WIAS Preprint No. 1952, (2014)

Unique determination of balls and polyhedral scatterers with a single point source wave


  • Hu, Guanghui
  • Liu, Xiaodong

2010 Mathematics Subject Classification

  • 35R30 78A45 78A46


  • inverse acoustic scattering, uniqueness, polyhedral scatterers, balls, point source wave




In this paper, we prove uniqueness in determining a sound-soft ball or polyhedral scatterer in the inverse acoustic scattering problem with a single incident point source wave in R^N (N=2,3). Our proofs rely on the reflection principle for the Helmholtz equation with respect to a Dirichlet hyperplane or sphere, which is essentially a 'point-to-point' extension formula. The method has been adapted to proving uniqueness in inverse scattering from sound-soft cavities with interior measurement data incited by a single point source. The corresponding uniqueness for sound-hard balls or polyhedral scatterers has also been discussed.

Appeared in

  • Inverse Problems, 30 (2014) pp. 065010/1--065010/14.

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