A Numerical Study of the Probe Method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source $\Phi(\cdot,z)$ with source point z to define an indicator function $\hat{I}(z)$ which can be reconstructed from Cauchy data or far field data. The indicator function $\hat{I}(z)$ can be shown to blow off when the source point z tends to the boundary $\partial D$, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.