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Fig. 2. In the case of industrial X-ray tomography, the voxel size was 70 by 70 by 70 µm3. But the gray value of each voxel corresponded to the material density in a cuboid of size 70 by 70 by 210 µm3. We reconstructed the material density in cubic voxels of size 70 by 70 by 70 µm3 using the Fourier transformation technique. In the first row, vertical cross sections through the scanned sand sample are shown (A) before and (B) after noise filtering and inverse Fourier transformation. In the last image (C), the image is segmented into solid phase (black) and pore space (white). In the second row, the calculated density distribution in a vertical cross section of a simulated sample is shown. In the first image (D), the gray values were calculated for cubes of size 70 by 70 by 70 µm3. In the next image (E), the density in cuboids of size 70 by 70 by 210 µm3 is given. Due to the anisotropic mass contribution, the shape of the spheres is slightly distorted in the vertical direction. (F) From this asymmetric density distribution, the material density in cubes was calculated using Fourier transformation. The cross section shown in Part F is similar to the "true" structure shown in D. The same technique was applied for the measured data shown above. The numbers denote the volume that determined the gray values of the voxels.
