Characterization of Material Structure by Dynamic Tomography

Abstract

Common tomographic techniques assign a measure of material properties to a discrete element in the object space in order to characterize a specimen. The discretization of the object space, i.e. the size of a single volume element, is limited by the sensing mechanisms and the equipment used for the data acquisition. In any case the result of reconstruction gives a statistical average of the accessed material property within the considered element in the object space. To evaluate the integrity of a component the determined measures have to be correlated with its mechanical properties. Considering modem materials like reinforced plastics or metal foams the mechanical properties of the component are not determined by every single structural element like a single fiber in a composite material. Moreover the ensemble average and correlation properties as a means of statistical measure of all structural elements form the mechanical properties of the component. Accordingly a statistical description of the material properties on a macroscopic scale allow the characterization of its mechanical behavior or lifetime. The paper presents a special reconstruction algorithm that allows the statistical description of complex object structures including its dynamical properties. The proposed algorithm is based on a modified Kalman filter using statistical prior. The introduced prior includes knowledge about the covariance properties as well as assumptions about the probability density distribution function of the object structure. The resulting filter is recursive giving the optimal or quasi-optimal solution of the related inverse problem at every reconstruction step. The applicability of the developed algorithm is discussed for the investigation of an aluminum foam specimen and compared to standard 3D CT.