Modregger Peter, Kagias Matias, Irvine Sarah C, Brönnimann Rolf, Jefimovs Konstantins, Endrizzi Marco, Olivo Alessandro
Department of Medical Physics and Bioengineering, University College London, Gower Street, WC1E 6BT London, United Kingdom.
Swiss Light Source, Paul Scherrer Institut, 5232 Villigen, Switzerland.
Phys Rev Lett. 2017 Jun 30;118(26):265501. doi: 10.1103/PhysRevLett.118.265501.
Small angle x-ray scattering has been proven to be a valuable method for accessing structural information below the spatial resolution limit implied by direct imaging. Here, we theoretically derive the relation that links the subpixel differential phase signal provided by the sample to the moments of scattering distributions accessible by refraction sensitive x-ray imaging techniques. As an important special case we explain the scatter or dark-field contrast in terms of the sample's phase signal. Further, we establish that, for binary phase objects, the nth moment scales with the difference of the refractive index decrement to the power of n. Finally, we experimentally demonstrate the utility of the moments by quantitatively determining the particle sizes of a range of powders with a laboratory-based setup.
小角X射线散射已被证明是一种获取低于直接成像所暗示的空间分辨率极限的结构信息的有价值方法。在此，我们从理论上推导出了将样品提供的亚像素差分相位信号与折射敏感X射线成像技术可获取的散射分布矩联系起来的关系式。作为一个重要的特殊情况，我们根据样品的相位信号解释了散射或暗场对比度。此外，我们确定，对于二元相位物体，第n阶矩与折射率减量之差的n次幂成比例。最后，我们通过基于实验室的装置定量测定一系列粉末的颗粒尺寸，实验证明了矩的实用性。
