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The microwave imaging system currently being developed at the Technical University of Denmark is described and its performance tested on simulated data. The system uses an iterative Newton-based imaging algorithm for reconstructing the images in conjunction with an efficient method-of-moments solution of the associated forward scattering problem. A cylindrical multistatic antenna setup with 32 horizontally oriented antennas is used for collecting the data. It has been found that formulating the imaging algorithm in terms of the logarithm of the amplitude and the unwrapped phase of the measured signals improves its performance when compared to the more commonly used complex phasor formulation. This improvement is illustrated by imaging a simulated hemispherical breast model using both formulations. In addition to this, the importance of using the correct position and orientation of the antennas in the measurement system is shown by imaging the same breast model using a measurement setup in which the antennas are vertically oriented. Index Terms--Biomedical imaging, cancer, electromagnetic scattering inverse problems, microwave imaging, nonlinear equations.

The adaptive integral method (AIM) is combined with the higher order method of moments (MoM) to solve integral equations. The technique takes advantage of the low computational complexity and memory requirements of the AIM and the reduced number of unknowns and higher order convergence of higher order basis functions. The classical AIM is appropriately modified to allow larger discretization elements and, consequently, higher basis function expansion orders. Numerical examples based on the higher order hierarchical Legendre basis functions show the advantages of the proposed technique over the classical AIM based on low-order basis functions in terms of memory and computational time. Index Terms--Adaptive integral method (AIM), higher order hierarchical Legendre basis functions, integral equations, method of moments (MoM), scattering.

A theoretical investigation of the use of a coupled line section as an impedance transformer is presented. We show how to properly select the terminations of the coupled line structures for effective matching of real and complex loads in both narrow and wide frequency ranges. The corresponding circuit configurations and the design procedures are proposed. Synthesis relations are derived and provided for efficient matching circuit construction. Design examples are given to demonstrate the flexibility and limitations of the design methods and to show their validity for practical applications. Wideband matching performance with relative bandwidth beyond 100% and return loss RL > 20 dB is demonstrated both theoretically and experimentally. Good agreement is achieved between the measured and predicted performance of the coupled line transformer section. Index Terms--Coupled transmission lines, directional coupler, impedance matching, impedance matrix, microstrip lines, strip lines.

Breast-cancer screening using microwave imaging is emerging as a new promising technique as a supplement to X-ray mammography. To create tomographic images from microwave measurements, it is necessary to solve a nonlinear inversion problem, for which an algorithm based on the iteratire Gauss-Newton method has been developed at Dartmouth College. This algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the Tikhonov algorithm. In this paper, a new algorithm for determining the iteration update values in the Gauss-Newton algorithm is presented which is based on the conjugate gradient least squares (CGLS) algorithm. The iterative CGLS algorithm is capable of solving the update problem by operating on just the Jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations. The new algorithm is compared to the Gauss-Newton algorithm with Tikhonov regnlarization and is shown to reconstruct images of similar quality using fewer iterations. Index Terms--Biomedical electromagnetic imaging, cancer, electromagnetic scattering inverse problems, image reconstruction, imaging, inverse problems, microwave imaging, nonlinear equations.

A hybrid global-local optimization technique for the design of antennas is presented. It consists of the subsequent application of a genetic algorithm (GA) that employs coarse models in the simulations and a space mapping (SM) that refines the solution found in the previous stage. The technique is particularly suited to optimization problems for which long computational times are required to achieve accurate solutions. Index Terms--Antenna arrays, genetic algorithms (GAs), optimization methods, space mapping (SM).

This paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments (MoM). The basis is derived from orthogonal Legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features. Expressions are presented for wire, surface, and volume elements but emphasis is given to the surface elements. In this case, the new hierarchical basis leads to a near-orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge. In addition, all higher order terms in the expansion have two vanishing moments. In contrast to existing formulations, these properties allow the use of very high-order basis functions without introducing ill-conditioning of the resulting MoM matrix. Numerical results confirm that the condition number of the MoM matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions. As a consequence of the excellent condition numbers, we demonstrate that even very high-order MoM systems, e.g., tenth order, can be solved efficiently with an iterative solver in relatively few iterations. Index Terms--Basis functions, hierarchical systems, high-order methods, integral equations, method of moments (MoM), orthogonal functions, polynomial approximation.

The plane-wave scattering matrix is used to characterize antennas that are located just above a planar interface that separates two media. The plane-wave transmitting spectrum for the field radiated downward into the lower medium is expressed directly in terms of the current distribution of the transmitting antenna. The transmitting spectrum for a reciprocal antenna determines the plane-wave receiving spectrum for the field that propagates upward in the lower medium. A measurement procedure is discussed for determining the plane-wave transmitting and receiving spectra from measurements with a probe that is located in the lower medium. Index Terms--Ground-penetrating radar (GPR), planar interface, planar near-field measurements, plane-wave scattering matrix, subsurface imaging, surface-penetrating radar (SPR).

This paper presents an efficient technique for the analysis of electromagnetic scattering by arbitrarily shaped perfectly conducting objects in layered media. The technique is based on a higher order method of moments (MoM) solution of the electric field, magnetic field, or combined-field integral equation. This higher order MoM solution comprises higher order curved patches for the geometry modeling and higher order hierarchical basis functions for expansion of the electric surface current density. Due to the hierarchical property of the basis functions, the order of the expansion can be selected separately on each patch depending on the wavelength in the layer in which the patch is located and the size of the patch. In this way, a significant reduction of the number of unknowns is achieved and the same surface mesh can be reused in a wide frequency band. It is shown that even for fairly large problems, the higher order hierarchical MoM requires less memory than existing fast multipole method (FMM) or multilevel FMM implementations. Index Terms--Combined-field integral equation (CFIE), electromagnetic scattering, higher order hierarchical vector basis functions, layered media, Legendre polynomial, method of moments (MoM), perfectly conducting (PEC) object.

An exact line integral representation is derived for the magnetic physical optics field scattered by a perfectly electrically conducting planar plate illuminated by electric or magnetic Hertzian dipoles. The positions of source and observation points can be almost arbitrary. Numerical examples are presented to illustrate the exactness of the line integral representation. Index Terms--Line integral, magnetic field, physical optics.

A three-dimensional (3-D) inversion scheme for fixed-offset ground penetrating radar (GPR) is derived that takes into account the loss in the soil and the planar air--soil interface. The forward model of this inversion scheme is based upon the first Born approximation and the dyadic Green function for a two-layer medium. The forward model is inverted using the Tikhonov-regularized pseudo-inverse operator. This involves two steps: filtering and backpropagation. The filtering is carried out by numerically solving Fredholm integral equations of the first kind and the back-propagation is performed using fast Fourier transforms (FFTs). Numerical results are provided to illustrate the performance of the inversion scheme. Index Terms--Diffraction tomography, ground penetrating radar (GPR), inverse scattering, pseudo-inverse operator.