Localisation and permittivity extraction of an embedded cylinder using decomposition of the time reversal operator

In this study, first, the problem of time reversal imaging of an embedded dielectric or metallic cylinder inside another dielectric cylinder is studied. The direct problem is carried out numerically using the finite-element method. The background dyadic Green function (DGF) is computed analytically by computing radiated fields of an infinitesimal electric dipole near an infinitely long dielectric cylinder. The time reversal technique is then applied using this background DGF to image the embedded cylinder. Results demonstrate that while using a free-space DGF for imaging yields erroneous results, by employing a proper background DGF, the scatterer inside the cylinder is correctly localised. Next, the authors extract permittivities in two different scenarios with two different techniques. In the first case, the permittivity of a background cylinder that contains a metallic cylinder inside it is extracted by calculating the image entropy. In the second case, the permittivity of an embedded cylinder inside a priori known background dielectric cylinder is estimated by a new method based on an optimisation and evaluation of the largest eigenvalues of the multistatic data matrices. The proposed techniques are then verified using simulated and measured data. For measurements, a newly developed combined tapered sectorial antenna is designed, fabricated, and characterised.