Abstract
In this paper, a time domain enclosure method for an inverse obstacle scattering problem of electromagnetic wave is introduced. The wave as a solution of Maxwell's equations is generated by an applied volumetric current having an {\it orientation} and supported outside an unknown obstacle and observed on the same support over a finite time interval. It is assumed that the obstacle is a perfect conductor. Two types of analytical formulae which employ a {\it single} observed wave and explicitly contain information about the geometry of the obstacle are given. In particular, an effect of the orientation of the current is catched in one of two formulae. Two corollaries concerning with the detection of the points on the surface of the obstacle nearest to the centre of the current support and curvatures at the points are also given.
Highlights
In this paper, we consider an inverse obstacle scattering problem of a wave whose governing equation is given by Maxwell’s equations
The problem therein aims at extracting information about the geometry of an unknown cavity from the wave in time domain which is produced by the initial data localized inside the cavity and propagates therein
Single measurement version of the time domain enclosure method finds an application to an inverse initial boundary value problem for the heat equation in three-space dimensions
Summary
We consider an inverse obstacle scattering problem of a wave whose governing equation is given by Maxwell’s equations. The inverse obstacle scattering problem is to: extract information about the geometry of the obstacle from the observed wave. Our main interest is to find an analytical method or formula that extracts the geometry of the obstacle from the data by using the governing equation of the wave. We have already some applications to inverse obstacle scattering problems whose governing equation is given by the classical wave equation in three-space dimensions [14, 15, 16, 17, 18]. The method enables us to extract information about the geometry of unknown obstacle from a single reflected wave over a finite time interval. In the following subsection we describe our solution to Problem
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