# XCT and DLW: Synergies of Two Techniques at Sub-Micrometer Resolution
## 3 Results
### Resolution of XCT Measurements on DLW Structures  
For sample 1, although the fractal pyramid's recursive depth of four is clearly visible by the human eye in the 3D rendering of the XCT scan (cf. Figure 7a), it was not possible to find a reliable workflow to validate the exact sizes of the stacked pyramidal shapes in 3D. A strong X-ray phase contrast on the object's surfaces, and the nested nature of the pyramidal shapes, hinder a clear determination of starting and end points for measurements. Direct length measurements and 3D volume measurements are influenced by artefacts and phase contrast, which are issues to be addressed in upcoming studies. However, the bulk four-sided pyramid (sample 2) with infill structures arranged in a checkerboard manner with a nominal cell repetition size of 4 um (wall and cavity) are a suitable feature to be measured. When slicing parallel to the pyramid base, a mesh-like structure of the infill walls is visible (see Figure 8a), which serves as a repeatable measure in this structure. An intensity line profile was measured along the mesh-cells, as indicated by the red and blue arrows in Figure 9a and plotted in Figure 9b. By calculating the turning points of the line profile slope from the peaks of the first derivative, an average cell repetition size of blue cells \(cr_{blue}=4.00\pm 0.08\,\mathrm{\SIUnitSymbolMicro m}\) and red cells \(cr_{red}=4.03\pm 0.1\,\mathrm{\SIUnitSymbolMicro m}\) could be shown. The cell size is measured as a distance in between turning points corresponding to the  
Figure 8: A SEM image of a bulk pyramid (sample 2) with complete fabricated tip is shown in (**a**). XCT images of a sample 2 variant with missing tip is shown in: (**b**) horizontal (X-plane) and (**c**) vertical (Z-plane) XCT view with highlighted defects (red arrows), and (**d**) as a 3D rendering (clipped). start of a mesh-solid/end of a mesh-cavity and start of a mesh-cavity/end of a mesh-solid. A single mesh-solid line shows an average thickness of about \(s_{blue}=1.51\pm 0.06\,\mathrm{\SIUnitSymbolMicro m}\) and \(s_{red}=1.57\pm 0.06\,\mathrm{\SIUnitSymbolMicro m}\), whereas the mesh-cavities have an average thickness of about \(l_{blue}=2.49\pm 0.08\,\mathrm{\SIUnitSymbolMicro m}\) and \(l_{red}=2.47\pm 0.07\,\mathrm{\SIUnitSymbolMicro m}\). However, the true sizes of the pyramid's internal features are unknown, but the \"coarse\" cell repetition size of about \(4\,\mathrm{\SIUnitSymbolMicro m}\) matches the nominal input parameters of the slicer very well. The present reference phantom designs and XCT scanning setup are not optimal yet. However, the aim of the study is to highlight the synergies (and challenges) in between DLW and XCT/XRM (at their resolution limits). Detailed studies which focus on the nano fabrication of trustable and repeatable structure sizes are needed. Additionally, experiments utilizing an XRM with a basic spatial resolution up to \(50\,\mathrm{nm}\) are emphasised. For future reference structures (phantoms) in the field of XCT/XRM, the proposed DLW-fabricated structures are generally suitable. The fractal pyramid shows self-similar geometries that decrease in size per recursive step and intuitively demonstrate the XCT/XRM resolution limit in 3D when the recursive step size is pushed to its limits. The measurement of hidden, mesh-like walls within the second pyramid naturally illustrates the superiority of the non-destructive XCT/XRM 3D imaging technique in this aspect over SEM or light microscopy very clearly. For demonstrations of the XCT/XRM smallest feature detectability and DLW-producibility near the absolute resolution limit of DLW/XCT/XRM, future stud  
Figure 9: (**a**) Horizontal slice through the structure, the blue and red arrows mark a line measurement; (**b**) Zoom-in of high-resolution image area corresponding to the white circle in (**a**). Square-like areas of the same gray value correspond to a cut of a voxel with a nominal size of \(0.33\times 0.33\times 0.33\times 0.33\,\mathrm{\SIUnitSymbolMicro m}^{3}\).