## 2 Materials and Methods  
### Two-Dimensional Multi-Lens Array Design and Fabrication  
The design of a 2D array of CRLs, suitable for sub-pixel resolution scanning transmission hard X-ray microscopy, is presented. A Medipix Merlin 3.0 photon-counting detector (FoV 14 mm \(\times\) 14 mm, 256 \(\times\) 256 pixels, 55 um pixel size, CERN, Geneva, Switzerland) working in charge summing mode was used to fix the physical aperture of the individual CRLs [12]. In a 2D array of CRLs, the period of the focal points grid has to be equal to the pixel pitch of the detector; so, the individual CRLs physical apertures are 55 um \(\times\) 55 um. Deep X-ray lithography was used to fabricate such an array of CRLs [13]. This technique provides structures with parallel, smooth sidewalls with a roughness of about 20 nm [14]. It allows for producing the required parabolic shape of the refracting surfaces, sub-micrometer radii of curvature, and structure heights of up to 2.5 mm at KIT/IMT. We made an SHS of 34 \(\times\) 34 single CRLs, resulting in a total entrance aperture of 1.87 mm \(\times\) 1.87 mm, produced in a 2 mm high resist of type SU-8. SU-8 is an epoxy-based negative resist, which is radiation stable up to a deposited dose of at least 2 MJ/cm\({}^{3}\)[15]. The SU-8 resist (micro resist technology GmbH, Berlin) comes on a 525 um silicon substrate. The X-ray absorber working mask was made of 20 um gold absorbers on a 2.5 um titanium membrane and was used to create SU-8 1D CRLs via deep X-ray lithography. The exposure dose was 19,845 mA*min/cm\({}^{3}\). After irradiation, it was post-exposure baked on the hot plate at 66 \({}^{\circ}\)C for 20 h. Then, unexposed resist was removed from the substrate during the development process. The developer solution was as follows: propylene glycol methyl ether acetate (PGMEA) for 2 h then rinsed in isopropanol for 30 min. After that, it was air-dried. Lithographic processes only provided 1D line focus lenses. Consequently, the substrate was cut by a diamond wafer saw, and to realize a point focus SHS, one of the line focus lenses had to be rotated 90\({}^{\circ}\) around the optical axis and mounted in an interdigitated way [16; 17]. We characterized the array of CRLs at the Diamond Light Source beamline B16 to demonstrate its functionality at high photon energies. The array of CRLs was designed for 34 keV. At this energy, the photon flux is about \(1\times 10^{9}\) ph/sec/mm\({}^{2}\). The vertical and horizontal focal lengths,\(f_{\rm v,h}\), of the multi-lens array were chosen as \(f_{\rm v,h}\) = 359 mm, a good compromise between small focus due to source demagnification, angular resolution, diffraction limit, and short focal length [18]. The number of lens elements per focusing direction is \(N\) = 92, the radius of curvature \(R_{\rm v,h}\) = 15.9 um, and the physical aperture \(A_{\rm ph}\) = 55 um, resulting in an angle between adjacent parabolas of \(\alpha\) = 60\({}^{\circ}\) (Figure 2). The parameters for vertically (v) and horizontally (h) focusing lens elements are identical. The size of the elliptical source of the Diamond Light Source is approximately s\({}_{\rm x,y}\) = 56 um \(\times\) 126 um (vertical \(\times\) horizontal, FWHM), the image distance is \(L_{2}\) = 362 mm and the source distance is \(L_{1}\) = 46.059 m.  
Each lens element has two rectangular stabilization parts with \(b\) = 40 um at the edges of each single lens array, resulting in a total lens element width of 34 \(\times\) 55 um + 2 \(\times\) 40 um = 1950 um. To obtain mechanically stable lens elements, the web distance, \(w\), was chosen to be relatively large; \(w\) = 25 um.