## 3 Results and Discussion
Energy calibration of the detectors was performed using the 1460 keV peak of \({}^{40}\)K and the 5512 keV NRF peak of \({}^{208}\)Pb. The spectra measured by the two HPGe detectors were summed after the 2 keV per channel rebinning of the energy axis. The NRF peak at 5512 keV was clearly seen in the summed spectra of the HPGe detectors (Figure 6). As shown in Figure 7, the observed NRF peak was fitted with a Gaussian function using the least squares method. The area of the fitted Gaussian function was used as the NRF yield. The normalized NRF count rate was calculated by dividing the NRF yield by the acquisition time and count rate of the plastic scintillator detector. Next, we calculated the transmission factor at the resonance energy (\(\varepsilon_{\rm on}\)) for each \(\theta\) and \(x\) of the CT target. \(\varepsilon_{\rm on}\) was  
Figure 6: Typical summed spectrum of the two HPGe detectors with 2 keV rebinning. Figure 7: Gaussian fitted NRF peak of \({}^{208}\)Pb at 5512 keV. calculated by the normalized NRF count rate obtained in the presence and absence of the CT target according to the following formulas:  
\[\varepsilon_{\text{on}} =e^{[-(\frac{\hbar}{\rho})_{\text{ave}}\times\rho_{\text{ave}}\times L +\varepsilon_{\text{NRF}}\times N_{\text{t}})]} \tag{3}\] \[\varepsilon_{\text{on}} =\left[\frac{\varepsilon_{\text{on}}(\text{with CT target})}{ \varepsilon_{\text{on}}(\text{without CT target})}\right] \tag{4}\]  
where \(\sigma_{\text{NRF}}\) is the \({}^{208}\)Pb NRF cross section and \(N_{\text{t}}\) is the areal density of the nuclide in the CT target in the gamma ray beam path. We used the same procedure of calculations as that of previous studies (see [2; 15; 21]). The nuclear resonance attenuation factor \(\varepsilon_{\text{NRF}}\) was obtained by the following equation [2; 15]:  
\[-\ln(\varepsilon_{\text{NRF}})=-[\ln(\varepsilon_{\text{on}})-\ln(\varepsilon_ {\text{off}})] \tag{5}\]  
As the sign-inverted natural logarithm of the attenuation factor (\(-\ln(\varepsilon)\)) is proportional to the number of isotope or scattering sources in the CT target, the images in 2D-CT and 3D-CT are reconstructed using the sign-inverted natural logarithm of the attenuations (\(-\ln(\varepsilon_{\text{NRF}})\), \(-\ln(\varepsilon_{\text{on}})\), and \(-\ln(\varepsilon_{\text{off}})\)). In the NRF-CT imaging, several CT reconstruction algorithms could be used. Due to the limited number of the measured projections in the current study, one of the iterative algorithms, called the algebraic reconstruction technique (ART) [26; 27; 28], was used. A program was developed in LabVIEW to reconstruct the images. The ART is a sequential approximation method for image reconstruction from a series of angular projections (sinogram). To perform the ART algorithm, the sinogram data points were to be processed in a series of steps. We created a two-dimensional primary image as a two-dimensional matrix with zero in every cells. The cell number of the matrix was determined based on the projection numbers obtained during the experiment. The primary matrix in our case was 7 \(\times\) 7. To mitigate the errors of the matrix rotation caused by the small matrix size of the sinogram, pre- and post-processing were implemented. The difference between the projections calculated from the reconstructed image and the measured projections was computed and used to correct the reconstructed image iteratively. The convergence of the reconstruction was evaluated by the root-mean-square difference between the previous and current reconstructed images. More details of the reconstruction process are provided in [15]. For each \(z\) layer, three reconstructed images for off-resonance, on-resonance and pure NRF attenuations were obtained with a 4 mm pixel size. Figure 8a shows a cross-sectional slice image of the CT target arrangement at \(z\) = 3 mm from the CT target bottom. This shows that \({}^{206}\)Pb and \({}^{208}\)Pb rods were inserted into the first two holes of the aluminum holder, whereas an iron rod was inserted into the third hole.