## 2 Materials and Methods
### Image Reconstruction  
In this study, the five imaging tasks shown in Figure 2 were considered. First, head equivalent and body (thorax or abdomen) equivalent elliptical water phantoms were tested, since the designs of WBs in the FDB and U-typed openings in the SB were expected to best fit the elliptical cylinders. Second, typical head, thorax and abdomen scans of an adult were selected to investigate the practical performances of the FDB and SB.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Item** & **Material** & **Density** & **Size** \\ \hline HB attenuator & CeCl\({}_{3}\) solution & 1.23 mg/mL & Variable (a) \\ HB container & Aluminum & 2.7 mg/mm\({}^{3}\) & 0.5 mm thickness \\ WB attenuator & Air & 1.29 mg/mm\({}^{3}\) & Variable (a) \\ WB container & C-525 plastic & 1.29 mg/mm\({}^{3}\) & 0.2 mm thickness \\ \hline \end{tabular} \({}^{\text{(a)}}\) The WB attenuator is an elliptic cylinder, and its size will change with the scanning subject.  
\end{table}
Table 1: Material composition inside of the FDB [27].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Body Part**} & \multicolumn{4}{c}{**WB in the FDB (mm)**} & \multicolumn{2}{c}{**Opening of the SB (mm)**} \\ \cline{2-6}  & **Major Axis** & **Minor Axis** & **Length** & **Width** & **Depth** \\ \hline Head & 40.8 & 30.4 & 60.0 & 76.0 & 43.0 \\ Thorax & 72.0 & 40.6 & 80.0 & 88.0 & 43.0 \\ Abdomen & 62.0 & 41.6 & 80.0 & 88.0 & 43.0 \\ \hline \end{tabular}
\end{table}
Table 2: Sizes of WBs in the FDB and openings of the SB that are designed in this study.  
Figure 2: Image tasks considered in this work. (**a**) Head-equivalent water phantom, (**b**) body-equivalent water phantom, (**c**) adult head, (**d**) adult thorax and (**e**) adult abdomen.  
For a more accurate simulation of the images, the energy spectrum of the X-ray source was also considered in this work, and it was generated using the software Spektr 3.0 (The I-STAR Lab, Baltimore, MD, USA) [31] at a tube peak voltage of 120 kVp. The photon numbers reaching the detection panel were first calculated by using the Beer-Lambert law [32] in which the radiation attenuation length is calculated based on [PERSON]'s algorithm [33]. Additionally, Poisson noise was further added to the primary signal to acquire the noise-added sinogram and reconstruct the image by using the FDK algorithm [34]. Then, another independent Poisson noise was added again to reconstruct another image to study the image noise. The noise was evaluated based on the different HU values for the same regions of interest (ROIs) in the two images with an index of the inverse of image variance (\(\sigma^{2}\)) [28; 35].  
To simulate the images using the angular TCM technique, the product of tube current and exposure time for each projection, denoted as exposure (\(E\)), was calculated based on the following algorithm [36].  
\[E(p)=E_{\text{ref}}(e^{\alpha(L(p)-L_{\text{ref}})}) \tag{1}\]  
where \(L(p)\) is the maximum radiological path length in projection \(p\). \(E_{\text{ref}}\) and \(L_{\text{ref}}\) are the reference \(E\) value and radiological path length, respectively. \(\alpha\) was set at 0.5. In general, \(L(p)\) can be estimated using the two localizer radiographs and is calculated as follows:  
\[L(p)=L_{\text{AP}}+\frac{L_{\text{LAT}}-L_{\text{AP}}}{2}(1+cos(2\varphi)) \tag{2}\]  
where \(L_{\text{AP}}\) and \(L_{\text{LAT}}\) are the maximum radiological path lengths for anteroposterior (AP) and lateral (LAT) radiographs, respectively, and \(\varphi\) is the tube angle (\(\varphi\) = 0 corresponds to the lateral view).  
For a more comprehensive comparison of the radiation dose and image quality using different attenuators and techniques, six scanning protocols were simulated in this study and are listed in Table 3.