## 3 Results and Discussion
### X-ray Characterization of the Multi-Lens Array at B16, Diamond Light Source
From that position of the array of CRLs, the foci are easily centered on the detector pixels by shifting them by half a pixel pitch in vertical and in the horizontal direction. The size of the point foci is much smaller than the pixel size \(p=55\)\(\upmu\)m. Each focus must illuminate only one pixel. The sample was positioned at 349 mm behind the entrance aperture of the array of CRLs and 12 mm in front of the detector. A Siemens star, which was fabricated at KIT/IMT using deep X-ray lithography and an electroplating technique (Figure 4a), was used as a sample. The test pattern consisted of a 1 mm thick polyimide substrate (Vespel SEK-3000, DuPont) with 110 \(\upmu\)m thick gold structures on top. The polyimide substrate was nearly transparent for 34 keV X-rays (transmission ca. 96 %), the gold structures absorbed 98% of the X-rays. The smallest features in the test pattern had a size of 2 \(\upmu\)m \(\times\) 4 \(\upmu\)m.  
Sample scanning was performed using a piezo stage (Attocube ECSx5050 nanopositioner, Haar, Germany) with 1 \(\upmu\)m steps within the 55 \(\upmu\)m pixel size. At each sample step, one low resolution image was acquired with an exposure time of 1 s (Figure 4b). Scanning one line (vertical or horizontal) took about 5 min: 110 s exposure time for 55 low resolution images plus 55 images without a sample in the beam plus 170 s for the sample moving and overhead times. Due to beam time constraints at Diamond  
Figure 4: **(a) Scanning electron microscope image of the test pattern (gold Siemens star) used for the 34 keV sub-pixel resolution hard X-ray imaging. (b) Low resolution image acquired by the Medipix Merlin 3.0 photon-counting detector. The number of pixels is \(34\times 34\) (pixel size: 55 \(\upmu\)m \(\times\) 55 \(\upmu\)m) and equals the size of the 2D multi-lens array. The axes correspond to the pixel number. **  
B16, we could only complete two line scans, one in the vertical and one in the horizontal direction instead of a full raster scan. All X-ray images were flat field and dark field corrected. Sub-pixel resolution image reconstruction was performed according to:  
\[A_{\text{SR}}(Mx+m,\ Ly+l)=\frac{I(x,y)}{I_{0}(x,y)}\left[S\left(\frac{m\times p }{M},\frac{l\times p}{L}\right)\right], \tag{3}\]  
Incident X-ray point focus intensity generated by the 2D multi-lens, \(I_{0}(x,y)\); intensity variation due to the absorption by the sample, \(I(x,y)\); \(m\), \(l\) represent the step number, therefore, \(m=1,\ldots,M\) and \(l=1,\ldots,L\); and \(S\left(\frac{m\times p}{M},\ \frac{p\times p}{L}\right)\) is the raster scanning of the sample in two directions [26]. Figure 5 shows the sub-pixel image of the Siemens star obtained from the two line scans performed. The artifact in the upper right corner in Figure 5 is the result of erroneous signals of the detector. These could not be avoided in the actual measurement as their location changed. Black pixels in between the bright lines correspond to missing values due to the sparse scanning. It should be noticed that the scanning time for a complete raster-scan would be in the range of ca. 50 min. Nevertheless, under comparable conditions, it is still much faster than the conventional single lens scanning transmission X-ray microscopy. A complete raster-scan of the sample within the area equal to the pixel size would give a complete 3.5 megapixel 2D sub-pixel resolution image with 1870 px \(\times\) 1870 px.