Several x-ray phase contrast extraction algorithms use a set of images acquired along the rocking curve of a perfect flat analyzer crystal to study the internal structure of objects. By measuring the angular shift of the rocking curve peak, one can determine the local deflections of the x-ray beam propagated through a sample. Additionally, some objects determine a broadening of the crystal rocking curve, which can be explained in terms of multiple refraction of x rays by many subpixel-size inhomogeneities contained in the sample. This fact may allow us to differentiate between materials and features characterized by different refraction properties. In the present work we derive an expression for the beam broadening in the form of a linear integral of the quantity related to statistical properties of the dielectric susceptibility distribution function of the object.
© 2012 Optical Society of America
Original Manuscript: March 28, 2012
Revised Manuscript: July 4, 2012
Manuscript Accepted: July 10, 2012
Published: August 15, 2012
Sergei V. Gasilov and Paola Coan, "X-ray phase contrast imaging of objects with subpixel-size inhomogeneities: a geometrical optics model," J. Opt. Soc. Am. A 29, 1870-1876 (2012)