Processing of ultrasonic array data is traditionally based on having parallel transmission circuits that enable staggered firing of transmitter elements to produce the desired wavefront. This paper describes an alternative approach in which the full matrix of time domain signals from every transmitter–receiver pair is captured and post-processed. Various post-processing approaches are modelled and assessed in terms of their ability to image a point-like reflector. Experimental results are then presented which show good quantitative agreement with the modelled results. An advanced processing algorithm is also implemented which allows the array to be focused at every point in the target region in both transmission and reception. This approach is shown to offer significant performance advantages for NDE.

Post-processing of the full matrix of ultrasonic transmit-receive array data for non-destructive evaluation

Modeling the propagation of elastic waves using a modified finite-difference grid

An imaging system with three-dimensional (3-D) capability can be implemented by using a stepped frequency radar which synthesizes a two-dimensional (2-D) planar aperture. A 3-D image can be formed by coherently integrating the backscatter data over the measured frequency band and the two spatial coordinates of the 2-D synthetic aperture. This paper presents a near-field 3-D synthetic aperture radar (SAR) imaging algorithm. This algorithm is an extension of the 2-D range migration algorithm (RMA). The presented formulation is justified by using the method of the stationary phase (MSP). Implementation aspects including the sampling criteria, resolutions, and computational complexity are assessed. The high computational efficiency and accurate image reconstruction of the algorithm are demonstrated both with numerical simulations and measurements using an outdoor linear SAR system.

3-D radar imaging using range migration techniques

This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.

/pdf/inverse-problems-in-elasticity-1dpbui74d3.pdf

Inverse problems in elasticity

Review of progress, QNDE

https://www.uni-kassel.de/fb16/tet/marklein/paper/wave_motion_1995_paper.pdf

Numerical modeling of elastic wave propagation and scattering with EFIT — elastodynamic finite integration technique

Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique

The synthetic aperture focusing technique (SAFT) is briefly reviewed and addressed as a heuristic digital ultrasonic imaging scheme which exploits the idea of back-propagating a set of measured and digitally stored A-scans. It is shown that for a far-field experimental set-up, ie for small, isolated defects remote to the transducer, SAFT reduces to the filtered back-projection imaging scheme which is well known within the framework of conventional X-ray computer tomography. Therefore, alternative data processing via Fourier transforms only, similar to the Fourier slice theorem of tomography, is possible, which sheds considerable light upon the heuristic SAFT pixel-space envelope-detection scheme. The resulting imaging identity has been termed POFFIS (physical optics far-field inverse scattering). The far-field assumption is then omitted yielding a Fourier-transform-SAFT algorithm (FT-SAFT) whose results are identical to back-propagation imaging with the definite advantage of fast processing capabilities based upon standard hardware and allowing immediate implementation of high resolution procedures as well as inclusion of mode-conversion effects; the theoretical background is pulse-echo diffraction tomography. The above results are supported and illustrated by application of all three algorithms — SAFT, POFFIS, FT-SAFT — to experimental data obtained from scanning a line aperture for several test specimens.

Synthetic aperture focusing technique signal processing

Pulse-echo methods (radar, impact-echo, ultrasonic impulse-echo) and simulation of wave propagation are applied for testing concrete speciments with metal ducts. The results of nondestructive testing of the same specimens by nine workgroups are described and compared. The research aims for the experiments are thickness measurement, location of a metal duct and of voided regions inside the duct. The results show the remarkable progress achieved in the past few years: the thickness and location of a duct could be measured for one specimen with great precision. In some cases voided regions in the duct could be located.

Karl-Jörg Langenberg

Papers

Numerical modeling of elastic wave propagation and scattering with EFIT — elastodynamic finite integration technique

Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique

Synthetic aperture focusing technique signal processing

Comparison of pulse-echo methods for testing concrete

Introduction to the special issue on inverse problems