An Extended Method for Fitting the First Order Polarization Tensor to a Spheroid

Polarization Tensor (PT) has been widely used in some of the applications of electric and electromagnetic such as electrical imaging, metal detection and electrosensing fish. Furthermore, in these applications, polarization tensors can capture significant information such as material, shape and orientation about the related objects (medical images in electrical imaging or metallic target in metal detection). Some physical information about the unknown objects can then be characterized from the given first order polarization tensor that representing the object. Therefore, it is beneficial to determine an ellipsoid based on the given first order polarization tensor due to the possible similarities between the ellipsoid and the unknown object. The main objective of this study is to present a method in order to determine the semi axes of the spheroid, which is an ellipsoid with two identical axes. The method is an extension of the previous method which is only applicable to two types of spheroid. Using the rotation of the first order polarization tensor, we will show that this extended method can be used to determine all semi axes for any types of spheroid, depending on the given first order PT. After that, some numerical examples are provided specifically to compare between the first order PT for the spheroid with the given first order PT for verifying the results obtained. It is expected that the computed first order PT for the spheroid will be almost similar to the given first order PT.