Fitting the first order PT by spheroid : A semi analytical approach

Polarization Tensor (PT) has many applications in science and engineering. It can be used to improve reconstruction of image in medical imaging, improve metal detection for security screening or landmine clearance and also to study electrosensing fish. In some applications, it is useful to determine an ellipsoid that has the same PT with some other objects and this is possible because the explicit formula of the PT for ellipsoid can be set equal to some given PT and then solve to obtain all three axes of the ellipsoid. Therefore, in this study, based on a given first order PT, we will discuss a new method to determine the two distinct semi axes of a spheroid (an ellipsoid with two equal axes) so that the first order PT for the spheroid is similar to the given first order PT. In order to achieve this, we rely on some results about the depolarization factors for ellipsoid established in our previous study. Our new proposed method has suggested that the semi axes of the spheroid can be determined almost analytically from the explicit formula of the semi axes derived from the first order PT for spheroid where, a few examples have also been given here. The numerical results in the examples have also shown that the first order PT for a few spheroids computed based on the values of the semi axes are similar to the original given first order PT.