Two-Dimensional X-Ray Grating Interferometer

We report on the design and experimental realization of a 2D x-ray grating interferometer. We describe how this interferometer has been practically implemented, discuss its performance, and present multidirectional scattering (dark-field) maps and quantitative phase images that have been retrieved using this device.

Figure 1

Schematic representation of a 2D x-ray grating interferometer setup. The gratings $G1$ and $G2$ are placed in series in the x-ray path, separated by a distance $D$. $\phi (x,y)$ denotes the phase-shift profile of $G1$, $T(x,y)$ the intensity transmission of $G2$.

Figure 2

Theoretical and experimental results of a 2D raster phase-stepping scan performed over one grating period. (The two-period representation used in this figure has been chosen for clarity. It is obtained by tiling the data). Panels (a) and (b) show the detector signal in a single pixel as a function of the grating coordinates $x_g$ and $y$. Panel (a) displays the calculated detector signal for ideal conditions (perfect gratings, fully coherent flat beam). Panel (b) shows the experimentally measured signal. The signal integrated along the $x$ and $y$ coordinates is shown in (c); the contrast curves along the diagonals $d1$ and $d2$ are shown in (d).

Figure 3

Horizontal (a) and vertical (b) components of the refraction angle signal of a leaf recorded with a 2D grating interferometer. Note the superior quality of the 2D phase map retrieved with the 2D interferometer [(d) and detail (f)] over the one that would have been obtained with a 1D interferometer giving signal only along $x$ (c). The section profile across a linear feature in the phase map [plot in (e), profile position indicated by an arrow in (f)] has a FWHM of 3.9 pixels ($30\mu \mathrm{m}$).

Figure 4

Scattering (dark-field) images of the central part of the leaf along the four directions ($x$, $y$, $d1$, and $d2$) as indicated in the bottom right of each image. Strong scattering details in the object are represented by dark regions in the images. Images $v_x$ and $v_y$ have a better signal-to-noise ratio than $v_{d1}$ and $v_{d2}$ because the visibility is higher along the main axes than along the diagonals (Fig. 2). Details highlighted with circles and squares are examples of features for which the diagonal information helps to determine with more accuracy their preferential scattering direction.