## 4 Discussion
The histogram shown in Figure 7b has been obtained by varying the input parameters, such as the in-plane rotation of the grating and blurring of the image to match the experimental conditions and decouple the influence of generalized pattern defects from local imperfections. As one can see from the projection images shown in Figure 6c, there was a slight in-plane rotation of the grating present when the grating was placed in the holder. The rotation angle of 0.6 degrees was included in the empirical simplified model to better represent the acquired images and account for smoothening of the ripples in the histogram. It is important to emphasize that the simulated data only included general distortions uniformly applied to the entire pattern and no local defect impact was considered. By comparison of the histogram obtained from the experimental data (Figure 6c) and the simulated one (Figure 7b), it is clearly seen that the pure pattern blurring cannot explain the distribution obtained for the gratings. In particular, the splitting of the peaks corresponding to gold absorption, especially evident for the 10 \(\upmu\)m period grating (Figure 8a), cannot be attributed to uniform effects present in the pattern but, rather, local defects of mainly random and rare appearance. One kind of such an effect is gold overplating, which causes the appearance of higher absorption levels. However, at the designed X-ray energy, the gold structures, with an average height of 15 \(\upmu\)m, transmit only 0.5% of the incoming radiation [20]. This means that the gold structures higher than 14 \(\upmu\)m will not make a considerable effect on the intensity modulation. Overplated structures that contribute to the gold pillars higher than 20 \(\upmu\)m will not make any impact on the absorption signal histograms obtained from the measurements at the energy of 8.5 keV. Another local effect present at the characterized gratings is pattern impurity due to partial gold deposition between the structures, which led to an overall decrease in transmission, thus, a decrease in intensity and additional broadening of the zero-centered peak. To analyze this effect in greater detail, the decomposition of real data histogram profiles into several Gaussian-shape signals has been performed. Examples for 10 \(\upmu\)m and 50 \(\upmu\)m period gratings are shown in Figure 8. It is evident in Figure 8a that an additional contribution of the signal at approximately 30 a.u. is present, corresponding to the gold height about 1 \(\upmu\)m. This signal is attributed to the impurity of the pattern and contributed to the broadening of the zero-centered peak. The impurity of the pattern for the tested grating might be due to a slight undercut of the photoresist layer during reactive ion etching prior to electroplating. The effect was stronger for smaller periods, as observed with SEM (Figure 5b,c), in this case the gold nucleation points were placed closer to each other, and undesirable diffusion of Au\({}^{+}\) between the structures in the undercut area occurred. In turn, the contrast between absorbing and non-absorbing areas on the projected images was strongly decreased by this effect for smaller periods. For example, for the 10 \(\upmu\)m period grating, the highest pillars were about 9 \(\upmu\)m (Figure 5c), thus, approximately 5% of the radiation was transmitted through such structures, and the transmission of the wafer carrier was reduced by the impurities of the pattern, resulting in a decreased intensity modulation. However, not only did impurities contribute to the overlapping of the peaks on the histogram for 10 \(\upmu\)m period; as it was mentioned above, there is a third Gaussian centered at approximately 110 a.u. (the yellow dashed line in Figure 8a), which can be correlated with the gold height of about 4 \(\upmu\)m using information obtained with SEM. This implies that the gold height is not homogeneous and pillars of different height were obtained during the electroplating.