## Abbreviations
\begin{tabular}{l l} G \((x_{\text{gc}},y_{\text{gc}})\) & center-of-gravity and its coordinates \\ P\({}_{e}\)\((y_{e},z_{e})\) & ejection point and its coordinates \\ P\({}_{n}\)\((y_{n},H_{\text{2}Bg})\) & preset falling point and its coordinates \\ P\({}_{0}\)\((y_{0},H_{\text{2}Bg})\) & free parabolic falling point and its coordinates \\ \(I\) & energy intensity after attenuation \\ \(I_{0}\) & energy intensity before attenuation \\ \(\mu\) & linear attenuation coefficient \\ \(t\) & thickness of material \\ \(\mu_{m}\) & mass attenuation coefficient \\ \(\rho\) & density \\ \(\rho t\) & mass thickness \\ \(\sigma\) & cross-section \\ \(N_{A}\) & Avogadro's constant \\ \(A\) & relative atomic mass \\ \(Z\) & atomic number \\ \(Z_{\textit{eff}}\) & effective atomic number \\ \(E\) & energy \\ \(\sigma_{pe}\) & cross-section of photoelectric effect \\ \(\sigma_{\text{sc}}\) & cross-section of photon scattering \\ \(R\)/R\_value & transparency natural logarithm ratio of low energy to high energy \\ \(T\) & energy integral value of transmission signal \\ \(T_{d}\) & decrease value of energy integral of transmission signal after attenuation \\ \(T_{L}\) & low-energy integral value of transmission signal after attenuation \\ \(T_{H}\) & high-energy integral value of transmission signal before attenuation \\ \(T_{L0}\) & high-energy integral value of transmission signal before attenuation \\ \(S_{L}\) & shading of low-energy \\ \(S_{H}\) & shading of high-energy \\ \(N\)\((E)\) & photon number from E to dE \\ \(P_{d}\)\((E)\) & photon detection probability (efficiency) under energy \(E\) \\ \(H_{\text{2}d}\) & the shortest distance from focus to detector \\ \(d_{x}\) & the distance from the detected pixel to the focus foot point on the detector \\ \(x\) & channel serial number in X direction \\ \(f_{R}\)\((S_{L},x)\) & R\_value fitting binary function of \(S_{L}\) and \(x\) \\ \(f_{1}\)\((S_{L},x)\) & thickness fitting binary function of \(S_{L}\) and \(x\) \\ \(\textit{Beta1}\)\(-\)\(\textit{Beta6}\) & fitting coefficient of binary nonlinear polynomial surface \\ \(d_{RM}\) & mean of R\_value distance from effective points to R\_value calibration surface \\ \(R_{M}\) & mean of R\_value \\ \(\alpha_{1}\) & overexposure discrimination threshold coefficient of light metals \\ \(\alpha_{2}\) & underexposure discrimination threshold coefficient of light metals \\ \(\alpha_{3}\) & overexposure discrimination threshold coefficient of heavy metals \\ \(\alpha_{4}\) & underexposure discrimination threshold coefficient of heavy metals \\ \(\alpha_{5}\) & discrimination threshold coefficient of light metals and heavy metals \\ \(S_{LM}\) & mean of shading of low-energy \\ \(P_{x}\) & the x-accuracy (pitch) of the line scan detector, i.e., the resolution of the detector \\ \(P_{y}\) & the y-accuracy of the line scan detector \\ \(m\) & mass \\ \(g\) & acceleration of gravity \\ \(H_{\text{2}d}\) & vertical height from belt to falling point \\ \(v\) & line speed of belt conveyor \\ \(t_{e}\) & time from material off belt to ejection point \\ \(\theta\) & elevation angle of gas-ejection \\ \(I_{e}\) & impulse of gas-ejection \\ \(F_{eM}\) & the mean action force of gas-ejection \\ \(\triangle t\) & the action time of gas-ejection \\ \end{tabular}