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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 25093–25112

Theory of oblique and grazing incidence Talbot‑Lau interferometers and demonstration in a compact source x‑ray reflective interferometer

Han Wen, Camille K Kemble, and Eric E. Bennett  »View Author Affiliations

Optics Express, Vol. 19, Issue 25, pp. 25093-25112 (2011)

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With the advent of Talbot-Lau interferometers for x-ray phase-contrast imaging, oblique and grazing incidence configurations are now used in the pursuit of sub-micron grating periods and high sensitivity. Here we address the question whether interferometers having oblique incident beams behave in the same way as the well-understood normal incidence ones, particularly when the grating planes are non-parallel. We derive the normal incidence equivalence of oblique incidence geometries from wave propagation modeling. Based on the theory, we propose a practical method to correct for non-parallelism of the grating planes, and demonstrate its effectiveness with a polychromatic hard x-ray reflective interferometer.

© 2011 OSA

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(340.7450) X-ray optics : X-ray interferometry
(110.3175) Imaging systems : Interferometric imaging

ToC Category:
X-ray Optics

Original Manuscript: October 20, 2011
Revised Manuscript: November 11, 2011
Manuscript Accepted: November 12, 2011
Published: November 23, 2011

Han Wen, Camille K Kemble, and Eric E. Bennett, "Theory of oblique and grazing incidence Talbot‑Lau interferometers and demonstration in a compact source x‑ray reflective interferometer," Opt. Express 19, 25093-25112 (2011)

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  1. D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. E. Pritchard, “An interferometer for atoms,” Phys. Rev. Lett. 66(21), 2693–2696 (1991). [CrossRef] [PubMed]
  2. J. F. Clauser and S. F. Li, “Talbot-vonLau atom interferometry with cold slow potassium,” Phys. Rev. A 49(4), R2213–R2216 (1994). [CrossRef] [PubMed]
  3. P. Cloetens, J. P. Guigay, C. De Martino, J. Baruchel, and M. Schlenker, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett. 22(14), 1059–1061 (1997). [CrossRef] [PubMed]
  4. C. David, B. Nohammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81(17), 3287–3289 (2002). [CrossRef]
  5. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jap. J. Appl. Phys. Part 2-Letters 42, 866–868 (2003).
  6. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005). [CrossRef] [PubMed]
  7. H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).
  8. E. Lau, “Beugungserscheinung an Dopperlrastern,” Ann. Phys. (Leipzig) 6(7-8), 417–427 (1948). [CrossRef]
  9. J. Jahns and A. W. Lohmann, “Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28(3), 263–267 (1979). [CrossRef]
  10. B. J. Chang, R. Alferness, and E. N. Leith, “Space-invariant achromatic grating interferometers: theory,” Appl. Opt. 14(7), 1592–1600 (1975). [CrossRef] [PubMed]
  11. S. K. Lynch, C. Liu, L. Assoufid, N. Y. Morgan, D. Mazilu, E. E. Bennett, C. K. Kemble, X. Xiao, and H. H. Wen, “Multi-layer coated micro-grating array for x-ray phase-contrast imaging,” Proc. SPIE 8076, 80760F.1-80760F.10 (2011).
  12. J. Thibaud, “Soft x-ray emission and absorption spectra with tangential grating,” Nature 121(3044), 321–322 (1928). [CrossRef]
  13. L. A. Sayce and A. Franks, “N.P.L. gratings for x-ray spectroscopy,” Proc. R. Soc. London Ser. A Math. Phys. Sci. 282(1390), 353–357 (1964). [CrossRef]
  14. J. Filevich, K. Kanizay, M. C. Marconi, J. L. A. Chilla, and J. J. Rocca, “Dense plasma diagnostics with an amplitude-division soft-x-ray laser interferometer based on diffraction gratings,” Opt. Lett. 25(5), 356–358 (2000). [CrossRef] [PubMed]
  15. Y. Liu, X. Tan, Z. K. Liu, X. D. Xu, Y. L. Hong, and S. J. Fu, “Soft x-ray holographic grating beam splitter including a double frequency grating for interferometer pre-alignment,” Opt. Express 16(19), 14761–14770 (2008). [CrossRef] [PubMed]
  16. D. Stutman, M. Finkenthal, and N. Moldovan, “Development of microperiodic mirrors for hard x-ray phase-contrast imaging,” Appl. Opt. 49(25), 4677–4686 (2010). [CrossRef] [PubMed]
  17. C. K. Kemble, J. Auxier, S. K. Lynch, E. E. Bennett, N. Y. Morgan, and H. Wen, “Grazing angle Mach-Zehnder interferometer using reflective phase gratings and a polychromatic, un-collimated light source,” Opt. Express 18(26), 27481–27492 (2010). [CrossRef] [PubMed]
  18. J. D. Jackson, “Scalar diffraction theory” in Classical Electrodynamics (Wiley, New York 1998), pp. 478–481.
  19. T. Donath, M. Chabior, F. Pfeiffer, O. Bunk, E. Reznikova, J. Mohr, E. Hempel, S. Popescu, M. Hoheisel, M. Schuster, J. Baumann, and C. David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106(5), 054703 (2009). [CrossRef]
  20. D. L. Voronov, M. Ahn, E. H. Anderson, R. Cambie, C. H. Chang, E. M. Gullikson, R. K. Heilmann, F. Salmassi, M. L. Schattenburg, T. Warwick, V. V. Yashchuk, L. Zipp, and H. A. Padmore, “High-efficiency 5000 lines/mm multilayer-coated blazed grating for extreme ultraviolet wavelengths,” Opt. Lett. 35(15), 2615–2617 (2010). [CrossRef] [PubMed]
  21. J. Rizzi, T. Weitkamp, N. Guérineau, M. Idir, P. Mercère, G. Druart, G. Vincent, P. da Silva, and J. Primot, “Quadriwave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging,” Opt. Lett. 36(8), 1398–1400 (2011). [CrossRef] [PubMed]
  22. M. Testorf, J. Jahns, N. A. Khilo, and A. M. Goncharenko, “Talbot effect for oblique angle of light propagation,” Opt. Commun. 129(3-4), 167–172 (1996). [CrossRef]

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