Forward and inverse scattering problems for the objects located in a closed medium

In this thesis, reconstruction of dielectric objects buried in a perfectly electric conducting enclosure is realized. Free space magnetic permeability is assumed for all cases. Our motivation is to observe the influence of reflected field from conducting boundary. It is predicted that reflections may form as image sources and hereby they result in better reconstruction. Primarily, synthetic data for scattered field is measured for arbitrary shaped objects. Then location, geometry and physical properties of scatterers are investigated for two cases: in an existing circular conducting boundary and in a free space. The approach used to solve this problem is based on a semi-numerical technique called method of moments (MoM). All implementations are coded in MATLAB environment. MoM is a frequency domain solver that has been widely used since 1960s. It aims to discretize time-harmonic electromagnetic field integral equations and design a linear matrix system. Applying linear algebra, matrix equations can be solved at ease. Integral equation in MoM solution involves Green's function as its definition of Fredholm equation. Since Green's function is evaluated analytically, MoM is approved as a semi-numerical method. Scattering problems are grouped into two categories such as forward and inverse scattering. Forward one is used to compute scattered field under the assumption of known source, scatterer and medium properties. Conversely, inverse one deals with acquiring the profile of objects when incident and scattered field data is known. Forward scattering problems are defined as well-posed problems; since their solution exists, is unique and stable. However, ill-posedness may arise for inverse scattering problems. Therefore, they need to be reformulated. Supplementary assumptions must be done to make the problem solvable. This operation is called regularization. A. N. Tikhonov proposed a regularization method that is recognized by his own name in 1963. During thesis, we benefit Tikhonov regularization to eliminate ill-posedness of problems. Forward scattering problems concerning closed medium can be identified by an integral equation involving Green's function as it is mentioned. Therefore, we begin with finding Green's function of closed medium. Then, scattered field is calculated numerically. Integral equation is discretized and total field is computed for each cell. The decrease in cell size serves better object modeling, so cell side is chosen at most λ/16. Accuracy of MoM process is very important for us and verification is necessary. For this purpose, analytic solution for closed medium is also performed. By the way, Green's function is employed as a 2D transverse magnetic (TM) polarized line source. When a single source is injected into simulation area, some deficiencies are encountered in imaging. Therefore, multi-source illumination is preferred in most cases. Besides, plenty of observers are located around the scatterer in a certain distance. Next, inversion algorithm is applied to achieve shape reconstruction. By doing so, Born Approximation and Newton methods are utilized. Born Approximation requires some restrictions to be satisfied. It provides improvements in outcomes if operating frequency and/or contrast are low. To explore object function, Born method enables us to use incident field in integral (data) equation instead of total one. In other words, scattered field is ignored. Then, discretization is performed for integral equation. However, ill-posedness is shown up while applying linear algebra. Hence, Tikhonov regularization is implemented. On the other hand, Newton method does not need any provision, so it is more advanced. It is an iterative method presented to find object function. It starts with guessing an initial value for sought object function. In every step, a new guess object function is proposed to reach or get close to real value of it. We selected a condition for error tolerance to halt the process when object function is close enough to real value. After reconstruction for closed medium is fulfilled, conducting surrounding is removed. Forward and inverse problems are solved for unbounded medium using appropriate Green's function. The background medium can be a free space or dielectrically filled. Several tests are practiced to observe the impact of conducting boundary on reconstruction and localization of object in closed mediums. The selection of radius of conducting enclosure is very important. The most favorable distance between observers and conducting enclosure "λ/4" is also affirmed. In addition, size of reconstruction area is examined. Born method offers us quality imaging for particular cases. The increase in contrast deteriorates the results. Therefore, Newton method is also applied to same settings. The drawback of Newton is to find a convenient initial value for contrast. If it is not picked properly in the beginning, simulation duration lasts longer or forever. In conclusion, forward problem is verified by means of analytic solution. Born and Newton methods are successfully performed for inversion. The reconstruction and localization is succeeded. Multi-source effect is analyzed and its performance is highlighted. Unfortunately closed medium solutions do not provide great enhancement in imaging as supposed. For most cases, shape reconstruction is not corrupted at least. There has to be some advantages of closed mediums, because they preserve the simulation area.