A unified theoretical framework based on the scalar wave equation is presented for transmission tomography of weakly inhomogeneous objects embedded in a known uniform background medium The developed formulation differs from the usual treatments of diffraction tomography in that it is not limited to applications employing plane-wave illumination and planar measurement boundaries and can be extended to weakly inhomogeneous objects embedded in non-uniform backgrounds and to the class of strongly scattering objects The new formulation is based on the mathematical operations of propagation and backpropagation which are generalisations of the conventional tomographic operations of projection and backprojection to the case of diffracting wavefields The projection and backprojection operations are then obtained from the generalised operations in the zero wavelength limit A class of reconstruction algorithms are developed within the new formulation that are generalisations, to the case of diffraction tomography, of the class of iterative ART (algebraic reconstruction technique) algorithms of conventional (X-ray) tomography The reconstruction algorithms developed (called generalised ART algorithms) are shown to be applicable to situations where the tomographic data are sparse (limited-view problem) and to the incorporation of a priori information into the reconstruction process

Reconstructive tomography with diffracting wavefields

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

The use of ultrasonic waves in nondestructive evaluation is reviewed. Perspective is provided by a summary of the role played by nondestructive evaluation in the manufacture and utilization of structural components. Included are discussions of the methodologies for predicting part serviceability and of the constraints placed on the nondestructive measurement process by the mechanical designs and functions of structural components. The principles of active (ultrasonic) and passive (acoustic-emission) testing techniques are then reviewed. Specific examples of applications from several industries illustrate the capabilities and limitations of state-of-the-art techniques based on these principles. Detailed discussion is then given of present research and development activities designed to overcome these limitations, with particular emphasis on those areas best addressed by the tools of electrical engineering. Included are discussions of instrumentation, inspection performance modeling, flaw sizing techniques (including imaging systems), material property measurement techniques, and acousticemission techniques. The paper concludes with a consideration of important directions of future work.

Ultrasonics in nondestructive evaluation

Quantitative ultrasonic techniques for determining the serviceability of structural components are reviewed. Particular emphasis is placed on the use of forward and inverse elastic wave scattering theory as a fundamental foundation for predicting such engineering parameters as the probability of flaw detection and for developing improved techniques for flaw sizing. Ultrasonic measurement techniques for the determination of distributed failure-related properties such as residual stresses are discussed, and the status of the prediction of failure by the detection of acoustic emission precursors is reviewed.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1143&context=ameslab_pubs

Quantitative Ultrasonic Nondestructive Evaluation Methods

This paper proposes a method for eddy current non-destructive examination of carbon fibres from carbon epoxy composites as well as the regions impacted with bullets from Kevlar textures. In this aim, an eddy current focused micro sensor, send-receiver type with orthogonal coils was developed. The obtained data were post processed using an incoherent holographic technique. By a small modification of lift-off, the successive layers of fibres can be visualised and, implicitly, their integrity. Using a similar method, the boundaries of the region impacted by a bullet from Kevlar textures were completely emphasised.

/pdf/eddy-current-examination-of-carbon-fibres-in-carbon-epoxy-2rq3athog8.pdf

Eddy current examination of carbon fibres in carbon-epoxy composites and Kevlar

For the purpose of ultrasonic nondestructive testing of materials, holography in connection with digital reconstruction algorithms has been proposed as a modern tool to extract crack sizes from ultrasonic scattering data. Defining the typical holographic reconstruction algorithm as the application of the scalar Kirchhoff diffraction theory to backward wave propagation, we demonstrate its general incapability of reconstructing equivalent sources, and hence, geometries of scattering bodies. Only the special case of a planar measurement recording surface, that is to say, a hologram plane, and a planar crack with perfectly rigid boundary conditions parallel to the hologram plane and perpendicular to the incident field yields a nearly perfect correlation between crack size and reconstructed image; the reconstruction algorithm is then referred to as the Rayleigh-Sommerfeld formula; it therefore represents the optimal case matched to that special geometrical situation and, hence, may be interpreted as a quasi-matched spatial filter. Using integral equation theory and physical optics, we compute synthetic holographic data for a linear cracklike scatterer for both plane and spherical wave incidence, the latter case simulating a synthetic aperture impulse echo situation, thus illustrating how the Rayleigh-Sommerfeld algorithm or its Fresnel approximation increasingly fail for cracks inclined to the hologram plane and excited nonperpendicularly. Furthermore, we point out how the physical data recording process may additionally influence the reconstruction accuracy, and, finally, guidelines for a careful and serious application of these holographic reconstruction algorithms are given. The theoretical results are supported by measurements.

Potential and limits of holographic reconstruction algorithms

Generalized holography is understood as a heuristic solution of an inverse-scattering problem based on the time-harmonic formulation of Huygens’s principle. It is checked against a scalar two-dimensional numerical-scattering experiment: Simulated data for a cylindrical object with arbitrary elliptical cross section are inserted into the algorithm, and the results are critically discussed. We find that generalized holography yields only sparse improvement over conventional holography—the images obtained are only poor solutions to the inverse-scattering problem—but, on the other hand, its mathematical consequences, such as the Porter–Bojarski integral equation, may serve as an intuitive means to predict the performance of holographic schemes for certain specialized canonical inverse-scattering problems; once the limitations are known, considerable advantage can be drawn for practical applications, and improved extensions are readily proposed yielding very general diffraction tomography algorithms.

M. Berger

Papers

Potential and limits of holographic reconstruction algorithms

Imaging performance of generalized holography