Identification of the unique spheroid by rotated and scaled first order polarization tensor

Abstract

In the applications of electric and electromagnetic, polarization tensor is usually used to describe the perturbation in electrical field induced by the presence of conducting objects. Due to the fact that polarization tensor carries information about geometry and conductivity of those presented conducting objects, it is possible to substantially use the polarization tensor to describe the objects including reconstructing their images. Some recent applications of polarization tensor include electrical imaging for medical or industrial purposes, characterization of objects by weakly electrosensing fish and also metal detection. Specifically, this research is concerned with the first order polarization tensor when the conducting object is a conducting spheroid. Given the first order polarization tensor of any object, a spheroid can be numerically determined so that the spheroid has the same first order polarization tensor. Here, the main purpose of this research is to investigate the rotated or the scaled first order polarization tensor that is related to a unique spheroid. In order to achieve the objectives of this research, the depolarization factors of both prolate and oblate spheroids are first investigated. It is proven that the eccentricity of both spheroids are unique based on their depolarization factors. After that, the effect of scaling on the first order polarization tensor to the volume, depolarization factors, eccentricity and also semi axes of the spheroid are revealed. Some numerical calculations to identify the volume and semi axes of the spheroid based on a few scaled first order polarization tensors are presented in this research. Furthermore, the effect of rotation on the first order polarization tensor to the conductivity, volume, depolarization factors as well as semi axes of the spheroid are also identified. By the implementation of rotation, a new and improvised flowchart is provided in finding the semi axes of a spheroid based on the different forms of the first order polarization tensor. Last but not least, this research described the uniqueness of the spheroid at a fixed conductivity based on either rotated or scaled first order polarization tensor. As a conclusion, this research would be beneficial in gaining the information about the object specifically for spheroid based on the given first order polarization tensor.