## 3 Results and Discussion
### X-ray Characterization of the Multi-Lens Array at B16, Diamond Light Source
Let us consider the manufacturing of a 2D nickel CRL array with the same parameters at those used for the SU-8 2D array of biconcave parabolic shaped CRLs described in the Materials and Methods section: \(R_{\text{v,h}}\) = 15.9 \(\upmu\)m, \(A_{\text{ph}}\) = 55 \(\upmu\)m. The refractive index decrement for a nickel at 100 keV is \(\delta=\) 1.76\(\cdot\)10\({}^{-7}\), consequently, according to Equation (2), to obtain the same focal distance of \(f_{\text{v,h}}\) = 359 mm, the number of 1D planar lenses is 63 in a vertical direction and 63 in a horizontal direction. The nickel CRLs are manufactured by deep X-ray lithography and electroplating [23]. In order to use the gold absorber mask developed for SU-8 CRLs in this work, we only need to inverse the tone of the resist from negative to positive, using polymethylmethacrylate (PMMA). A PMMA foil of 2 mm will be glued on to the 525 \(\upmu\)m silicon substrate. After X-ray exposure at the KARA-Litho 2 synchrotron facility, the mask pattern will be copied into the resist layer. Then, the irradiated parts will be removed from the substrate during the development process in the GG-developer and rinsed in BDG-rinse (ethanol 60 vol% + DI water 40 vol%) and washed in distilled water. After air-drying, the nickel structures will be electroplated, and the remaining resist will be stripped to produce nickel lenses without any resist residues. The substrate will be cut, and the 1D nickel CRLs array will be arranged in the orthogonal direction as described in this work. Figure 3: X-ray characterization of 2D multi-lens array: (**a**) High resolution detector image of the 34 \(\times\) 34 foci generated by the multi-lens array. (**b**) SIE of the 34 \(\times\) 34 arrays at the focal distance, using an area of 1.8 \(\upmu\)m \(\times\) 1.8 \(\upmu\)m (\(E\) = 34 keV). SIE of the first and second sub-CRL columns was weak due to a small misalignment of one mounting frame connecting the two 1D half lenses (shadowing). Horizontal (**c**) and vertical (**d**) focal width (full width half maximum, FWHM) of the 34 \(\times\) 34 multi-lens array shown as a contour plot. The ordinate states the row number of sub-CRLs and the abscissa states the column number of sub-CRLs (Si substrates to the right and bottom, corresponding to Figure 2a). Application of the 2D Multi-Lens Array for 2D Sub-Pixel Resolution Scanning Transmission X-ray Imaging  
The low spatial resolution of the standard non-scanning technique using an array of CRLs is determined by the distance between neighboring point foci. Scanning the sample with sub-pixel size steps overcomes this limitation. In visible light microscopy, generating a high resolution image from a set of low resolution images, which are sub-pixel shifted, is known as the pixel super-resolution (SR) technique [24]. To avoid confusion, we here use the term sub-pixel resolution instead of super-resolution, where the resolution is below the diffraction limit [25]. Two dimensional sub-pixel resolution scanning transmission X-ray imaging is a straightforward extension of the one-dimensional method described in [9] and is shown in Figure 1. The point foci with an intensity \(I_{0}\)(x, y) created by the 2D multi-lens array, are recorded by a Medipix Merlin 3.0 photon-counting detector. The region of interest of the Medipix detector was chosen to be \(34\times 34\) pixels corresponding to the geometrical size of the 2D multi-lens array. The 2D multi-lens array is positioned in the beam and aligned parallel to the detector by rotating it around the optical axis. It is parallel when a detector pixels row switches from completely dark to fully illuminated when shifting the foci of the 2D multi-lens array over the border between pixels in the vertical direction. In the same way, a column of foci is positioned above the border between detector pixels by moving the foci of the 2D multi-lens array over the detector pixels in a horizontal direction.