## 4 Discussion  
To understand the data obtained from the measurements and evaluate the quality of the microstructure patterns over a large area, we correlated the grating defects and flaws with respective projection image distortions. In order to investigate possible generalized imperfections of the grating and its alignment in the setup, ideal data arrays were simulated, and their changes caused by the introduction of rotation and blurring were analyzed in terms of the absorption signal histograms. It is important to note that the proposed quality evaluation algorithm is giving useful information only for intrinsically periodic structures, such as gratings. The main idea of the grating quality evaluation algorithm was to test the grating in a radiography setup to compare the intensity distribution obtained on the detector plane with the simulated intensity map from an ideal grating. By modifying the simulated ideal grating, one can estimate, quantitatively, the intensity modulation and characterize structural changes in the real grating. Using a simplified empirical model, an ideal grating was represented by a two-dimensional array of data with exactly the same dimension as the digital image obtained from the real data files acquired with the detector, taking into account the magnification. The array was filled with a constant value, and an intensity distribution histogram was obtained. This gave a discrete spectrum consisting of two peaks at absorption signals for the wafer (if normalized by the absorption level of the wafer, this peak is centered at zero) and the gold structures. The ratio of peaks is 1:3, as the gold structures cover one-third of the illuminated grating area in the simulated experiment. When the arrays and associated intensity distribution histograms were obtained, the approximation of real gratings was achieved by adding a background function representing noise introduced by the experimental setup. This was done by introducing random fluctuations around the central value as detector noise (Gaussian distribution) or by using a real signal recorded by the detector in the experiment. The intensity distribution histogram with added noise is shown in Figure 7a. As the grating was supported by the substrate, it introduced a certain absorption, which decreased the signal-to-noise ratio and could also be treated as a contribution to the background. The detector noise was further estimated together with the contribution of 200-\(\upmu\)m-thick silicon absorption, thus, the histogram peaks were shifted in a way that the zero position corresponds to the radiation passing between the grating structures, and the second peak was placed at the absorption level of the gold structures, which was determined by the gold height. Figure 7: Simulated gratings intensity distribution histograms with added detector noise and cropped simulated data arrays with dimensions corresponding to the periods of 50 \(\upmu\)m (green), 25 \(\upmu\)m (orange), and 10 \(\upmu\)m (blue): (**a**) ideal data arrays; and (**b**) tilted at \(-0.6^{\circ}\) and blurred data arrays. The simulation represents the influence of generalized pattern defects and was used to decouple them from the impact of local imperfections. However, in reality, not only does the presence of the detector noise decrease the efficiency of the intensity modulation, but also causes blurring by the imperfectly steep profile of structure sidewalls. Note that this manufacturing-driven blurring is independent of the blurring of the projected grating edges by the source focal spot size (focal spot size in case of an X-ray tube or lens focusing spot for a lens system). Despite the different origin, both result in blurring of the projected image, which is stronger for smaller periods: one can see that for the simulated grating with a 10 \(\upmu\)m period that the intensity distribution is not discrete anymore and peaks associated with the absorption of the wafer and the structures are merged and are not clearly distinguished, as can be seen in Figure 7b.