## 3 Results and Discussion  
### X-ray Characterization of the Multi-Lens Array at B16, Diamond Light Source  
The 2D multi-lens array (KIT/IMT layout number 1836 #21, lot 16-365 ao20190611a) was characterized at the B16 bending magnet test beamline of the Diamond Light Source (Didcot, United Kingdom). A channel-cut monochromator, based on a Si (311) crystal, placed 20 m from the source, was used to generate 34 keV X-rays with an energy resolution of \(\Delta\)E/E = 10\({}^{-4}\). Point foci were measured using a high resolution indirect detector consisting of a 5 \(\upmu\)m thick LuAG:Eu scintillator (FEE, Idar-Oberstein, Germany) combined with 10\(\times\) magnification Olympus UPlanSApo microscope objective, an Optique Peter microscope system, and a pco.4000 CCD camera with 4008 px \(\times\) 2672 px (PCO AG, Kelheim, Germany), resulting in an effective pixel size of 0.9 \(\upmu\)m \(\times\) 0.9 \(\upmu\)m in the scintillator plane. The FoV of the detector was 3.6 mm (v) \(\times\) 2.4 mm (h). The 2D multi-lens array was placed on a motorized hexapod allowing for precise alignment. The focal distance was determined by scanning the detector along the optical axis with 2 mm steps; at each position, an image (Figure 3a) was recorded. The data were analyzed by fitting all foci using the 2D Gaussians method, and the full width half maximum (FWHM) was calculated in both directions for every position measured along the optical axis. In this way, the measured focal length was \(f_{\text{exp,v,h}}\) = (362 \(\pm\) 4) mm, which presents a good agreement with the design value \(f_{\text{v,h}}\) = 359 mm. The focal spot sizes (FWHM) are shown in Figure 3c in the horizontal direction and in the vertical direction in Figure 3d. The measured vertical and horizontal size of the point foci were (2.10 \(\pm\) 0.81) \(\upmu\)m and (3.55 \(\pm\) 0.62) \(\upmu\)m, respectively. As expected, the horizontal spot size was larger than the vertical one due to the source shape. Since the main advantage of the array of CRLs concerns the increase of the photon flux density owing to its focusing properties, we used the spectral intensity enhancement (SIE) as a parameter to quantify the photon flux. The SIE is the official definition of the formerly so-called \"intensity gain\" [3],  
Figure 2: 2D biconcave parabolic polymer (SU-8) multi-lens array for 34 keV fabricated by deep X-ray lithography and mechanical assembly: (**a**) 3D model of two interdigitated planar compound refractive lenses (CRLs) on the silicon substrate (blue) with vertically focusing lens elements (red) and horizontally focusing lens elements (beige). (**b**) The design parameters are \(A_{\text{ph}}\)—physical aperture, \(N_{\text{v}}\) and \(N_{\text{h}}\)—number of lens elements in the vertical and in a horizontal directions, respectively, \(R\)—radius of curvature, \(d\)—air gap, \(\alpha\)—angle between adjacent parabolas, \(w\)—web distance, \(b\)—rectangular parts at the edges for stabilizing the single lens arrays, \(L_{\text{CRL}}\)—total length of the multi-lens array. (**c**) Optical microscope image of the fabricated 34 \(\times\) 34 multi-lens array and (**d**) top view. it is defined as the ratio of radiation power through a chosen reference area at the smallest beam dimension location with and without X-ray optics [21]. The reference area of 1.8 \(\upmu\)m \(\times\) 1.8 \(\upmu\)m in the focal plane with and without the array of CRLs was used for the SIE calculation of each point foci. In this study, the average measured SIE was 16 (Figure 3b). It had a higher SIE in the middle of the array, matching the horizontal FWHM (Figure 3c). The average transmission of the 2D multi-lens array (measured via the SIE for a 55 \(\upmu\)m \(\times\) 55 \(\upmu\)m reference area, which corresponds to the size of a single 2D subCRL) was \(T_{\text{avg}}\) = 66%. For photon energies above 80 keV nickel CRLs are used to reduce the number of lens elements and thus the total length of the CRL to make it fit onto one lithography mask [22].