# On finding the surface admittance of an obstacle via the time domain enclosure method

## TL;DR

This paper presents a method to determine the surface admittance and curvature of an unknown obstacle in electromagnetic scattering problems using time domain data from a single wave measurement.

## Contribution

It introduces a novel approach to extract surface admittance and curvature information from finite time electromagnetic data using the enclosure method.

## Key findings

- Surface admittance can be identified from observed data.
- Curvature information at the closest surface points can be extracted.
- A single wave measurement provides significant surface information.

## Abstract

An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an unknown obstacle. The condition is described by using an unknown positive function on the surface of the obstacle which is called the surface admittance. The wave is generated at the initial time by a volumetric current source supported on a very small ball placed outside the obstacle and only the electric component of the wave is observed on the same ball over a finite time interval. It is shown that from the observed data one can extract information about the value of the surface admittance and the curvatures at the points on the surface nearest to the center of the ball. This shows that a single shot contains a meaningful information about the quantitative state of the surface of the obstacle.