Sketch of the Talbot grating interferometer for differential phase-contrast imaging, using a coherent microfocus x-ray source (S). The incident wave front travels through an object (O) which causes phase shifts. The phase grating G1 produces a periodical intensity pattern at a distance from G1 exploiting the Talbot effect. This pattern can be sampled by stepping an absorption grating G2 at that distance in front of a pixelated detector.
Schematic of the modulation curves obtained by each detector pixel with (dashed) and without (solid) an object in an ideal case scenario. The differential phase can be calculated by the difference of the modulations’ phases. The dotted lines show the modulations average values of the intensities and . The amplitudes of the modulation is referred to as and .
Actually measured intensity modulation curves. According to the color scheme used in Fig. 2, the reference image is shown as solid line while the object image is shown dashed.
Measurement (dots) and simulation (crosses) of the standard deviation of the phase shift as a function of . The dashed-dotted line shows the theoretically predicted behavior. Additionally, the maximum possible value of the standard deviation of a uniform distribution is shown as dashed line.
Standard deviation of the phase shift corrected with the visibility versus the number of phase steps. The measurement’s data are shown solid and the simulation results dotted. A constant overall number of photons was used in each case.
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