Skip to main content
Log in

Detection of sub-pixel fractures in X-ray dark-field tomography

  • Published:
Applied Physics A Aims and scope Submit manuscript

Abstract

We present a new method for detecting fractures in solid materials below the resolution given by the detector pixel size by using grating-based X-ray interferometry. The technique is particularly useful for detecting sub-pixel cracks in large samples where the size of the sample is preventing high-resolution μCT studies of the entire sample. The X-ray grating interferometer produces three distinct modality signals: absorption, phase and dark field. The method utilizes the unique scattering features of the dark-field signal. We have used tomograms reconstructed from each of the three signals to detect cracks in a model sample consisting of stearin.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. T. Suzuki, M. Aoki, M. Ohtsu, Damage identification of cracked concrete by X-ray computed tomography method. In: Proceedings of FraMCoS-7, May 23–28, (2010), pp. 1143–1148

  2. B.D. Metscher, Biological applications of X-ray microtomography: imaging microanatomy, molecular expression and organismal diversity. Microsc. Anal. 27(2), 13–16 (2013)

    Google Scholar 

  3. W.A. Kalender, X-ray computed tomography. Phys. Med. Biol. 51, R29–R43 (2006)

    Article  ADS  Google Scholar 

  4. F. Beckmann, R. Grupp, A. Haibel, M. Huppmann, M. Nöthe, A. Pyzalla, W. Reimers, A. Schreyer, R. Zettler, In-situ synchrotron X-ray microtomography studies of microstructure and damage evolution in engineering materials. Adv. Eng. Mater 9(11), 939–950 (2007)

    Article  Google Scholar 

  5. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, Ch. Bronniman, C. Grunzweig, C. David, Hard-X-ray dark-field imaging using a grating interferometer. Nat. Mater. 7, 134–137 (2008)

    Article  ADS  Google Scholar 

  6. M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, F. Pfeiffer, Quantitative X-ray dark-field computed tomography. Phys. Med. Biol. 55, 5529–5539 (2010)

    Article  Google Scholar 

  7. W. Cong, F. Pfeiffer, M. Bech, G. Wang, X-ray dark-field imaging modeling. J Opt. Soc. Am. A 29(6), 908–912 (2012)

    Article  ADS  Google Scholar 

  8. V. Revol, I. Jerjen, C. Kottler et al., Sub-pixel porosity revealed by X-ray scatter dark field imaging. J. Appl. Phys. 110, 044912 (2011)

    Article  ADS  Google Scholar 

  9. W. Yashiro, A. Momose, Effects of unresolvable edges in grating-based X-ray differential phase imaging. Opt. Express 23(7), 9233–9251 (2015)

    Article  ADS  Google Scholar 

  10. M. Bech, X-ray imaging with a grating interferometer. PhD Thesis, University of Copenhagen, 2009

  11. Atsushi Momose, Shinya Kawamoto, Ichiro Koyama, Yoshitaka Hamaishi, Kengo Takai, Yoshio Suzuki, Demonstration of X-ray Talbot Interferometry. Jpn. J. Appl. Phys. 42(7B), 866 (2003)

    Article  ADS  Google Scholar 

  12. Atsushi Momose, Phase-sensitive imaging and phase tomography using X-ray interferometers. Opt. Express 11(19), 2303 (2003)

    Article  ADS  Google Scholar 

  13. C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, P. Cloetens, Hard X-ray phase imaging and tomography using a grating interferometer. Spectrochim. Acta Part B 62, 626–630 (2007)

    Article  ADS  Google Scholar 

  14. C. David, B. Nöhammer, H.H. Solak, E. Ziegler, Differential X-ray phase contrast imaging using a shearing interferometer. Appl. Phys. Lett. 81, 3287 (2002)

    Article  ADS  Google Scholar 

  15. F. Pfeiffer, C. Kottler, O. Bunk, C. David, Hard X-ray phase tomography with low-brilliance sources. Phys. Rev. Lett. 98, 108105 (2007)

    Article  ADS  Google Scholar 

  16. Timm Weitkamp, Ana Diaz, Christian David, Franz Pfeiffer, Marco Stampanoni, Peter Cloetens, Eric Ziegler, X-ray phase imaging with a grating interferometer. Opt. Express 12(16), 6296 (2005)

    Article  ADS  Google Scholar 

  17. J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, C. David, Quantitative phase-contrast tomography of a liquid phantom using a conventional X-ray tube source. Opt. Express 17(12), 10010–10018 (2009)

    Article  ADS  Google Scholar 

  18. M.S. Nielsen, T. Lauridsen, M. Thomsen, T.H. Jensen, M. Bech, L.B. Christensen, E.V. Olsen, M. Hviid, R.K. Feidenhans’l, F. Pfeiffer, X-ray tomography using the full complex index of refraction. Phys. Med. Biol. 57(19), 5971–5979 (2012)

    Article  Google Scholar 

  19. M. Willner, J. Herzen, S. Grandl, S. Auweter, D. Mayr, A. Hipp, M. Chabior, A. Sarapata, K. Achterhold, I. Zanette, T. Weitkamp, A. Sztrókay, K. Hellerhoff, M. Reiser, F. Pfeiffer, Quantitative breast tissue characterization using grating-based X-ray phase-contrast imaging. Phys. Med. Biol. 59(7), 1557–1571 (2014)

    Article  Google Scholar 

  20. W. Yashiro, Y. Terui, K. Kawabata, A. Momose, On the origin of visibility contrast in X-ray Talbot interferometry. Opt. Express 18(16), 16890 (2010)

    Article  ADS  Google Scholar 

  21. F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, P. Lura, Dark-field X-ray imaging of unsaturated water transport in porous materials. Appl. Phys. Lett. 105, 154105 (2014)

    Article  ADS  Google Scholar 

  22. Andreas Dominik Malecki, X-ray Tensor Tomography. PhD Thesis, Technische Universität München (2013)

  23. Z. P. Bazant, H. Ohtsubo, K. Aoh, Stability and post-critical growth of a system of cooling or shrinkage cracks. Int. J. Fract. 15(5), 443–456 (1979)

    Article  Google Scholar 

  24. S. Tarasovs, A. Ghassemi, Self-similarity and scaling of thermal shock fractures. Phys. Rev. E 90, 012403 (2014)

    Article  ADS  Google Scholar 

  25. D.P.H. Hasselman, Unified theory of thermal shock fracture initiation and crack propagation in brittle ceramics. J. Am. Ceram. Soc. 52(11), 600–604 (1969)

    Article  Google Scholar 

  26. F. Pfeiffer, T. Weitkamp, O. Bunk, C. David, Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources. Nat. Phys. 2, 258–261 (2006)

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge Maria Thomsen, Mikkel Schou Nielsen and Katrine R. Rosenmejer Nielsen (all from University of Copenhagen) for their help and assistance. We also thank the Danish Strategic Research Council for support from the NEXIM project and we also thank support from the CIA-CT project.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Torsten Lauridsen.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lauridsen, T., Willner, M., Bech, M. et al. Detection of sub-pixel fractures in X-ray dark-field tomography. Appl. Phys. A 121, 1243–1250 (2015). https://doi.org/10.1007/s00339-015-9496-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00339-015-9496-2

Keywords

Navigation