## 2 Early Development in MCT Beamline
### Spatial Resolution of the White-Beam Detector
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Objective** & **NA** & \
\begin{tabular}{c} **Scintillator** \\ **Thickness** \\ **(\(\upmu\)m)** \\ \end{tabular} & **FOV (mm\({}^{2}\))** &
\begin{tabular}{c} **Effective** \\ **Pixel Size** \\ **(\(\upmu\)m)** \\ \end{tabular} & \(\sigma_{d}\) **(\(\upmu\)m)** \\ \hline \(1\times\) & 0.035 & 500 & 16.6 \(\times\) 14.0 & 6.5 & 5.03 \\ \(5\times\) & 0.21 & 35 & 3.3 \(\times\) 2.8 & 1.3 & 0.97 \\ \(20\times\) & 0.42 & 10 & 0.8 \(\times\) 0.7 & 0.33 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The calculated detector standard deviation, \(\sigma_{d}\), for MCT white-beam detector. In order to evaluate the PSF for our imaging system, we use a MicroCT Bar Pattern Phantom (QRM GmbH, Germany) and a resolution test pattern (Xadia X500-200-30, ZEISS, California, USA) with a known size of line width. The first one will be used for the \(1\times\) objective lens, while the second one for the \(5\times\) and \(20\times\) objective lenses as they have different ranges of feature sizes. The MicroCT Bar Pattern phantom is composed of a silicon chip with various line widths. The Xadia X500-200-30 consists of an electroplated gold pattern on a Si\({}_{3}\)N\({}_{4}\) membrane and incorporates line patterns of different sizes. We use three different sample-to-detector distances for this study, i.e., 160 mm, 700 mm, and 1410 mm. These will vary the geometrical magnification value of M. The experiment is conducted using white beam mode with an in vacuo filter of 0.2 mm diamond, 5 mm Al, and 0.1 mm Cu in the beam path. The images are corrected with a flat-field image and dark current image to account for the non-uniformity of the imaging system. The flat-field images were conducted with the X-ray illumination on, but without a sample within the field-of-view (FOV). The dark-current images were conducted without X-rays. The imaging results for both resolution phantoms are shown in Figures 5 and 6 for horizontal and vertical orientations, respectively. The images have been cropped to highlight the important regions of the test patterns. The corresponding theoretical res\({}_{\text{FWHM}}\) values as shown in Table 2 are also presented in Figure 5 for easy comparison between the theoretical value and the experimental result. The results obtained for the resolution test patterns from Figures 5 and 6 show good agreement with the theoretical horizontal and vertical resolution values. For example, in Figure 5, for the \(1\times\) objective lens at 160 mm and 700 mm distances, we do not resolve the \(10\leavevmode\
obreak\ \upmu\)m linewidth in the experimental results. These are in good agreement with the theoretical values of 11.85 \(\upmu\)m and 13.16 \(\upmu\)m, respectively. Note that the FWHM values of each pattern are the same with the corresponding linewidths. In another word, the theoretical FWHM values can be compared with the experimental linewidth values. Similarly, the smallest line width visible at 160 mm using the \(20\times\) objective lens is slightly below 2 \(\upmu\)m. This is in good agreement with the corresponding theoretical resolution FWHM value of 1.92 \(\upmu\)m. One minor exception in Figure 6 for the \(5\times\) objective lens at 160 mm distance is where the experimental result shows a slightly bigger value than the theoretical vertical resolution of 2.47 \(\upmu\)m.