Fig. 1. Schematic of experimental setup for X-ray Talbot interferometry of laser-driven shock waves. A ps laser pulse is focused on a thin wire to produce X-rays that propagate through the target of interest, which has previously been irradiated with a ns laser beam. The Talbot interferometer, placed downstream of the target, is formed by the gratings G₁ and G₂. Finally, the X-rays are detected by a digital detector protected from electromagnetic pulses by a Faraday cage.²³ Note that an 8 cm-long deflecting magnet (0.5 T), placed in front of the grating G₁, is not shown. The inset shows an example of the spectrum of a 5 μm tungsten wire measured at PHELIX in the range from 8 to 18 keV. See the supplementary material for an enlarged version.

Fig. 2. Moiré fringe patterns obtained at PHELIX (a) and LULI (b). The color code is the same for both images and indicates the deposited X-ray energy in keV. The axis indicates the spatial extent in the object plane. Vertical red lines in the images mark the pixels from which the lineouts in (c) and (d) were generated. The fringe visibilities obtained at the PHELIX and LULI lasers were 15% ± 3% and 28% ± 3%, respectively. Note that the vertical stripes in the image obtained at PHELIX stem from defects in the absorption grating used.

Fig. 3. Retrieved transmission image (a) and differential phase-contrast image (b) from data acquired at the PHELIX laser. The 23 μm wide areas (10 pixels) marked by the red dashed lines are used used to generate the lineouts plotted in Fig. 4. The expected density distribution is simulated with FLASH and shown in (c) and (d). Because of the cylindrical nature of the experiment, only half of ech simulated image is displayed.

Fig. 4. Lineouts from the areas marked in red in Fig. 3 averaged along the r axis: (a) transmission image; (b) differential phase-contrast image. The red lines are obtained from the simulated images and the blue crosses from the data obtained in the experiment. The light blue bands indicate the standard deviation of the data. The dark blue lines show the data along the z direction smoothed.

Fig. 5. Experimental results from the LULI beamtime: (a) transmission; (b) DPC; (c) dark-field image. The dark spot in the transmission image is a sapphire bead, which will not be discussed in this paper. The highly absorbing vertical area on the left side is a copper flag to shield the detector from preplasma emission.

Table 1. Parameters of imaging setup used at the PHELIX facility. The thickness of the grating G₁ was chosen such that it was π-shifting for 11 keV. The duty cycle (DC) is the ratio of the grating bar width to the period. The grating G₁ was fabricated on a 500 μm polyimide wafer and the grating G₂ on a 200 μm graphite wafer.

Table 2. Parameters of the imaging setup used at the LULI facility. The thickness of the grating G₁ was chosen such that it was π-shifting for 10 keV. The grating G₁ was fabricated on a 10 μm polyimide membrane wafer and the G₂ grating on a 500 μm polyimide wafer.