Probing flexible thermoplastic thin films on a substrate using ultrasonic waves to retrieve mechanical moduli and density: Inverse problem

Forward and inverse acoustic scattering problems involving the mass density

“…Other than these remarks , the noticeable feature of figs. [42][43][44][45], also discernible to some extent in figs. [36][37][38][39][40][41], is the dispersive nature of the retrieved mass density contrast even though the actual mass density contrast was assumed to be non-dispersive (i.e., to not depend on f ).…”

“…are really justified (i.e., lead to accurate parameter retrievals), but when this question relates to the retrieval of the density it is understandable that it has not been considered to be interesting since it is not possible to retrieve the density from the scattered field with a trial model based on the constant-density assumption. Less comprehensible is the fact that the question of the influence of the constant-density assumption on the quality of the retrieval of another parameter such as the wavespeed in, or compressibility of, the medium in the obstacle has not received much attention [53,44,94] either, except insofar as porous media are concerned [31]. Nevertheless, it should be underlined that in the area of electromagnetic scattering, the (acoustic) constant-density assumption becomes the oft-employed assumption of constant permeability ( [72,60], p. 2), which is now routinely dropped, notably to account for the exotic properties of metamaterials [10,69,70,25,91].…”

“…Nevertheless, it should be underlined that in the area of electromagnetic scattering, the (acoustic) constant-density assumption becomes the oft-employed assumption of constant permeability ( [72,60], p. 2), which is now routinely dropped, notably to account for the exotic properties of metamaterials [10,69,70,25,91]. Also, more and more studies of acoustic (and elastic wave) inverse scattering no longer appeal to the constant-density assumption [64,12,33,52,68,17,43,53,90,92,44,59,94] A less-radical (than the constant-density) assumption is that: a) the density of the host is spatially-constant, b) the density of the obstacle, different from that of the host, is also spatiallyconstant, and c) the mass-density contrast ǫ (involving the difference of the two constant densities) is small. If the inverse problem is to retrieve the obstacle mass-density (which appears, for instance, to be of interest in certain biomedical applications [96,43,95,53,90]), an important question would appear to be: how small must ǫ (which is unknown, like the obstacle mass density, when it is the sought-for-parameter) be for the retrieval of ǫ (or of another constitutive parameter such as the wavespeed in the obstacle) to be reliable if at the outset the small-ǫ assumption is incorporated in the trial model?…”