Diffusion-Based Thermal Tomography

Thermal imaging is one of the fastest growing areas of nondestructive testing. The basic idea is to apply heat to a material and study the way the temperature changes within the material to learn about its composition. The technique is rapid, relatively inexpensive, and, most importantly, has a wide coverage area with a single experimental measurement. One of the main research goals in thermal imaging has been to improve flaw definition through advanced image processing. Tomographic imaging is a very attractive way to achieve this goal. Although there have been some attempts to implement tomographic principles for thermal imaging, they have been only marginally successful. One possible reason for this is that conventional tomography algorithms rely on wave propagation (either electromagnetic or acoustic) and are inherently unsuitable for thermal diffusion without suitable modifications. In this research program, a modified approach to thermal imaging is proposed that fully accounts for diffusion phenomena in a tomographic imaging algorithm. Here, instead of the large area source used in conventional thermal imaging applications, a raster scanned point source is employed in order to provide the well-defined source-receiver positions required for tomographic imaging. An algorithm for the forward propagation problem, based on the Galerkin finite element method in connection with the corresponding weak formulation for the thermal diffusion is considered. A thermal diffusion modified version of the algebraic reconstruction technique (ART) is used for image reconstruction. Examples of tomographic images are presented from synthetically generated data to illustrate the utility of the approach.