title: Spherical grating based x-ray Talbot interferometry.
abstract: OBJECTIVE
  Grating interferometry is a state-of-the-art x-ray imaging approach, which can acquire information on x-ray attenuation, phase shift, and small-angle scattering simultaneously. Phase-contrast imaging and dark-field imaging are very sensitive to microstructural variation and offers superior contrast resolution for biological soft tissues. However, a common x-ray tube is a point-like source. As a result, the popular planar grating imaging configuration seriously restricts the flux of photons and decreases the visibility of signals, yielding a limited field of view. The purpose of this study is to extend the planar x-ray grating imaging theory and methods to a spherical grating scheme for a wider range of preclinical and clinical applications.
  
  
  METHODS
  A spherical grating matches the wave front of a point x-ray source very well, allowing the perpendicular incidence of x-rays on the grating to achieve a higher visibility over a larger field of view than the planer grating counterpart. A theoretical analysis of the Talbot effect for spherical grating imaging is proposed to establish a basic foundation for x-ray spherical gratings interferometry. An efficient method of spherical grating imaging is also presented to extract attenuation, differential phase, and dark-field images in the x-ray spherical grating interferometer.
  
  
  RESULTS
  Talbot self-imaging with spherical gratings is analyzed based on the Rayleigh-Sommerfeld diffraction formula, featuring a periodic angular distribution in a polar coordinate system. The Talbot distance is derived to reveal the Talbot self-imaging pattern. Numerical simulation results show the self-imaging phenomenon of a spherical grating interferometer, which is in agreement with the theoretical prediction.
  
  
  CONCLUSIONS
  X-ray Talbot interferometry with spherical gratings has a significant practical promise. Relative to planar grating imaging, spherical grating based x-ray Talbot interferometry has a larger field of view and improves both signal visibility and dose utilization for pre-clinical and clinical applications.
authors.affiliation: Biomedical Imaging Center, Rensselaer Polytechnic Institute, Troy, New York 12180.
authors.forename: Wenxiang
authors.initials: W
authors.lastname: Cong
authors.affiliation: Biomedical Imaging Center, Rensselaer Polytechnic Institute, Troy, New York 12180.
authors.forename: Yan
authors.initials: Y
authors.lastname: Xi
authors.affiliation: Biomedical Imaging Center, Rensselaer Polytechnic Institute, Troy, New York 12180.
authors.forename: Ge
authors.initials: G
authors.lastname: Wang
mesh_terms: D003198:Computer Simulation; D017076:Computer-Aided Design; D004867:Equipment Design; D019544:Equipment Failure Analysis; D007368:Interferometry / Q000295:instrumentation* / Q000379:methods; D008962:Models, Theoretical; D012031:Refractometry / Q000295:instrumentation* / Q000379:methods; D012542:Scattering, Radiation; D014961:X-Ray Diffraction / Q000295:instrumentation* / Q000379:methods; D014965:X-Rays