Kirchhoff scattering from non-penetrable targets modeled as an assembly of triangular facets

Frequency and time domain solutions for the scattering of acoustic waves from an arbitrarily shaped target using the Kirchhoff approximation are developed. In this method, the scattering amplitude is analytically evaluated on a single triangle and scattering from a triangularly facetted target is computed by coherently summing the contributions from all the triangles that make up its surface. In the frequency domain, the solution is expressed in terms of regular (non-singular) functions, which only require the knowledge of the directions of the incident and scattered fields, the edge vectors for the triangles and position vectors to one of their vertices. To derive representations using regular functions in the time domain, the scattered signal is expressed by different expressions for various limiting cases. The frequency domain solution is validated by comparing its results to the solutions of problems for which the Kirchhoff approximation has analytic solutions. In order of increasing complexity, they include the square plate, the circular plate, the finite cylinder and the sphere. The time domain solution is validated by comparing it to the time domain solution of the Kirchhoff approximation for a rigid sphere.