Microwave imaging problem with veselago lens structure

Abstract

Veselago lens structure has been known by researchers for many years. By using such structures, it has been shown that the electromagnetic wave can be focused at the desired point. Also, it has became interesting for microwave imaging problems with this focusing feature. However, many researches are carried out to produce metamaterials under this subject. In recent years, promising developments in producing these metamaterials have increased the interest to this subject. The aim of this thesis is to find images of the objects in 2D space using the Veselago lens structure. These lenses, which have a metamaterial layer, help to focus the electromagnetic wave at a certain point. The metamaterials are artificial materials that have a negative value for both the dielectric constant and the magnetic permeability. However, Veselago lenses have 3 layers, one of which is metamaterial. In such structures, the first and third layers are the same mediums and have positive permittivity and permeability. The second layer in the middle is a metamaterial medium, and its electromagnetic characteristic parameters are equal to the negative of the values which the other two layers have. Also, the Veselago lens structure mentioned here is given in this study. First, the expressions of Green's functions for the three-layered space that will be used throughout the calculations are found. To do this, the boundary conditions on the surfaces between the layers are used. Thus, the unknown coefficients are found from a linear equation systems and Green's functions is formed. It is calculated for the cases where the source are in the first or third layer. In addition, the accuracy of this Green's function is tested by comparing it with another expression in the literature. In order to obtain the representations of Green's functions in the spatial domain, the inverse Fourier transform is applied to the expressions in the spectral domain. It can be given attention to the branch point singularities in the complex plane while calculating the integral for this transformation. These branch point singularities are avoided by choosing the integral path on the real axis and inserting some conductivity for each medium. However, it is necessary to have information about the scattered field from the object for imaging. Therefore, the scattering field from an object has been calculated theoretically and it is obtained synthetically. Two different types of objects are considered for this purpose. The first one is when the scatter is a dielectric object. In this case, the calculation way of the scattered field from an object by the method of moments (MoM) is shown. MoM is a method being used commonly for such problems. In here, the object is divided into cells and a linear equation system is solved to find the total field in each cell. Then, by using the information of total field in the object, the scattered field at any point on the space is found with the data equation. In addition, the objects having a perfect electric conductor (PEC) surface is included in at the study. For this second case, the way in which the scattered field being obtained by an integral equation method (IEM) is described. This method and MoM are quite similar to each other. Firstly, the surface of the object is divided into cells and the surface current density of each cell is found with a linear equation system. Similarly, the scattered field at any point on the space is found by using these surface current densities of the cells. After the methods for finding the scattered field from the object, imaging algorithms being used in this thesis are mentioned. Such algorithms basically aim to find the image of the object in a reconstruction domain by using the information of scattered field. In addition, the information of scattered field is obtained separately for each pair of source and measurement points since the configurations with multi-source and multi-measurement points are used in this study. Firstly, Born approximation being a basic method is introduced. In this technique, a matrix system is obtained from the data equation by ignoring the scattered field. After a necessary regularization, this system is solved and an object function is found. The Born approximation is valid only for weakly scattering objects and gives information about the dielectric constant of the object. Secondly, another imaging algorithm is reverse time migration (RTM). For this, there is an image function that basically calculates the correlation. Thus, the geometric properties of the object are determined. If it is compared with Born approximation, RTM method is easier and faster to implement. Also, unlike the Born approximation, this method can be used for the objects which have a PEC surface. However, RTM method provides the possibility of detecting only the geometrical properties of the object, and it does not provide any information about the electromagnetic properties of the object. In the chapter of numerical examples, the results of these two imaging algorithms are given. First of all, two different illumination-measurement configurations being used in this study are defined. The main difference between these two configurations is whether the sources are in the object layer or not. The cases of illumination from the opposite layer of the object are more practical configurations in terms of feasibility. However, the image quality increases with the illuminations from the object layer. After introducing the illumination-measurement configurations used in this study, it is shown the way of constructing the letter-shaped objects to be used for imaging are defined in numerical examples. For this, a layout with a certain number of cell elements is used and the necessary cell elements are selected from this scheme to form the desired letter-shaped objects. Then, Born approximation and RTM method are applied for these configurations and the results are given. In the results, it is showed that the image quality is improved by the focusing effect of the Veselago lens structure. However, objects with different shapes are used. Also, the effects of dielectric constant and metamaterial thickness on imaging results are investigated. Finally, in this chapter, the results of numerical examples are given for scattered field data with noise and the sensitivity of results is examined to noise. Finally, in the chapter of conclusions, the findings of this thesis are presented and the results are discussed. It is given a comparison between Born approximation and RTM method by including their advantages and disadvantages. The effect of using different illumination-measurement configurations on imaging is mentioned. In addition, the illumination-measurement configurations used in this study is compared in terms of feasibility. In addition, some recommendations for the future research are given.