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(a) Measured energy spectra for different configurations of the GI, acquired by using a threshold sweep scan with an exposure time of 5 s per sweep step. The mean energies are marked with the vertical lines. (b) Energy resolved X-ray transmission through all gratings (solid line) and through G1 and G2 only (dashed line). For both curves, the lowest transmission (highest absorption) is at around 18 keV.
(a) Theoretical visibility as a function of energy for a perfect GI with ideal absorption gratings. (b) Measured (solid line) and simulated (dashed line) visibility as a function of X-ray energy on the experimental interferometer. Forthe simulation, an energy bandwidth of 3 keV (standard deviation) has been used, which approximately corresponds to the energy resolution of the detector. The dashed vertical lines indicate the bandwidth selections for the images in Fig. 3 .
Tomographic slice of a phantom in phase and absorption contrast, reconstructed in different energy windows, which are also marked in Fig. 2(b) . The phantom is made of PMMA and contains hollow rods filled with water. Some of the rods were not filled with water and appear as dark spots in the slice (seearrows). The rods filled with water can be resolved in the phase contrast image, but not in the absorption, which is due to the low difference between the attenuation coefficients of PMMA and water. The phase contrast images in the first row show the strong dependency of the SNR on the selection of the energy window. Each window has a different mean visibility (see Fig. 2 ), which is the reason why the phase image in the middle row (22–35 keV) has low noise while the images in the left and right rows (10–22 keV and 40–50 keV, respectively) are strongly distorted by noise. This effect is not observable in the absorption images, as their noise properties are independent on the visibility.
Standard deviation of the noise ( ) in the refraction angle measurement (or DPC image) as a function of energy bandwidth around the design energy. The noise is minimized if the energy bandwidth is 13 keV. The error bars indicate the uncertainty (standard deviation) of .
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