Uniqueness of the solution to inverse obstacle scattering problem
نویسندگان
چکیده
منابع مشابه
Uniqueness of the Solution to Inverse Obstacle Scattering Problem
It is proved that the scattering amplitude known at a fixed frequency, a fixed direction of the incident plane wave and all directions of the scattered wave in a solid angle, however small, determine uniquely the shape of a strictly convex obstacle with a smooth but not analytic boundary on which the Dirichlet boundary condition is assumed.
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It is proved that if the scattering amplitudes for two obstacles (from a large class of obstacles) differ a little, then the obstacles differ a little, and the rate of convergence is given. An analytical formula for calculating the characteristic function of the obstacle is obtained, given the scattering amplitude at a fixed frequency.
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It is proved that the scattering amplitude A(β, α0, k0), known for all β ∈ S2, where S2 is the unit sphere in R3, α0 ∈ S2 is fixed, k0 > 0 is fixed, determines the surface S of the obstacle and the boundary condition on S uniquely. The boundary condition on S is either the Dirichlet, or Neumann, or the impedance one. The uniqueness theorems for the solution of inverse scattering problems with n...
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1 . I N T R O D U C T I O N During the last two decades or so, inverse scattering problems for the Helmholtz equation have enjoyed a remarkable degree of popularity, both in pure and applied contexts (see the monograph [1] and the references therein). One of the most important theoretical considerations in inverse scattering problems is uniqueness. Different approaches have been proposed [2-10]...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 2005
ISSN: 0375-9601
DOI: 10.1016/j.physleta.2005.08.088