X-ray-refractive-index measurements at photon energies above 100 keV with a grating interferometer

The knowledge of the x-ray index of refraction of materials is important for the interpretation or simulation of many x-ray physics phenomena. But its precise and accurate experimental determination is challenging, particularly in the hard x-ray energy range above 100 keV. In this article we present and discuss experimental measurements of the real and imaginary part of the index of refraction for different materials based on x-ray grating interferometry at energies above 130 keV.

Figure 1

Schematic representation of the grating interferometer setup used in this study.

Figure 2

Scanning electron microscope images of the absorption grating G2 used for the experiment.

Figure 3

(a) Visibility map, measured without a sample in the beam. (b) Example of an absorption projection of the sample, and T corresponds to the percentage of the transmitted x rays. (c) Differential-phase projection of the sample, and $\alpha$ corresponds to the refractive angle.

Figure 4

Absorption (a) and phase (b) slices of the phantom sample. These images have been obtained by averaging 51 slices taken at the position indicated by the dashed lines in Fig. 3. The squares in (b) show the regions of interest used for the analysis described in the main text. Numbers in (a) label the rods, and the corresponding materials can be found in Table 1.

Figure 5

Measured attenuation coefficients $\mu$ with respect to the corresponding measured electron densities ${\rho }_e$. Standard deviations are indicated by error bars, and the solid blue line represents the linear attenuation coefficient for Compton scattering ${\mu }_{\mathrm{inc}}={\sigma }_{\mathrm{inc}}\times {\rho }_e$, where ${\sigma }_{\mathrm{inc}}$ is the photon cross section corresponding to the incoherent scattering and ${\rho }_e$ is the theoretical electronic density of each material.