Special features of the ultrasonic tomography of thick-sheet products

Abstract

The special features of the beam tomography of thick-sheet products are considered, and a few techniques aimed at improving the efficiency of tomographic reconstruction based on limited data collected by ultrasound methods are proposed. Results of computational modeling and experimental reconstruction of the physical-mechanical characteristics of a thick-sheet product containing a welded joint and a thermal inhomogeneity obtained using the suggested information technologies are presented. † The high interference resistance of ultrasonic computerized tomography methods makes it possible to reconstruct in a material bulk rather low-contrast spatial distributions of the acoustic characteristics of the material, such as the propagation velocities or attenuation of different types of ultrasonic waves. In turn, this provides fundamentally new opportunities for determining the spatial distribution of physicomechanical characteristics in a material whose structure and stress-strained state change heterogeneously.The architecture of a tomographic system is determined by the geometry of the objects under examination as well as by the physics of the way in which information about the required characteristics is acquired. These factors impose certain restrictions on the quality of tomographic reconstruction. Thick-sheet products are one of the most topical objects for testing. It is possible to obtain analytical relationships for the reconstruction procedures in tomography of sheet products. When different inhomogeneous media, such as an ocean or the ionosphere, are inspected and geophysical or nondestructive testing problems are involved, the common feature of studies on thick-sheet products is that consideration is often limited to plane-parallel layer models.The completeness of data collection is one of the key problems in tomographic reconstruction. This paper considers a methodology for evaluating the completeness of data collection for beam tomography problems and suggests an analytical expression for this evaluation.It follows from the analytical expression for evaluating data-collection completeness that the quality of inhomogeneities' reconstruction across the thickness of the product depends on their spatial spectrum in the plane of the product. Computational modeling yielded relationships that suggest, in a certain region of the spatial frequency spectrum, the quality of the reconstruction across the thickness improves with an increase in the high-frequency constituents of the spatial spectrum of inhomogeneities in the plane of the product. This is limited by the common tendency that the quality of the tomographic reconstruction deteriorates as the spectrum of inhomogeneities broadens. Based on these two controversial tendencies, the class of objects is chosen (according to the spatial frequencies spectrum) for which the tomographic reconstruction algorithms are optimal. Thick-sheet products with welded joints are among such objects. The results of computerized simulation of tomographic reconstruction as a functio...