Current quantitative X-ray microanalysis methods are only available for homogeneous materials. This paper presents a newly developed inverse modeling algorithm to determine both the structure and composition of two-dimensional (2D) heterogeneous materials from a series of X-ray intensity measurements under different beam energies and beam positions. It utilizes an iterative process of forward modeling to determine the optimal specimen to minimize the relative differences between the simulated and experimental characteristic X-ray intensities. The Monte Carlo method is used for the forward modeling to predict the X-ray radiation for a given specimen and experimental setup. Several examples of applications are presented for different types of samples with one-dimensional (1D) and 2D structures, in which the simulated X-ray intensities from phantom samples are used as input. Most of the results obtained from our algorithm agree well with the phantom samples. Some discrepancies are found for the voxels located at deeper depths of the 2D samples. And the discrepancies may be attributed to errors from the Monte Carlo simulations and from the variation of the X-ray range with beam energy. As a proof-of-concept work, this paper confirms the feasibility of our inverse modeling algorithm applied to 2D heterogeneous materials.

中文翻译：

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应用于二维异质材料的定量 X 射线微量分析的逆向建模

当前的定量 X 射线微量分析方法仅适用于均质材料。本文提出了一种新开发的逆向建模算法，可通过在不同光束能量和光束位置下的一系列 X 射线强度测量来确定二维 (2D) 异质材料的结构和成分。它利用正向建模的迭代过程来确定最佳样本，以最大限度地减少模拟和实验特征 X 射线强度之间的相对差异。Monte Carlo 方法用于正向建模，以预测给定样本和实验装置的 X 射线辐射。针对具有一维 (1D) 和 2D 结构的不同类型的样品，提供了几个应用示例，其中来自体模样本的模拟 X 射线强度用作输入。从我们的算法中获得的大多数结果与体模样本非常吻合。对于位于 2D 样本更深深度的体素，发现了一些差异。并且这种差异可能归因于蒙特卡罗模拟的误差以及 X 射线范围随束能量的变化。作为概念验证工作，本文证实了我们的逆向建模算法应用于二维异质材料的可行性。并且这种差异可能归因于蒙特卡罗模拟的误差以及 X 射线范围随束能量的变化。作为概念验证工作，本文证实了我们的逆向建模算法应用于二维异质材料的可行性。并且这种差异可能归因于蒙特卡罗模拟的误差以及 X 射线范围随束能量的变化。作为概念验证工作，本文证实了我们的逆向建模算法应用于二维异质材料的可行性。