Detection of small electromagnetic inhomogeneities with inaccurate frequency
For researchers using subspace migration to detect small inhomogeneities, this work explains the effect of unknown frequency, but it is an incremental theoretical analysis without practical improvement.
The paper identifies the mathematical structure of subspace migration imaging when the applied frequency is unknown, showing how inaccurate frequency leads to inaccurate location detection, and validates the analysis with numerical simulations.
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.