Inverse modeling for quantitative X-ray microanalysis applied to 2D heterogeneous materials.

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.