Calculation of effective atomic numbers using a rational polynomial approximation method with a dual-energy X-ray imaging system

The study aims to develop a rational polynomial approximation method for improving the accuracy of the effective atomic number calculation with a dual-energy X-ray imaging system. This method is based on a multi-materials calibration model with iterative optimization, which can improve the calculation accuracy of the effective atomic number by adding a rational term without increasing the computation time. The performance of the proposed rational polynomial approximation method is demonstrated and validated by both simulated and experimental studies. The twelve reference materials are used to establish the effective atomic number calibration model, and the value of the effective atomic numbers are between 5.444 and 22. For the accuracy of the effective atomic number calculation, the relative differences between calculated and experimental values are less than 8.5% for all sample cases in this study. The average calculation accuracy of the method proposed in this study can be improved by about 40% compared with the conventional polynomial approximation method. Additionally, experimental quality assurance phantom imaging result indicates that the proposed method is compliant with the international baggage inspection standards for detecting the explosives. Moreover, the experimental imaging results reveal that the difference of color between explosives and the surrounding materials is in significant contrast for the dual-energy image with the proposed method.