This paper investigates the effect of the geometry and the impedance of an obstacle on the accuracy of the linear sampling method for a two-dimensional acoustic inverse obstacle scattering problem with an impedance boundary condition. Our theoretical results show the dependence of the blowup rate of the so-called indicator function of the linear sampling method on these parameters. These results are obtained using asymptotic expansions near the obstacle boundary of the solution to an interior problem. In design problems, we propose, based on the above dependence, a surface coating procedure for improving or destroying the reconstruction accuracy. Numerical examples are given to illustrate the theoretical results.
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