Supplementary material
S1 Imaging setup and data acquisition
A schematic of the imaging setup is shown in Fig. 1a. The setup consists of an X-ray source, a pixel detector and the grating interferometer. As the name suggests, the principle of the grating interferometer is based on interference, exploiting the wave nature of X-rays. The first grating, referred to as the source grating or G0 (see Fig. 1a), is positioned directly after the source. G0 is an absorption grating, usually made of gold lines. Since gold is a strong X-ray absorber (high atomic number), the source grating acts as an attenuation grid consisting of opaque and transmitting lines. Due to the finite focal spot size of the source, the slits of G0 split the source into an array of micron-sized sources. Such small sources are necessary for the generation of constructive interference.
The second grating, referred to as the beam splitter grating or G1, is placed between the source grating and the detector. G1 is a so-called phase grating, whose lines are typically made of low-absorbing silicon. These lines periodically introduce a phase shift of zero and π to the X-ray wave, generating a so called periodic phase modulation. This phase modulation generates interference, called a periodic intensity modulation, downstream of G1, appearing as fringes of high intensity. A sample placed in front of G1, which refracts the beam, causes a transversal displacement of those fringes, which can be measured. From the geometrical parameters of the system, the refraction angle caused by the sample can then be calculated. Since the refraction angle is proportional to the first spatial derivative of the phase signal, the refraction image is often referred to as the differential phase contrast (DPC) image.
The displacement of the interference fringes could most efficiently be measured by the pixel detector itself. However, since detector pixels are typically larger than the spatial period of the fringes, a direct measurement of the fringe-shift is impossible. This is solved by using a third grating, referred to as the analyzer grating or G2. Similar to G0, it is an absorption grating (i.e., with gold lines) having the same periodicity as the interference fringes. It acts as a mask which either attenuates (low intensity on pixel) or transmits (high intensity on pixel) the fringes, hence encoding the mean fringe shift within a detector pixel into an intensity value (DPC signal).
The retrieval of the DC image involves a slightly different analysis of the interference fringes. Instead of a transversal fringe shift, scattering leads to a reduction in amplitude of the intensity modulation, being the quantity to be measured in this case.
S2 Color coded image fusion
For the fusion of the PC image with the absorption or the DC image, a color coded superposition of the images was applied. While absorption or DC images are displayed in the conventional gray scales (identical values for RGB), the overlaid PC image is displayed in a single RGB color channel (here, the blue channel is used). By using a vector notation for the RGB channels in a pixel, the image fusion can be expressed by
(A1.1)
(A1.2)
The three vector components represent the RGB channels, indicated by subscripts in the fused image. Ai is the absorption signal, Di and Pi are given by Eq. (1) and αA and αD are tuning parameters, which control the opacity of the PC and DC image, respectively, and can be continuously adjusted by the user.