Inversion of synthetic and experimental acoustical scattering data for the comparison of two reconstruction methods employing the Born approximation
Résumé
This work is concerned with the reconstruction, from measured (synthetic or real) data, of a 2D penetrable fluid-like object of arbitrary cross-section embedded in a fluid of infinite extent and insonified by a plane acoustic wave. Green's theorem is used to provide a domain integral representation of the scattered field. The introduction therein of the Born approximation gives rise to a linearized form of the inverse problem. The actual inversion is carried out by two methods. The first diffraction tomography (DT), exhibits the contrast function very conveniently and explicitly in the form of a wave number/incident angle Fourier transform of the far backscattered field and thus requires measurements of this held for incident waves ail around the object and at all frequencies. The second discretized domain integral equation with Born approximation method, is numerically more intensive, but enables a wider choice of configurations and requires less measurements (one or several frequencies, one or several incident waves, choice of measurement points) than the DT method. A comparison of the two methods is carried out by inversion of both simulated and experimental scattered field data.