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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 12 — Jun. 6, 2011
  • pp: 11578–11583

Numerical model for tomographic image formation in transmission x-ray microscopy

Michael Bertilson, Olov von Hofsten, Hans M. Hertz, and Ulrich Vogt  »View Author Affiliations

Optics Express, Vol. 19, Issue 12, pp. 11578-11583 (2011)

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We present a numerical image-formation model for investigating the influence of partial coherence, sample thickness and depth-of-focus on the accuracy of tomographic reconstructions in transmission x-ray microscopes. The model combines wave propagation through the object by finite difference techniques with Fourier methods. We include a ray-tracing model to analyse the origin of detrimental stray light in zone plate-based x-ray microscopes. These models allow optimization of x-ray microscopy systems for quantitative tomographic imaging of thick objects. Results show that both the depth-of-focus and the reconstructed local absorption coefficient are highly dependent on the degree of coherence of the optical system.

© 2011 OSA

OCIS Codes
(110.4980) Imaging systems : Partial coherence in imaging
(340.0340) X-ray optics : X-ray optics
(340.7460) X-ray optics : X-ray microscopy
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
X-ray Optics

Original Manuscript: April 12, 2011
Revised Manuscript: May 24, 2011
Manuscript Accepted: May 26, 2011
Published: May 31, 2011

Virtual Issues
Vol. 6, Iss. 7 Virtual Journal for Biomedical Optics

Michael Bertilson, Olov von Hofsten, Hans M. Hertz, and Ulrich Vogt, "Numerical model for tomographic image formation in transmission x-ray microscopy," Opt. Express 19, 11578-11583 (2011)

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  1. A. Sakdinawat and D. Attwood, “Nanoscale X-ray imaging,” Nat. Photonics 4(12), 840–848 (2010). [CrossRef]
  2. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435(7046), 1210–1213 (2005). [CrossRef] [PubMed]
  3. D. Weiss, G. Schneider, B. Niemann, P. Guttmann, D. Rudolph, and G. Schmahl, “Computed tomography of cryogenic biological specimens based on X-ray microscopic images,” Ultramicroscopy 84(3-4), 185–197 (2000). [CrossRef] [PubMed]
  4. H. N. Chapman and K. A. Nugent, “Coherent lens-less X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010). [CrossRef]
  5. National Center for X-Ray Tomography, http://ncxt.lbl.gov/ BESSY II X-ray Microscope, http://www.bessy.de/bit/bit_station_list.php
  6. P. A. C. Takman, H. Stollberg, G. A. Johansson, A. Holmberg, M. Lindblom, and H. M. Hertz, “High-resolution compact X-ray microscopy,” J. Microsc. 226(2), 175–181 (2007). [CrossRef] [PubMed]
  7. M. Uchida, G. McDermott, M. Wetzler, M. A. Le Gros, M. Myllys, C. Knoechel, A. E. Barron, and C. A. Larabell, “Soft X-ray tomography of phenotypic switching and the cellular response to antifungal peptoids in Candida albicans,” Proc. Natl. Acad. Sci. U.S.A. 106(46), 19375–19380 (2009). [CrossRef] [PubMed]
  8. G. Schneider, P. Guttmann, S. Heim, S. Rehbein, F. Mueller, K. Nagashima, J. B. Heymann, W. G. Müller, and J. G. McNally, “Three-dimensional cellular ultrastructure resolved by X-ray microscopy,” Nat. Methods 7(12), 985–987 (2010). [CrossRef] [PubMed]
  9. B. R. Frieden, “Optical transfer of the three-dimensional object,” J. Opt. Soc. Am. 57(1), 56–66 (1967). [CrossRef]
  10. N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. 2(2), 121–127 (1985). [CrossRef]
  11. Y. Wang, C. Jacobsen, J. Maser, and A. Osanna, “Soft X-ray microscopy with a cryo scanning transmission X-ray microscope: II. Tomography,” J. Microsc. 197(1), 80–93 (2000). [CrossRef] [PubMed]
  12. O. von Hofsten, P. A. C. Takman, and U. Vogt, “Simulation of partially coherent image formation in a compact soft X-ray microscope,” Ultramicroscopy 107(8), 604–609 (2007). [CrossRef] [PubMed]
  13. M. Nevière and E. Popov, Light Propagation in Periodic Media, (Marcel Dekker, 2003).
  14. J. Zhenle, F. Junmei, and F. Enxin, “A simple wide-angle beam-propagation method for integrated optics,” Microw. Opt. Technol. Lett. 14(6), 345–347 (1997). [CrossRef]
  15. A. N. Kurokhtin and A. V. Popov, “Simulation of high-resolution x-ray zone plates,” J. Opt. Soc. Am. A 19(2), 315–324 (2002). [CrossRef]
  16. G. R. Hadley, “Transparent boundary condition for beam propagation,” Opt. Lett. 16(9), 624–626 (1991). [CrossRef] [PubMed]
  17. B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E = 50-30,000 eV, Z = 1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993). [CrossRef]
  18. C. MessaoudiI, T. Boudier, C. Sorzano, and S. Marco, “TomoJ: tomography software for three-dimensional reconstruction in transmission electron microscopy,” BMC Bioinf. 8(1), 288 (2007). [CrossRef]
  19. https://www.sonoma.edu/users/c/cannon/biomineralTEM.html

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