## 4 Conclusions  
The two-dimensional (2D) X-ray compound refractive lens arrays, fabricated via deep X-ray lithography out of an epoxy-based radiation stable polymer, for hard X-ray imaging applications (above 15 keV) is presented. The array of CRLs has precise biconcave parabolic refractive surfaces with only 20 nm roughness, providing the smallest point foci and highest and most homogeneous SIE, compared to the existing 2D array of CRLs fabricated by other techniques. Under 34 keV monochromatic X-ray illumination at the B16 beamline at the Diamond Light Source, it generated 1156 point foci, with an average size (FWHM) of 2.10 \(\upmu\)m \(\times\) 3.55 \(\upmu\)m, allowing for a large field of view of 3.5 mm\({}^{2}\) for X-ray imaging applications to study optically thick samples with sub-pixel resolution.  
Figure 5: The proof of concept of sub-pixel resolution image formation of a Siemens star, including only one horizontal and one vertical line sample scanning with the sub-pixel shift. Reconstructed 2D sub-pixel resolution image (step size: 1 \(\upmu\)m), which is a sum of the vertical and horizontal 1D sub-pixel resolution images. A complete raster-scan of the sample with \(55\times 55\) lines would give a complete image, where all areas now white hatched would be white with sharply defined edges. All axes correspond to the sub-pixel number.  
Moreover, the demand for the X-ray focusing optics for high photon energies is very high due to an exponential decrease of the spectral photon flux with increasing photon energy at bending magnet synchrotron radiation sources. The realization of a 2D array of CRLs made of nickel for the photon energies above 80 keV is feasible using the same technique and was discussed in this study. Therefore, the 2D multi-lens array is an attractive optical element for hard X-ray microscopy applications requiring large FoV and high spatial resolution at synchrotron facilities.  
[PERSON], [PERSON], and [PERSON] worked out the conceptual idea of super-resolution scanning transmission X-ray microscopy. [PERSON], [PERSON] designed and [PERSON] and [PERSON] fabricated the 2D multi-lens array. [PERSON] fabricated the test pattern. [PERSON], [PERSON], and [PERSON] performed the experiment. [PERSON], [PERSON], and [PERSON] developed the reconstruction algorithm and analyzed the microscopy data. [PERSON], [PERSON], and [PERSON] evaluated the data for the multi-lens array characterization. The manuscript was written by [PERSON] with support from all of the co-authors. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Exploratory Research for Advanced Technology (ERATO), grant number JPMJER1403.  
We thank Diamond B16 for the beam time provided and [PERSON] and [PERSON] For their kind support at the beamline. The research leading to this result has been supported by the project CALIPSOplus under Grant Agreement 730872 from the EU Framework Program for Research and Innovation HORIZON 2020. The authors acknowledge the support of the Karlsruhe Nano Micro Facility (KNMF), a Helmholtz Research Infrastructure at Karlsruhe Institute of Technology, and the Karlsruhe School of Optics and Photonics (KSOP). We acknowledge support by the KIT-Publication Fund of the Karlsruhe Institute of Technology.  
The authors declare no conflict of interest.