Localization of small perfectly conducting cracks from far-field pattern with unknown frequency

TL;DR

This paper investigates why subspace migration methods fail to accurately locate small conducting cracks when the applied frequency is unknown, by analyzing the mathematical structure involving Bessel functions.

Contribution

The paper provides a theoretical analysis linking subspace migration with Bessel functions, explaining inaccuracies with unknown frequency and suggesting potential improvements.

Findings

Subspace migration accuracy depends on known frequency.

Unknown frequency causes deviations explained by Bessel function structure.

Numerical simulations support the theoretical analysis.

Abstract

In inverse scattering problem, it is well-known that subspace migration yields very accurate locations of small perfectly conducting cracks when applied frequency is known. In contrast, when applied frequency is unknown, inaccurate locations are identified via subspace migration with wrong frequency data. However, this fact has been examined through the experimental results so, the reason of such phenomenon has not been theoretically investigated. In this paper, we analyze mathematical structure of subspace migration with unknown frequency by establishing a relationship with Bessel function of order zero of the first kind. Identified structure of subspace migration and corresponding results of numerical simulation answer that why subspace migration with unknown frequency yields inaccurate location of cracks and gives an idea of improvement.