Reconstruction of inclusions in solids using ultrasonic Born inversion

Abstract

Voids and inclusions in elastic solids are characterized experimentally using scattered ultrasonic waves. The flaws are reconstructed using a one-dimensional elastic wave inverse scattering algorithm based on the Born–Neuman expansion. This method emphasizes the role of low and intermediate frequency longitudinal waves. The utility of the inverse Born approximation is tested for several new circumstances. First the algorithm is tested for pitch-catch (bistatic) geometries. Secondly the effects of resonant excitation of the scatterer on flaw characterization are measured for several spherical flaws. The third and major result shows that the one-dimensional algorithm can be used to determine the size, shape and orientation of nearly ellipsoidal flaws when access angle is limited. The effects of varying access aperture on the reconstruction are reported. Another common experimental limitation in flaw characterization arises from interferences of the flaw signal with nearby surfaces. We briefly report that the same algorithm was successful in inverting several near surface flaws. In particular, we have successfully reconstructed, in the bulk of the sample, an approximately prolate spheroidal inclusion imbedded in plastic, an oblate spheroidal void in titanium, and in the near surface region an approximately prolate spheroidal inclusion.

Ultrasonic flaw classification and sizing

“…This approach has been developed based on ultrasonic scattering models such as the Bom approximation for volumetric flaws [49,50] or the Kirchhoff approximation for cracks [51]. Recently, a unified algorithm that can be applied to both volumetric flaws and cracks was developed by Schmerr and et al [52].…”

“…In between the two extremes of conventional methods and detailed scanning methods, there is a model-based approach called equivalent flaw sizing [49,50,51]. In this approach, flaws are reconstructed in terms of "bestfit" equivalent ellipsoids (for volumetric flaws) or ellipses (for cracks)…”

Multiviewing ultrasonic transducer system for flaw reconstruction

“…The flaw sizes (center to tangent plane distances) in the various directions are obtained by using the l-D inverse Born algorithm, as described in Refs. [4,5). Finally the flaw sizes in different directions are used in a best-fit-ellipsoid reconstruction of the flaw [1,5).…”

Ultrasonic Equivalent Flaw Sizing - A Time-of-Flight Approach

“…Previous equivalent flaw sizing methods have used the Born [1] or Kirchhoff [2] approximations in conjunction with non-linear optimization procedures. More recently, Chiou and Schmerr [3] have shown how the non-linear optimization problem in equivalent sizing can be reduced to a simpler linear least squaresjeigenvalue problem.…”