico, A., Mariano-Goulart, D., Telle, B.: Nibart: A new interval based algebraic reconstruction technique for error quantication of emission tomography images. In: MICCAI: Medical Image Computing and Computer-Assisted Intervention. London, United Kingdom (2009).Google Scholar
  9. 9.
    Hsieh, J.: Computed Tomography: Principles, Design, Artifacts, and Recent Advances. SPIE Press (2003).Google Scholar
  10. 10.
    Natterer, F.: The Mathematics of Computerized Tomography. Society for Industrial and Applied Mathematics (2001).Google Scholar
  11. 11.
    Guillet, J.P., Recur, B., Frederique, L., Bousquet, B., Canioni, L., Manek-Hönninger, I., Desbarats, P., Mounaix, P.: Review of terahertz tomography techniques. Journal of Infrared, Millimeter, and Terahertz Waves 35(4), 382–411 (2014).Google Scholar
  12. 12.
    Kaczmarz, S.: Approximate solution of systems of linear equations. International Journal of Control 57(6), 1269–1271 (1993).Google Scholar
  13. 13.
    Gordon, R., Bender, R., Herman, G.: Algebraic reconstruction techniques (art) for three-dimensional electron microscopy and x-ray photography. Journal of Theoretical Biology 29(3), 471–476 (1970).Google Scholar
  14. 14.
    Shepp, L.A., Vardi, Y.: Maximum likelihood reconstruction for emission tomography. IEEE Transactions on Medical Imaging 1(2), 113 – 122 (1982).Google Scholar
  15. 15.
    Slambrouck, K.V., Stute, S., Comtat, C., Sibomana, M., Velden, F.H.P.V., Boellaard, R., Nuyts, J.: Bias reduction for low-statistics pet: Maximum likelihood reconstruction with a modified poisson distribution. IEEE Transactions on Medical Imaging 34(1), 126 – 136 (1982).Google Scholar
  16. 16.
    Yokoi, T., Shinohara, H., Hashimoto, T., Yamamoto, T., Niio, Y.: Implementation and performance evaluation of iterative reconstruction algorithms in spect. In: Second International Workshop on EGS. Tsukuba, Japan (2000).Google Scholar
  17. 17.
    Recur, B., Guillet, J., Manek-Hönninger, I., Delagnes, J., Benharbone, W., Desbarats, P., Domenger, J.P., Canioni, L., Mounaix, P.: Propagation beam consideration for 3d thz computed tomography. Optics Express 20(6), 5817–5829 (2012).Google Scholar
  18. 18.
    Ferguson, B., Wang, S., Gray, D., Abbot, D., Zhang, X.C.: T-ray computed tomography. Optics Letters 27(15), 1312–1314 (2002).Google Scholar
  19. 19.
    Tepe, J., Schuster, T., Littau, B.: A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography. Journal Inverse Problems in Science and Engineering 25(10), 1448–1473 (2016).Google Scholar
  20. 20.
    Schuster, F., Coquillat, D., Videlier, H., Sakowicz, M., Teppe, F., Dussopt, L., Giffard, B., Skotnicki, T., Knap, W.: Broadband terahertz imaging with highly sensitive silicon cmos detectors. Optics express 19(8), 7827–7832 (2011).Google Scholar
  21. 21.
    Andersen, A., Kak, A.C.: Simultaneous algebraic reconstruction technique(sart) : A superior implementation of the art algorithm. Ultrasonic imaging 6(1), 81–94 (1984).Google Scholar
  22. 22.
    Elfving, T., Hansen, P.C., Nikazad, T.: Semiconvergence and relaxation parameters for projected sirt algorithms. SIAM Journal on Scientific Computing 34(4), A2000–A2017 (2012).Google Scholar
  23. 23.
    Flemming, H.: Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems. Linear Algebra and its Applications 130, 133–150 (1990).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LIRMMUniversity of Montpellier, CNRSMontpellierFrance
  2. 2.Department of Research and DevelopmentT-Waves TechnologiesMontpellierFrance

Personalised recommendations