Scattering of a spherical wave from a perfectly rigid slender body of arbitrary shape is considered. The point source is assumed to be located in the far field of each body cross section but may be placed in the near field of the target. The problem is investigated theoretically with the matched asymptotic expansions method and an approximate solution is derived for the scattered pressure, which takes into account the curvature of the incident wave front. The presented formalism combines the so-called slender-body approximation and the two-dimensional Kirchhoff theory. It allows a great simplification in the geometrical description of the body surface and leads to a practical method even for bodies of complex shape. In the monostatic case, it is theoretically shown that the obtained solution is asymptotically equivalent to that provided by geometrical optics for a large class of finite scatterers. Lastly, monostatic and bistatic angular distributions are computed for a prolate spheroid in the near and far fields to support the present theory.

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The echoes backscattered in the far field by a rigid prolate spheroid at low and medium frequencies are computed and commented. The so-called slender-body aproximation is applied to express the pressure backscattered by the body when insonified by a harmonic plane wave. The impulse response is then calculated by Fast Fourier Transform for different angles of incidence. The computed echoes exhibit two main peaks, one narrow and one spread out, corresponding respectively to the reflected echo and to the diffracted waves that encircle the body once ("creeping waves"). The time of arrival of the specular echo corresponds to that provided by Geometrical Optics. An explanation, resulting from the analysis of the computed echos, is proposed for the times of arrival of the diffracted waves at oblique incidence. However, a theoretical study is required to check the validity of that explanation.