Multiscale Tomographic Wave–Matter Interaction Modeling to Enable Artifact-Free Material Defect Reconstruction

Abstract

Technologies for material defect detection/metrology are often based on measuring the interactions between defects and waves. These interactions frequently create artifacts that skew the quantitative character of the relevant measurements. Since defects can have a significant impact on the functional behavior of the materials and structures they are embedded in, accurate knowledge of their geometric shape and size is necessary. Responding to this need, the present work introduces preliminary efforts toward a multiscale modeling and simulation framework for capturing the interactions of waves with materials bearing defect ensembles. It is first shown that conventional approaches such as ray tracing result in excessive geometric errors. Instead, a more robust method employing solutions to the wave equation (calculated using the Finite Element Method) is developed. Although the use of solutions to the general wave equation permits application of the method to many wave-based defect detection technologies, this work focuses exclusively on the application to X-ray computed tomography (XCT). A general parameterization of defect geometries based on superquadratic functions is also introduced, and the interactions of defects modeled in this fashion with X-rays are investigated. A synthetic two-dimensional demonstration problem is presented. It is shown that the combination of parameterization and modeling techniques allows the recovery of an accurate, artifact-free defect geometry utilizing classical inverse methods. The path forward to a more complete realization of this technology, including extensions to other wave-based technologies, three-dimensional problem domains, and data derived from physical experiments is outlined.