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In this paper a wave is generated by an initial data whose support islocalized at the outside of unknown obstacles and observed in a limited time ona known closed surface or the same position as the support of the initial data.The observed data in the latter process are nothing but the back-scatteringdata. Two types of obstacles are considered. One is obstacles with adissipative boundary condition which is a generalization of the sound-hardobstacles; another is obstacles with a finite refractive index, so-called,transparent obstacles. For each type of obstacles two formulae which yieldexplicitly the distance from the support of the initial data to unknownobstacles are given.

inverse problems

The enclosure method for inverse obstacle scattering problems with  dynamical data over a finite time interval II. Obstacles with a dissipative  boundary or finite refractive index and back-scattering data