Near-Field Measurement Models
In Chap. 12 we derived a variety of measurement models using both a direct approach and an approach based on reciprocity relations. In either case we assumed that incident and scattered waves can be treated as quasi-plane waves modified by appropriate diffraction correction terms; the scattering amplitude was assumed to be slowly varying so that it could be evaluated along a fixed set of incident and scattered directions. Although the quasi-plane wave (or paraxial) approximation of the incident and scattered fields is typically a very good assumption even in the near field (see Chap. 8, Problem 8.4), the combination of this assumption with the slowly varying scattering amplitude assumption can cause the LTI models developed in Chap. 12 to break down throughout the near field. This breakdown is particularly severe for very specular scatterers (such as cracks or flat-bottom holes). In Chap. 13 we construct near-field measurement models based only on a high-frequency, small-flaw assumption. These models reduce to those previously found when the directions of waves and the scattering amplitude do not vary significantly from their values along a set of fixed rays in the transmission and reception processes.
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