Characterization of the spheroids from the first order polarzation tensor

Abstract

Polarization tensor is an essential concept used in science and engineering. It has appeared in many electric and electromagnetic applications such as electrical imaging in medical, material science and metal detection. It has also been adapted biologically to study electrosensing in fish. In these applications, the polarization tensors are used to describe conducting objects such as tumors in human bodies and metal components in landmines, presented in electric or electromagnetic fields. Here, polarization tensors can capture significant information about the objects such as their material, shape and orientation. Inspired by many interesting topics on polarization tensor, this research is conducted with the main purpose to investigate specifically the first order polarization tensor when the conducting object is a spheroid (prolate and oblate). In this study, a new formula of the first order polarization tensor for ellipsoid, consisting of depolarization factors is used. It is proven that the properties of depolarization factors are as follows. One, the value of each depolarization factor for ellipsoid is between 0 and 1. Two, the depolarization factors can be used to identify the semi axes of a spheroid and that the semi axes of the spheroid can also be used to describe the depolarization factors. Next, this study also describes the spheroid based on the first order polarization tensor by considering the properties of the depolarization factors above. Specifically, the spheroid can be classified as a prolate or oblate spheroid based on the first order polarization tensor. In addition, the semi axes of either prolate or oblate spheroid can be used to describe the related first order polarization tensor. Furthermore, the volume and the depolarization factors for the spheroid can be determined analytically based on this first order polarization tensor. The conductivity of the prolate or oblate spheroid also can be classified based on the components of such first order polarization tensor. This study also proposes a combined approach of an analytical and numerical to determine the semi axes of a spheroid based on a given first order polarization tensor at some specified conductivity. Numerical examples are provided to present the values of all semi axes of the spheroid. Finally, in order to verify the results, the values of semi axes obtained are used to compute the first order polarization tensor and then compared with the given first order polarization tensor. The comparison has shown that the computed first order polarization tensor is almost similar to the given first order polarization tensor.