## 3 Results and Discussion
### Overexpression and Underexposure  
The \(S_{L}\)-\(R\) calibration curves of several metals selected from the actual measurement data of a certain channel are shown in Figure 9, indicating that the separation degree of each curve corresponding to each metal in the \(S_{L}\)-\(R\) plane was equivalent to the sorting ability of each. From Figure 9, it can be seen that though there was an evident discrimination between heavy metals and light metals, a tendency to an intersection of those still existed within the areas of the low \(S_{L}\) and the high \(S_{L}\). The sorting ability was limited to a certain scope whatever the discrimination existed in several heavy metals or in several light metals, and always accompanied by a fluctuation of the curve or intersection within areas of the low \(S_{L}\) and the high \(S_{L}\). One of the reasons for that was the unavoidable sensitivity of fluctuating measurement data in areas of overexposure and underexposure to the R_value calculation, so the easiest method to eliminate it was to remove the data during identification.  
Figure 8: (**a**) Shading of low-energy image; (**b**) shading of high-energy image.  
Figure 9: DE-XRT \(S_{L}\)-\(R\) calibration curve of one channel.  
As a matter of fact, the fluctuation of the measurement value of the energy integral of transmission signal \(T\) is inevitable. When an overly small S\({}_{L}\) means overexposure with small SNR (signal to noise ratio), small CR (contrast ratio), \(T/T_{0}\) approaching to 1 and \(\ln(T/T_{0})\) approaching 0, R_value is subject to large fluctuation in the measurements. Conversely, an overly large S\({}_{L}\) means underexposure. In that case, \(T/T_{0}\) tends to 0 and \(\ln(T/T_{0})\) has a large slope at this value point; correspondingly, SNR is also large. As a result, the R_value will fluctuate greatly too. Experiments have found that whether S\({}_{L}\) is overly small or overly large, the R_value will be inaccurately calculated and each curve of \(S_{L}\)-R image will intersect, possibly leading to false identification.  
The discriminant coefficients of overexposure and underexposure relate to the equipment, and can be obtained according to experiment and experience. In this paper, the discriminant coefficients \(\alpha 1\), \(\alpha 2\), \(\alpha 3\), and \(\alpha 4\) were, respectively, taken as 0.2, 0.8, 0.3, and 0.9, which were combined with the mean value of shading of low-energy \(S_{LM}\) to judge materials of overexposure or overexposure. Due to the overall mass thickness of the material as judgment basis, it was more convenient and reasonable than mechanical size screening. Meanwhile, overexposure and underexposure could also be used for judgment of effective points during material identification. The binary image of the effective points of a material is shown in Figure 10. Effective points are those which have disposed of the overexposed and the underexposed points in the material range. The differential values between each effective point R_value and corresponding calibration surface R_value were summed by algebra and averaged, whose mean value was used for material identification. Due to the application of the mean value, overexposed and underexposed points during identification could be eliminated and the chance of judgment depending on the R_value of individual pixels was avoided, which was equivalent to mean value filtering and consequently improved identification accuracy.