## Appendix A  
The technique of X-ray transmission is widely used in such domains as medicine, security inspection, industry, etc. When an ideal narrow beam, single energy and monochromatic X-ray penetrates through a material with thickness \(t\), its energy intensity is attenuated exponentially in accordance with the Beer\(-\)Lambert Law [19] as follows:  
\[I=l_{0}e^{-\mu t}=l_{0}e^{-\mu_{m}\rho t} \tag{1}\]  
where \(I_{0}\) (keV) and \(I\) (keV) are, respectively, the measured values of X-ray energy intensity before and after penetration, \(\mu\) (cm\({}^{-1}\)) is the linear attenuation coefficient, \(\mu_{m}\) (cm\({}^{2}\)/g) is mass attenuation coefficient, \(t\) (cm) is material thickness, \(\rho\) (g/cm\({}^{3}\)) is the material density, and \(\rho t\) (g/cm\({}^{2}\)) is also called mass thickness. For \(\mu\) and \(\mu_{m}\), the equations are as follows:  
\[\mu=\frac{\sigma N_{A}\rho}{A} \tag{2}\]  
\[\mu_{m}=\frac{\mu}{\rho}=\frac{\sigma N_{A}\rho}{A} \tag{3}\]  
where \(\sigma\) (cm\({}^{2}\)/atom) is cross-section, \(N_{A}\) (atom/mole) is Avogadro constant, and \(A\) (g/mole) is relative atomic mass. For medium and low energy (below 800 keV) X-ray transmission, the total cross-section can be composed of a photoelectric effect cross-section \(\sigma_{pe}\) and photon scattering cross-section \(\sigma_{sc}\). The photoelectric effect cross-section is a function of atomic number \(Z\) and energy \(E\)[27], which is proportional to \(Z^{4-5}\) and inversely proportional to \(E^{3}\). The photon scattering cross-section is proportional to \(E\), i.e.,  
\[\sigma(Z,E)=\sigma_{pe}(Z^{4\sim 5},E^{-3})+Z\sigma_{SC}(E) \tag{4}\]  
It should be noted that for high energy (MeV level) X-ray transmission [27; 32], the cross-section also includes that of electron pair effect \(\sigma_{pp}\), which is proportional to \(Z^{2}\). High energy X-ray is generally used in security inspection systems such as containers, and this paper will not discuss it. From the Equations (1) and (2), it can be concluded that:  
\[\ln(I_{0}/I)=\mu t=\sigma(Z,E)\frac{N_{A}}{A}\rho t \tag{5}\]  
For dual-energy monochromatic X-ray transmission, it can be obtained from Equation (5) that:  
\[\left\{ \begin{array}{ll}\ln(I_{10}/I_{1})=\mu_{1}t=\sigma(Z,E_{1})\frac{N_{ A}}{A}\rho t\\ \ln(I_{20}/I_{2})=\mu_{2}t=\sigma(Z,E_{2})\frac{N_{A}}{A}\rho t\end{array} \right. \tag{6}\]  
The R_value of dual-energy monochromatic XRT is defined as follows:  
\[R=\frac{\ln(I_{1}/I_{01})}{\ln(I_{2}/I_{02})}=\frac{\ln(I_{01}/I_{1})}{\ln(I _{02}/I_{2})}=\frac{\mu_{1}}{\mu_{2}}=\frac{\sigma(Z,E_{1})}{\sigma(Z,E_{2})} \tag{7}\]  
where \(I_{01}\) and \(I_{1}\) are, respectively, the measured values of the energy intensity of monochromatic X-ray before and after attenuation of energy \(E_{1}\), \(I_{02}\) and \(I_{2}\) are, respectively, the measured values of the energy intensity of monochromatic X-ray before and after attenuation of energy \(E_{2}\). The two ratios of \(I_{1}/I_{01}\) and \(I_{2}/I_{02}\) can be obtained by measurement. \(E_{1}\) and \(E_{2}\) are the energy of known constant monochromatic X-ray. The R_value is the ratio of the attenuation cross-section of two kinds of energy, which changes monotonously with \(Z\). From Equation (7), it can be seen that the R_value has nothing to do with the mass density and thickness of the material; in the low energy (10-100 kV) range, the photoelectric effect is dominant and the R_value is strongly related to \(Z\); in the medium energy (100-300 kV) region, the Compton effect is dominant and the R_value is weakly relatedto \(Z\). Therefore, the atomic number \(Z\) of materials can be identified by R_value, so as to identify material types. In engineering, the ideal narrow beam and monochromatic X-ray are not easy to obtain, and the bremsstrahlung X-ray source produced by cathode rays bombarding an anode target accelerated by electric field is the most common. This X-ray is a continuous spectrum whose maximum energy (keV) is equal to the tube voltage (kV) in value and the former is determined by the latter.