Detection of small electromagnetic inhomogeneities with inaccurate frequency

TL;DR

This paper analyzes the mathematical structure of subspace migration imaging for detecting small electromagnetic inhomogeneities when the applied frequency is inaccurate, revealing reasons for location errors and supporting findings with simulations.

Contribution

It establishes a mathematical relationship between subspace migration and Bessel functions, explaining inaccuracies caused by frequency errors in detection.

Findings

Identifies the connection between subspace migration and Bessel functions.

Explains why inaccurate frequencies lead to location errors.

Supports analysis with numerical simulations.

Abstract

Generally, in the application of subspace migration for detecting locations of small inhomogeneities, one begins reconstruction procedure with a priori information of applied frequency. However, mathematical theory of subspace migration has not been developed satisfactorily when applied frequency is unknown. In this paper, we identify mathematical structure of subspace migration imaging function for finding locations of small inhomogeneities in two-dimensional homogeneous space by establishing a relationship with Bessel functions of integer order zero and one of the first kind. This expression indicates the reason behind the appearance of inaccurate locations. Numerical simulations are performed to support our analysis.