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

TL;DR

This paper develops explicit formulas to determine the distance to unknown obstacles with dissipative boundaries or finite refractive index using back-scattering data in inverse obstacle scattering problems over finite time intervals.

Contribution

It introduces new explicit formulas for obstacle distance measurement in inverse scattering problems with dissipative or refractive obstacles using back-scattering data.

Findings

Explicit distance formulas for dissipative boundary obstacles

Explicit distance formulas for finite refractive index obstacles

Applicable to back-scattering data in limited time intervals

Abstract

In this paper a wave is generated by an initial data whose support is localized at the outside of unknown obstacles and observed in a limited time on a 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-scattering data. Two types of obstacles are considered. One is obstacles with a dissipative boundary condition which is a generalization of the sound-hard obstacles; another is obstacles with a finite refractive index, so-called, transparent obstacles. For each type of obstacles two formulae which yield explicitly the distance from the support of the initial data to unknown obstacles are given.