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2009-12-09 PIER Vol. 99, 453-463, 2009. doi:10.2528/PIER09111502

Analysis of Finite Periodic Dielectric Gratings by the Finite-Difference Frequency-Domain Method with the Sub-Entire-Domain Basis Functions and Wavelets

Gang Zheng, Bing-Zhong Wang, Hua Li, Xiao-Fei Liu, and Shuai Ding

In this paper, the finite-difference frequency-domain (FDFD) method, boundary integral equation (BIE) method and sub-entire-domain (SED) basis functions are combined to analyze scatterings from finite periodic dielectric gratings. The wavelet method is used to reduce the number of inner product operations in calculating the mutual-impedance elements between the SED basis functions. In the numerical examples, the RCS curves obtained by the method in this paper are in good agreement with those obtained by the classical full-domain FDFD method, but the computational times are largely reduced and no large matrix equation needs to be stored and solved in the former.

2009-12-08 PIER Vol. 99, 427-451, 2009. doi:10.2528/PIER09101901

Experiments with Lanczos Biconjugate a-Orthonormalization Methods for MoM Discretizations of Maxwell's Equations

Yan-Fei Jing, Bruno Carpentieri, and Ting-Zhu Huang

In this paper, we consider a novel class of Krylov projection methods computed from the Lanczos biconjugate A-Orthonormalization procedure for the solution of dense complex non-Hermitian linear systems arising from the Method of Moments discretization of Maxwell's equations. We report on experiments on a set of model problems representative of realistic radar-cross section calculations to show their competitiveness with other popular Krylov solvers, especially when memory is a concern. The results presented in this study will contribute to assess the potential of iterative Krylov methods for solving electromagnetic scattering problems from large structures enriching the database of this technology.

2009-12-08 PIER Vol. 99, 405-426, 2009. doi:10.2528/PIER09060403

Microwave Screen with Magnetically Controlled Attenuation

Sergey Nickolaevich Starostenko and Konstantin Rozanov

The effect of magnetic bias on dielectric spectra of composite sheets filled with Fe or Co-based microwires is studied experimentally and via simulation. The permittivity is measured using a free-space technique within the frequency band from 6 to 12 GHz. The bias is applied either parallel or perpendicular to the microwave electric field; the bias strength varies from 0 to 2.5 kOe. The composites with Fe-based wires reveal a single region of bias dependent permittivity under bias about 800-1000 Oe. The composites with Co-based wires reveal two such regions: the high-field region is close to that of composites with Fe wires, and the low-field region corresponds to the coercive field of Co wires (2-3 Oe). The high-field effect is related to the dependence of ferromagnetic resonance (FMR) parameters on bias; the low-field effect is related to the rearrangement of the domain structure of Co-based wires. The interference of magnetoimpedance and dipole resonance is analyzed, revealing the effects off wire length, diameter, parameters of magnetic resonance and composite structure. The results are considered in view of application to the problem of controlled microwave attenuation. Simulation shows that the narrower is the FMR spectrum and the higher is the admissible loss of a sheet in a transparent state, the wider is the dynamic range of attenuation control. The attenuation range of a lattice of continuous wires is smaller than that of a screen with identical wire sections, where the magnetoimpedance effect is amplified resonantly. At 15 GHz frequency the strength of the bias switching opaque sheet with Fe-based wires to the transparent state is about 2000 Oe. For 3 dB admissible loss, the range of attenuation control about 10 dB is feasible in a composite with aligned wire sections. If the aligned sections are distributed regularly, the loss in a transparent state is about 1 dB lower.

2009-12-02 PIER Vol. 99, 383-404, 2009. doi:10.2528/PIER09083006

Dark Soliton Behaviors Within the Nonlinear Micro and Nanoring Resonators and Applications

Somsak Mitatha

We propose some fascinating results regarding dark soliton pulse propagation within the nonlinear micro and nano waveguides. The system consists of nonlinear micro and nanoring resonators whereby the dark soliton is input into the system and travels within the waveguide. A continuous dark soliton pulse is sliced into smaller pulses by the nonlinear effect which is known as chaos. The nonlinear behaviors such as chaos, bistability and bifurcation are analyzed and discussed. The broad area of applications such as dark-bright soliton conversion and power amplification, binary code generation by the dark-bright soliton pair, dark soliton trapping and millimeter wave generation are proposed and discussed. The biggest advantage is that, where security is the most important consideration, power amplification can be used to perform the long distance link.

2009-12-01 PIER Vol. 99, 355-382, 2009. doi:10.2528/PIER09101001

Chitosan Spheroids with Microwave Modulated Drug Release

Zakaria Zabliza and Tin Wui Wong

The interplay effects of matrix formulations with microwave on drug release were investigated using an agglomerate system. Chitosan spheroids were formulated with stearic acid and/or sodium chloride by extrusion-spheronization technique, and chlorpheniramine maleate as water-soluble model drug. The spheroids were treated by microwave at 80 W for 5 to 40 min. The profiles of drug dissolution, drug content, drug-polymer interaction, polymer-polymer interaction, sodium leaching, matrix morphology and integrity were determined. Unlike chitosan matrix prepared by ionotropic gelation method, the retardation of drug release from chitosan spheroids by microwave required a more complex formulation containing both stearic acid and sodium chloride unless a high stearic acid fraction was used. These spheroids demonstrated a high resistance to disintegration during dissolution owing to salt-induced bridging by sodium chloride. In response to microwave, sodium chloride aided stearic acid spread and effected domain interaction via C=O moiety over a matrix with reduced specific surface area thereby reducing drug dissolution. The drug release of spheroids can be retarded by microwave through promoting the layering of hydrophobic stearic acid in a matrix structure sustained by sodium chloride.

2009-12-01 PIER Vol. 99, 339-354, 2009. doi:10.2528/PIER09102609

Effect of Temperature and Multiple Scattering on Rain Attenuation of Electromagnetic Waves by a Simple Spherical Model

Eko Setijadi, Akira Matsushima, Naoki Tanaka, and Gamantyo Hendrantoro

Specific rain attenuation is discussed from the viewpoint of numerical solution for scattering and absorption of electromagnetic waves related to dielectric spheres. Special attention is paid to the quantitative evaluations considering the change of temperature and the existence of multiple scattering effect. The analysis is based on the set of Stratton's vector spherical wave functions and its addition theorem, which lead to the simultaneous linear equations for the expansion coefficients with adaptively selected truncation numbers. Computed extinction cross sections lead directly to the specific rain attenuation, where the Weibull raindrop distribution model is used. It is discussed how the dependence of the permittivity of water on temperature and frequency affects the attenuation property. Furthermore, the effect of multiple scattering is evaluated in terms of the root mean square of attenuation deviation from the simple superposition of single scattering (Mie's) coefficients. Contrary to general belief, this deviation is the highest at around the boundary between microwave and millimeter wave bands.

2009-12-01 PIER Vol. 99, 323-338, 2009. doi:10.2528/PIER09102006

Analytical and Numerical Analyses of a Current Sensor Using Non Linear Effects in a Flexible Magnetic Transducer

Eric Vourc'h, Pierre-Yves Joubert, and Lionel Cima

A theoretical study and a simulation method are proposed for superparamagnetic current sensors implementing a uniformly wound toroidal core topology. So as to be easy to implement, this sensor topology can be made flexible thanks to the use of a core made up of a superparamagnetic powder embedded in a flexible plastic matrix. The measurement of DC and AC currents is possible provided that a sinusoidal magnetic field excitation is applied to the superparamagnetic transducer. An analytical model is proposed for computing the sensor output signal and we demonstrate that when the detection of the component at the second order harmonic of the excitation frequency is used, the measurement is independent of the conductor position in a given current range. For simulating the dynamic response of the sensor, we propose to combine the analytical model, or a finite elements model, with a time-discretization method. Furthermore, simulations are carried out considering a ring shaped sensor and the real magnetization characteristics of a superparamagnetic material. Simulations are provided over the [-10 kA 10 kA] range and for various amplitudes of the excitation signal. The results obtained with the analytical model, which is computationally efficient, are within 4% to 12.7% from the numerical results.

2009-12-01 PIER Vol. 99, 307-322, 2009. doi:10.2528/PIER09100907

Signal Processing for Noise Cancellation in Actual Electromagnetic Environment

Hisako Orimoto and Akira Ikuta

The observed phenomena in actual electromagnetic environment are inevitably contaminated by the background noise of arbitrary distribution type. Therefore, in order to evaluate the electromagnetic environment, it is necessary to establish some signal processing methods to remove the undesirable effects of the background noise. In this paper, we propose a noise cancellation method for estimating a specific signal with the existence of background noise of non-Gaussian distribution. By applying the well-known least mean squared method for the moment statistics with several orders, a practical method for estimating the specific signal is derived. The effectiveness of the proposed theoretical method is experimentally confirmed by applying it to an estimation problem in actual magnetic field environment.

2009-11-27 PIER Vol. 99, 289-306, 2009. doi:10.2528/PIER09102704

Numerical Analysis of Apodized Fiber Bragg Gratings Using Coupled Mode Theory

Nai-Hsiang Sun, Jiun-Jie Liau, Yean-Woei Kiang, Shih-Chiang Lin, Ru-Yen Ro, Jung-Sheng Chiang, and Hung-Wen Chang

In this paper, the coupled mode theory is used to analyze apodized fiber Bragg gratings (FBGs). Since the profile of gratings varies with the propagation distance, the coupled mode equations (CMEs) of apodized FBGs are solved by the fourth-order Runge-Kutta method (RKM) and piecewise-uniform approach (PUA). We present two discretization techniques of PUA to analyze the apodization profile of gratings. A uniform profile FBG can be expressed as a system of first-order ordinary differential equations with constant coefficients. The eigenvalue and eigenvector technique as well as the transfer matrix method is applied to analyze apodized FBGs by using PUAs. The transmission and reflection efficiencies calculated by two PUAs are compared with those computed by RKM. The results show that the order of the local truncation error of RKM is h-4, while both PUAs have the same order of the local truncation error of h-2. We find that RKM, capable of providing fast-convergent and accurate numerical results, is a preferred method in solving apodized FBG problems.

2009-11-26 PIER Vol. 99, 273-287, 2009. doi:10.2528/PIER09102404

Tunable Lateral Shift through Nonlinear Composites of Nonspherical Particles

Dongliang Gao and Lei Gao

The Goos-Hanchen (GH) shift of the reflected waves from nonlinear nanocomposites of interleaved nonspherical metal and dielectric particles are investigated both theoretically and numerically. First, based on spectral representation theory and effective medium approximation, we derive the field-dependent effective permittivity of the nonlinear composites. Then the stationary phase method is adopted to study the GH shifts from nonlinear composites. It is found that for a given volume fraction, there exist two critical polarization factors Lc1 and Lc2, and bistable GH shifts appear only when L < Lc1 or L < Lc2. Moreover, both giant negative and positive GH shifts accompanied with large reflectivity are found, hence they can be easily observed in experiments. The reversal of the GH shift may be controlled by adjusting both the incident angle and the applied field. Numerical simulations for Gaussian-type incident beam are performed, and good agreement between simulated data and theoretical ones is found especially for large waist width.

2009-11-24 PIER Vol. 99, 261-272, 2009. doi:10.2528/PIER09100702

Conductive Medium Modeling with an Augmented GIBC Formulation

Zhiguo Qian, Mei Song Tong, and Weng Cho Chew

This paper describes an augmented generalized impedance boundary condition (AGIBC) formulation for accurate and efficient modeling of conductive media. It is a surface integral equation method, so that it uses a smaller number of unknowns. The underlying GIBC provides a rigorous way to account for the skin effect. Combining with the novel augmentation technique, the AGIBC formulation works stably in the low-frequency regime. No looptree search is required. The formulation also allows for its easy incorporation of fast algorithms to enable the solving of large problems with many unknowns. Numerical examples are presented to validate the formulation.

2009-11-23 PIER Vol. 99, 245-260, 2009. doi:10.2528/PIER09101105

Exploitation of TE-TM Scattering Data for Microwave Imaging through the Multi-Scaling Reconstruction Strategy

Lorenzo Poli and Paolo Rocca

In this paper, the solution of two-dimensional inverse scattering problems is addressed by probing the unknown scenarios with TE and TM waves. To better exploit the information content of the scattered data the multi-zooming approach is used. The results of experiments with single as well as multiple scatterers are reported and discussed also in comparison with single-polarization inversions.

2009-11-23 PIER Vol. 99, 225-244, 2009. doi:10.2528/PIER09092309

Specialty Fibers Designed by Photonic Crystals

Najmeh Nozhat and Nosrat Granpayeh

In this paper, several kinds of photonic crystal fibers (PCFs) have been proposed and characterized. Two types of PCF structures have been proposed, air holes in silica or silica rods in air in a triangular lattice around the core. It has been shown that by reshaping the cladding holes, varying the diameters of the holes in one or two rows around the core or changing the refractive index of the holes, different types of specialty fibers, such as dispersion shifted fibers (DSFs), non-zero dispersion shifted fibers (NZ-DSFs), dispersion flattened fibers (DFFs), dispersion compensating fibers (DCFs), and polarization maintaining fibers (PMFs), can be designed. The PCF core is silica to support the propagation of lightwave by total internal reflection (TIR) in the third telecommunication window. The chromatic dispersion, confinement loss and modal birefringence of the proposed specialty fibers have been numerically derived.

2009-11-23 PIER Vol. 99, 211-224, 2009. doi:10.2528/PIER09101502

Study STAP Algorithm on Interference Target Detect Under Nonhomogenous Environment

Qingyong Gong and Zhao-Da Zhu

In conventional statistical STAP algorithms, the existence of interference target in training samples will lead to signal cancellation, resulting in the output SCR falling and the moving target detection performance degrading. The nonhomogeneity detector is an effective way to restrain the outlier, which can improve the covariance matrix estimation by detecting the samples containing outliers and rejecting them, and improve the STAP performance. A new interference target detection algorithm is proposed in this paper, the outlier detection is realized by using the samples' data phase information. Compared with traditional method, the improved algorithm is more sensitive to interfering target with different azimuth and intensity. Simulation results demonstrate the validity of this improved method.

2009-11-20 PIER Vol. 99, 195-209, 2009. doi:10.2528/PIER09092404

Convergence Study of Current Sampling Profiles for Antenna Design in the Presence of Electrically Large and Complex Platforms Using Fit-UTD Hybridization Approach

Heng-Tung Hsu, Fang-Yao Kuo, and Hsi-Tseng Chou

Designing antennas in the presence of electrically large and complex structures such as cars or aircrafts has become an important issue for next generation communication systems. Based on the principle of equivalence, the hybridization approach integrating FIT-UTD techniques has shown its superiority in terms of its computing efficiency. In such approach, discrete samplings of continuous electric or magnetic field components resulted from low frequency (LF) sub-domain are required to be converted to the excitation current sources for the high frequency (HF) sub-domain. Thus, the overall accuracy of the calculation results will strongly depend on the similarities between the sampled and original field distributions with both the magnitude and phase involved. In this paper, convergence study of electric and magnetic current sampling is performed. Impact of the different sampling profiles on the overall accuracy is also investigated through numerical examples. Results reveal that convergence of the far-field radiation patterns are closely related to the sampling profiles.

2009-11-19 PIER Vol. 99, 179-194, 2009. doi:10.2528/PIER09102603

Ideally Hard Struts to Achieve Invisibility

Jose-Manuel Fernandez Gonzalez, Eva Rajo-Iglesias, and Manuel Sierra-Castaner

In this work, ideally hard struts with different cross sections are analyzed. Firstly, the characterization of the invisibility of a given object in terms of an equivalent blockage width is discussed. Then, the effect of the incidence angle on struts for reducing electromagnetic blockage using the same ideally hard cylinders is analyzed. It is shown that the variation of incidence angle in azimuth is very sensitive in terms of blockage for both polarizations. Finally, design charts for ideally hard struts which reduce blockage simultaneously for TE and TM cases are presented. This can be used to define some performance goals for final realized struts.

2009-11-19 PIER Vol. 99, 163-178, 2009. doi:10.2528/PIER09102801

Exotic Characteristics of Power Propagation in the Chiral Nihility Fiber

Jian-Feng Dong

The novel characteristics of power propagation of guided modes in the chiral nihility fiber have been investigated theoretically. The formulas of electromagnetic fields in the core and cladding for guided modes are presented in detail. The dispersion equations, energy flux and power of guided modes are derived. The numerical results are given and discussed. Some exotic features of power propagation have been found in the chiral nihility fiber.

2009-11-18 PIER Vol. 99, 149-161, 2009. doi:10.2528/PIER09102201

Further Study of Rainfall Effect on VHF Forested Radio-Wave Propagation with Four-Layered Model

Yu Song Meng, Yee Hui Lee, and Boon Chong Ng

In this paper, rainfall effect on the VHF radio-wave propagation in a tropical forest is further studied in details. Theoretical study and experimental investigations are performed with the help of a four-layered model for forested environment. It is found that the lateral wave traveling along the air-canopy interface, the direct waves, and the ground reflected waves are the main modes for VHF radio-wave propagation in forest. The rainfall can affect these propagating waves to different extents. Especially, due to the increase in the dielectric permittivity of the wet canopy layer by rain water, the time of arrival of the direct wave traveling through the canopy layer can be delayed significantly. Finally, the dielectric permittivity for the wet canopy layer under different rain events is evaluated empirically.

2009-11-17 PIER Vol. 99, 131-148, 2009. doi:10.2528/PIER09091605

Maxwell Garnett Rule for Dielectric Mixtures with Statistically Distributed Orientations of Inclusions

Marina Koledintseva, Richard E. DuBroff, and Robert W. Schwartz

An analytical model of an effective permittivity of a composite taking into account statistically distributed orientations of inclusions in the form of prolate spheroids will be presented. In particular, this paper considers the normal Gaussian distribution for either zenith angle, or azimuth angle, or for both angles describing the orientation of inclusions. The model is an extension of the Maxwell Garnett (MG) mixing rule for multiphase mixtures. The resulting complex permittivity is a tensor in the general case. The formulation presented shows that the parameters of the distribution law for orientation of inclusions affect the frequency characteristics of the composites, and that it is possible to engineer the desirable frequency characteristics, if the distribution law is controlled.

2009-11-17 PIER Vol. 99, 109-129, 2009. doi:10.2528/PIER09092510

Synthesis of Monopulse Sub-Arrayed Linear and Planar Array Antennas with Optimized Sidelobes

Giacomo Oliveri and Lorenzo Poli

In this paper, three approaches for the synthesis of the optimal compromise between sum and difference patterns for sub-arrayed linear and planar arrays are presented. The synthesis problem is formulated as the definition of the sub-array configuration and the corresponding sub-array weights to minimize the maximum level of the sidelobes of the compromise difference pattern. In the first approach, the definition of the unknowns is carried out simultaneously according to a global optimization schema. Differently, the other two approaches are based on a hybrid optimization procedures, exploiting the convexity of the problem with respect to the sub-array weights. In the numerical validation, representative results are shown to assess the effectiveness of the proposed approaches. Comparisons with previously published results are reported and discussed, as well.

2009-11-14 PIER Vol. 99, 89-108, 2009. doi:10.2528/PIER09091203

Extended Exact Transfer Function Algorithm for Bistatic SAR of Translational Invariant Case

Jinping Sun, Shiyi Mao, Guohua Wang, and Wen Hong

This paper presents an Extended Exact Transfer Function (EETF) algorithm for Bistatic Synthetic Aperture Radar (BiSAR) imaging of a Translational Invariant (TI) case. This algorithm adopts directly the 2D transfer function of monostatic SAR (MoSAR), instead of deriving a new one, by converting the BiSAR into an equivalent MoSAR. A new azimuth phase compensation function is constructed through exploiting this equivalency. Geometry distortion correction for BiSAR imaging result is considered in the proposed algorithm. In addition, the applying condition of the algorithm is also discussed. One desirable property of the proposed algorithm is that the computing flow and efficiency are the same as ETF algorithm for MoSAR. The effectiveness is validated by point target simulations with Tandem and forward-looking configuration.

2009-11-10 PIER Vol. 99, 71-88, 2009. doi:10.2528/PIER09100301

FPGA-Based Chirp Generator for High Resolution UAV SAR

Chua Ming Yam and Voon Koo

This paper discusses the design and development of a FPGA-based chirp generator for high resolution Unmanned Aerial Vehicle (UAV) Synthetic Aperture Radar. The desired bandwidth of the chirp signal is 100 MHz (combination of I and Q channels) with a chirp rate of 5 MHz/μs. Two algorithms based on the Memory-based architecture and the Direct Digital Synthesizer (DDS) architecture are presented. The measurement results indicate that the DDS chirp generator is a preferred choice for high-resolution SAR application.

2009-11-10 PIER Vol. 99, 53-70, 2009. doi:10.2528/PIER09101603

Estimation of Core Temperature Elevation in Humans and Animals for Whole-Body Averaged SAR

Akimasa Hirata, Hironori Sugiyama, and Osamu Fujiwara

Biological effects due to whole-body radio-frequency exposure may be induced by core temperature elevation. According to the international safety guidelines/standards for human protection, the whole-body averaged specific absorption rate (WBA-SAR) is used as a metric. In order to understand the relationship between WBA-SAR and core temperature elevation, a theoretical solution or a closed formula for estimating core temperature elevation is essential. In the present study, we derived a formula for simply estimating core temperature elevation in humans and animals due to whole-body radio-frequency exposure. The core temperature elevation estimated with the formula is found to be in reasonable agreement with the computational results of finite-difference time-domain computation incorporated in anatomically-based models. Based on the formula, the WBA-SAR is found to be a good metric for estimating core temperature elevation. The main factors influencing the core temperature elevation are the perspiration rate and the body surface area-to-weight ratio.

2009-11-10 PIER Vol. 99, 37-52, 2009. doi:10.2528/PIER09091708

Resonant Transparency of a Three-Layer Structure Containing the Dense Plasma Region

Natalia Sternberg and Andrei I. Smolyakov

A study of electromagnetic wave propagation in dense plasmas when the wave frequency is below the cut-off frequency is presented. A three-layer symmetric structure consisting of dense plasma nested between two boundary layers is studied analytically and numerically. The permittivity of the dense plasma is negative, while the permittivity of each boundary layer is greater than 1. It is shown that total transmission of an electromagnetic wave can be achieved if an adequate incidence angle, dielectric permittivity of the boundary layers and corresponding boundary layer widths are chosen. It is found that plasma transparency is due to resonance between the evanescent waves in the dense plasma region and the standing waves in the boundary layers. Resonance conditions are derived analytically and the relationship between the corresponding parameters of the problem are studied numerically.

2009-11-10 PIER Vol. 99, 21-36, 2009. doi:10.2528/PIER09101204

Analysis of Scattering by Large Inhomogeneous BI-Anisotropic Objects Using AIM

Li Hu, Joshua Le-Wei Li, and Tat Yeo

In this paper, electromagnetic scattering of a plane wave by large inhomogeneous arbitrarily shaped bi-anisotropic objects is solved by Adaptive Integral Method (AIM). Based on Maxwell equations and constitutive relationship for general bi-anisotropic media and using Volume Integral Equations (VIE), the electromagnetic fields are derived as functions of equivalent volume sources. Then the integral equations are discretized using Method of Moments (MoM). Because of the dense matrix property, MoM cannot be used to solve electromagnetic scattering by large objects. Therefore, AIM is adopted to reduce the memory requirement and speed up the solution process. Comparison between AIM and MoM with respect to CPU time and memory requirement is done to show the efficiency of AIM in solving electromagnetic scattering by large objects. Numerical results are obtained for some canonical cases and compared with Mie theory, in which excellent agreement is observed. some new numerical results are also presented for the more general bi-anisotropic material media.

2009-11-10 PIER Vol. 99, 1-20, 2009. doi:10.2528/PIER09100204

Comparison of Planar and Circular Antenna Configurations for Breast Cancer Detection Using Microwave Imaging

Raquel Cruz Conceicao, Martin O'Halloran, Martin Glavin, and Edward Jones

Ultra Wideband (UWB) radar is a promising emerging technology for breast cancer detection based on the dielectric contrast between normal and tumour tissues at microwave frequencies. One of the most important considerations in developing a UWB imaging system is the configuration of the antenna array. Two specfic configurations are currently under investigation, planar and cylindrical. The planar configuration involves placing a conformal array of antennas on the naturally attened breast with the patient lying in the supine position. Conversely, the circular configuration involves the patient lying in the prone position, with the breast surrounded by a circular array of antennas. In order to effectively test the two antenna configurations, two 2D Finite-Difference Time-Domain (FDTD) models of the breast are created, and are used to simulate backscattered signals generated when the breast is illuminated by UWB pulses. The backscattered signals recorded from each antenna configuration are passed through a UWB beamformer and images of the backscattered energy are created. The performance of each imaging approach is evaluated by both quantitative methods and visual inspection, for a number of test conditions. System performance as a function of number of antennas, variation in tissue properties, and tumour location are examined.