Ultrasonic caustics in non-destructive evaluation

Doyle, P. A.

doi:10.1088/0022-3727/13/2/013

Cited by 11 publications

(3 citation statements)

References 27 publications

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“…Discontinuities in the surface, edges and faults, are discussed in terms of constraint catastrophes and the patterns they produce in echograms are classified. tomography (Doyle 1980) and so forth. This similarity calls for a topologically invariant description of the phenomena under consideration.…”

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confidence: 94%

Topological approach to remote sensing

Dangelmayr

Güttinger

1982

Geophysical Journal International

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The topological problem underlying remote sensing is analysed by determining the geometric singularities that an unknown surface or structure generically impresses on a sensing wavefield. It is shown that the analytical singularities observed in scattering amplitudes and echograms are produced by the topological singularities of the scattering system. Imposing the principle of structural stability on the inverse scattering problem, the singularities that generically occur in recorded signals, travel-time curves, surface contour maps and Fresnel-zone topographies can, together with the associated high-intensity diffraction patterns, be classified into a few universal standard forms described by catastrophe polynomials. As the source-receiver positions vary, the patterns change their morphologies in terms of specific bifurcation sets. By applying singularity and bifurcation theory to allow the effects of caustics (both in ray and wave theory) to be incorporated into three-dimensional techniques for reconstructing surfaces and subsurface structures from their echoes, the interpretation process is considerably simplified and permits an on-site 3D survey. Universal power laws for singularity-dominated echo amplitude variations with the source frequency are deduced. The shape of a scattering surface is reconstructed using the high-frequency regime alone. Discontinuities in the surface, edges and faults, are discussed in terms of constraint catastrophes and the patterns they produce in echograms are classified. on a sensing wave system because remote sensing is a structurally stable process. This view of the inverse scattering problem generalizes classical S-matrix theory in the sense that the observed analytical singularities in scattering amplitudes are linked with the topological singularities of the scatterer. Since the latter can be classified, so can the former, and a new structural approach to remote sensing emerges which considerably simplifies the interpretation process.Briefly the genesis of the theory is this. In order that the reconstruction of surfaces or subsurface structures from backscattered waves be physically feasible, the scattering process has to enjoy an inherent stability property, namely to preserve its quality under slight deformations of the scattering object. Otherwise we could hardly think about or describe it, and today's experiment would not reproduce yesterday's result. Imposing this principle of structural stability (Thom 1975) on the inverse scattering problem has two important consequences. First, it permits us to identify the significant patterns that can generically occur in travel-time curves, contour maps and Fresnel-zone topographies, and to classify them together with the associated diffraction patterns into a set of canonical normal forms or singularities. As the source-receiver positions vary, the patterns change their morphologies according to universal bifurcation sets (caustics). These bifurcation sets and the diffraction catastrophe amplitudes around them are produced by the...

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confidence: 94%

Topological approach to remote sensing

Dangelmayr

Güttinger

1982

Geophysical Journal International

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“…Frequently it is sufficient to locate the edge of such a crack, which acts as a scattering curve. A method of using only caustic information measured in the frequency domain for partial crack-edge mapping has been proposed by Doyle (1980). His method is simply to construct the projection (only) of the edge in the dominant ray direction as an involute of the far-field caustic, which needs additional information (such as travel times) to locate the edge and to pick the right member of the one-parameter family of involutes?.…”

Section: Introductionmentioning

confidence: 99%

Geometrical inversion for a scattering curve

Dangelmayr

Wright

1986

Inverse Problems

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A space curve S may be determined from measurements of its perpendicular distance from a known space curve Sigma . Such data might be found experimentally using monostatic radar, and S might be the edge of a surface. A unique inversion is possible if Sigma is chosen to lie in the caustic C of S, and a supplementary measurement is made of the orientation of C at some point of Sigma . Explicit algebraic inversion formulae are given for S and its main differential geometric properties. The effect of caustic singularities is considered. Sources of non-uniqueness and ways to overcome them are discussed in detail.

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“…They recorded the diffracted field using black and white photography, and described colour changes using visual observation only . Renewed interest in these experiments has been stimulated by the possibility of exploiting the geometry of caustics in the analogous ultrasonic case to invert scattering data for the ultrasonic characterization of defects in materials [4,5] .…”

Section: Introductionmentioning

confidence: 99%

Diffraction by Discs for a Point Source in the Near Field

Doyle¹

1983

Optica Acta: International Journal of Optics

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Ultrasonic caustics in non-destructive evaluation

Cited by 11 publications

References 27 publications

Topological approach to remote sensing

Topological approach to remote sensing

Geometrical inversion for a scattering curve

Diffraction by Discs for a Point Source in the Near Field

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