**List of Jour****nal Publications**

*This page cont**ains Joe LoVetri's research contributions that have already appeared in journals. *

**Last Update: November 22, 2014.**

**[JP62]** A. Baran, D. Kurrant, A. Zakaria, Fear, J. LoVetri, "Breast Imaging Using Microwave Tomography with Radar-Based Tissue-Regions Estimation," *Progress In Electromagnetics Research*, Vol. 149, 161–171, 2014.

- Microwave tomography (MWT) and a radar-based region estimation technique are combined to create a novel algorithm for biomedical imaging with a focus on breast cancer detection and monitoring. The region estimation approach is used to generate a patient-specific spatial map of the breast anatomy that includes skin, adipose and fibroglandular regions, as well as their average dielectric properties. This map is incorporated as a numerical inhomogeneous background into an MWT algorithm based on the finite element contrast source inversion (FEM-CSI) method. The combined approach reconstructs finer structural details of the breast and better estimates the dielectric properties than either technique used separately. Numerical results obtained with the novel combined algorithmic approach, based on synthetically generated breast phantoms, show significant improvement in image quality.

**[JP61]** M. Asefi, M. OstadRahimi, A. Zakaria, J. LoVetri, "A Three-Dimensional Dual-Polarized Near-field Microwave Imaging System"* IEEE Transactions on Microwave Theory and Techniques*, Vol. 62, No. 8, Aug., pp. 1790-1797, 2014.

- A novel 3-D dual-polarized microwave imaging
system based on the modulated scattering technique (MST) is
presented. The system collects the magnitude and phase of the
scattered field using 120 MST probes and 12 transmitter/collector
antennas distributed around an object-of-interest in the near-field

region. The 12 antennas form a middle circumferential layer while the printed MST probes are arranged on three circumferential layers including the middle layer. The antennas are linearly polarized double-layer Vivaldi antennas, each fixed inside its own cylindrical conducting cavity and slanted with respect to

the vertical axis of the imaging chamber. The MST probes are etched on both sides of a thin substrate and loaded with five evenly distributed p-i-n diodes along their length. These are positioned vertically and horizontally so that the z- and phi-components of the electric field is measured. Field data are collected using MST, calibrated, and then inverted using a multiplicatively regularized finite-element contrast source inversion algorithm. The system performance is evaluated by collecting and inverting data from different 3-D targets.

**[JP60]** M. OstadRahimi, L. Shafai, J. LoVetri, "Analysis of a Double-Layered Vivaldi Antenna Inside a Metallic Enclosure" *Progress In Electromagnetics Research*, Vol. 143, 503-518, 2013.

- A double-layered Vivaldi antenna enclosed by a metallic cylindrical cavity is investigated. The antenna is correlated to the same-size circular horn antenna to exploit the equivalent modal distribution of the Vivaldi-cavity antenna. It is shown that the TM11 and TE11 are the dominant modes and the proposed antenna operates similar to a dual-mode conical horn. The antenna is fabricated and successfully tested. The radiation characteristics, mutual coupling, as well as cross-polarization level are compared to a similarly sized Vivaldi without any metallic enclosure.

**[JP59]** A. Zakaria, I. Jeffrey, J. LoVetri, "Full-Vectorial Parallel Finite-Element Contrast Source Inversion Method," *Progress In Electromagnetics Research*, Vol. 142, pp. 463-483, 2013.

- The multiplicatively regularized fnite-element contrast source inversion algorithm (MR-FEM-CSI) is used to solve the full-vectorial three-dimensional (3D) inverse scattering problem. The contrast and contrast-source optimization variables are located at the centroids of tetrahedra within the problem domain; whereas the electric feld is expanded in terms of edge basis functions on the same tetrahedra. A dual-mesh is created in order to apply the multiplicative regularization. To handle large-scale problems the inversion algorithm is parallelized using the MPI library, with sparse matrix and vector computations supported by PETSc. The algorithm is tested using experimental datasets obtained from the Institut Fresnel database. A synthetic example shows that the technique is able to successfully image moisture hot-spots within a partially filled grain bin.

**[JP58]** C. Gilmore, A. Zakaria, S. Pistorius, J. LoVetri,"Microwave Imaging of Human Forearms: Pilot Study and Image Enhancement," *International Journal of Biomedical Imaging*," Vol. 2013, Article ID 673027, 17 pages, doi:10.1155/2013/673027.

- We present a pilot study using a microwave tomography system in which we image the forearms of 5 adult male and female volunteers between the ages of 30 and 48. Microwave scattering data were collected at 0.8 to 1.2GHz with 24 transmitting and receiving antennas located in a matching fluid of deionized water and table salt. Inversion of the microwave data was performed with a balanced version of the multiplicative-regularized contrast source inversion algorithm formulated using the finite-element method(FEM-CSI). T1-weighted MRI images of each volunteer’s forearm were also collected in the same plane as the microwave scattering experiment. Initial “blind” imaging results fromthe utilized inversion algorithm showthat the image quality is dependent on the thickness of the arm’s peripheral adipose tissue layer; thicker layers of adipose tissue lead to poorer overall image quality. Due to the exible nature of the FEM-CSI algorithm used, prior information can be readily incorporated into the microwave imaging inversion process. We show that by introducing prior information into the FEM-CSI algorithm the internal anatomical features of all the arms are resolved, significantly improving the images. The prior information was estimated manually from the blind inversions using an ad hoc procedure.

**[JP57]** M. OstadRahimi, P. Mojabi, A. Zakaria, J. LoVetri, L. Shafai, "Enhancement of Gauss-Newton Inversion Method for Biological Tissue Imaging,"* IEEE Transactions on Microwave Theory and Techniques*, Vol. 61, No. 9, Sept. 2013, pp. 3424-3434.

- The multiplicatively regularized Gauss–Newton inversion (GNI) algorithm is enhanced and utilized to obtain complex permittivity profiles of biological objects-of-interest. The microwave scattering data is acquired using a microwave tomography system comprised of 24 co-resident antennas immersed into a saltwater matching fluid. Two types of biological targets are imaged: ex vivo bovine legs and in vivo human forearms. Four different forms of the GNI algorithm are implemented: a blind inversion, a balanced inversion, a shape-and-location inversion, and a novel balanced shape-and-location inversion. The latter three techniques incorporate typical permittivity values of biological tissues as prior information to enhance the reconstructions. In those images obtained using the balanced shape-and-location reconstruction algorithm, the various parts of the tissue being imaged are clearly distinguishable. The reconstructed permittivity values in the bovine leg images agree with those obtained via direct measurement using a dielectric probe. The reconstructed images of the human forearms qualitatively agree with magnetic resonance imaging images, as well as with the expected dielectric values obtained from the literature.

**[JP56]** M. OstadRahimi, A. Zakaria, J. LoVetri, L. Shafai "A Near-Field Dual Polarized (TE-TM) Microwave Imaging System,"* IEEE Transactions on Microwave Theory and Techniques*, Vol. 61, No. 3, March 2013, pp. 1376-1384.

- In this paper, we introduce a novel dual polarized microwave imaging system. The system is comprised of a circular array of multiplexed antennas, distributed evenly around an object-of-interest (OI), along with a novel plurality of probes located at the antennas’ apertures. Each probe consists of several p-i-n diodes biased in two different states (open and short). The probes are used to measure field scattered by an OI based on the modulated scatterer technique. Half of the probes are oriented vertically with the second half oriented horizontally. The presence of the two probe-orientations enables the imaging system to collect two orthogonal field polarizations, transverse electric (TE) and transverse magnetic (TM), without the need for mechanical rotation. In order to illuminate the object with all possible polarizations of the electromagnetic field, the transmitting antennas are placed at a slant angle with respect to the longitudinal plane of the imaging chamber. Near-field data are collected using each probe set, then calibrated.We show that the calibrated data for each polarization can be used to reconstruct the dielectric profile of various objects using either two-dimensional TE or TM inversion algorithms.

**[JP55]** C. Gilmore,A. Zakaria, J. LoVetri, S. Pistorius "A Study of Matching Fluid Loss in a Biomedical Microwave Tomography System," *Medical Physics*, Vol. 40, No. 2, February 2013, 14 pages.

- Purpose: Effective imaging of human tissue with microwave tomography systems requires a matching fluid to reduce the wave reflections at the tissue boundary. Further, in order to match the idealized mathematical model used for imaging with the complicated physical measurement environment, loss must be added to the matching fluid. Both too little and too much loss result in low-quality images, but due to the nonlinear nature of the imaging problem, the exact nature of loss-to-image quality cannot be predicted a priori. Possible optimal loss levels include a single, highly sensitive value, or a broad range of acceptable losses. Herein, the authors outline a process of determining an appropriate level of loss inside the matching fluid and attempt to determine the bounds for which the images are the highest quality.

**[JP54]** A. Zakaria, A. Baran, J. LoVetri "Estimation and Use of Prior Information in FEM-CSI for Biomedical Microwave Tomography, *IEEE Antennas and Wireless Propagation Letters*, Vol. 11, pp. 1606-1609 (Invited Paper, Special Cluster on Microwave Imaging)

- Prior information is used to improve imaging results
obtained using the finite-element contrast source inversion
(FEM-CSI) of a microwave tomography (MWT) dataset collected
as part of a forearm imaging study. The data consist of field measurements
taken inside a prototype MWT system that uses simple
dipole antennas and a saltwater matching medium. Initial images
of the 2-D cross-sectional dielectric profile of the individuals’ arms
are reconstructed using FEM-CSI. These initial “blind” imaging
results show that the image quality is dependent on the thickness
of the arm’s peripheral adipose tissue layer: Thicker layers of adipose
tissue lead to poorer overall image quality. The poor image
quality for arms with high levels of adipose tissue is not improved
by changing the matching fluid’s complex dielectric constant.
Introducing prior information into the FEM-CSI algorithm in the
form of an inhomogeneous background consisting of an adipose
layer surrounding a muscle region provides substantial improvement

of the image quality: The internal anatomical features of the arm are resolved for each of the five datasets. Two methods are employed to estimate the arm periphery and adipose layer thickness from the blind imaging results: manual estimation and a novel image segmentation algorithm based on global optimization using simulated annealing.

**[JP53]** A. Zakaria, J. LoVetri "The Finite-Element Method Contrast Source Inversion Algorithm for 2D Transverse Electric Vectorial Problems," *IEEE Trans. on Antennas and Propagation*, Vol. 60, No. 10, October 2012, pp. 4757-4765.

- The contrast source inversion algorithmis formulated using the finite-element method for two-dimensional transverse electric microwave imaging problems. Edge-based triangular elements with vector basis functions are utilized to solve the TE electromagnetic problem. A single finite-element method (FEM) mesh is used to model both the electric field as well as the contrast-source and contrast variables used in the inverse problem. The electromagnetic field ismodeled by taking the unknown values to be the tangential components of the transverse electric field along the edges of each triangular element. The unknown contrast-source and contrast variables are located at the centroids of every triangular element of the same FEM mesh, but only inside the imaging domain. The adaptation of the FEM-contrast source inversion (FEM-CSI) algorithm to 2D-TE problems on such an arbitrary mesh requires the implementation of special transformation operators which are presented herein. The algorithm’s capabilities are demonstrated by inverting the Fresnel experimental TE datasets as well as synthetically generated data.

[**JP52**] D. Isleifson, I. Jeffrey, L. Shafai, J. LoVetri, D.G. Barber, "A Monte Carlo Method for Simulating Scattering from Sea Ice using FVTD," *IEEE Transactions on Geoscience and Remote Sensing*, Vol. 50, No. 7, July 2012, pp. 2658-2668.

- A scattering model based on a Monte Carlo method and the finite-volume time-domain (FVTD) method has been created for sea ice scattering simulations. Statistical methods were used to generate a Gaussian-distributed randomly rough surface. The Polder–Van Santen–de Loor (PVD) model was used to estimate the sea ice dielectric values with inputs based upon actual measured physical variables obtained during field-based experiments and well-known parameterizations. Scattering simulations were performed through an application of the scattered-field (SF) formulation invoked in an FVTD computational engine. Simulated SFs were compared with C-band scatterometer measurements and showed good agreement for copolarized signals in a series of case studies. The developed simulation method has the potential to be used for a variety of sea ice types under different physical conditions.

**[JP51]** I. Jeffrey, J. LoVetri, "Interfacing Thin-Wire and Circuit Subcell Models in Unstructured Time-Domain Field Solvers," *IEEE Transactions on Antennas and Propagation*, , Vol. 60, No. 4, pp. 1978-1986, April 2012.

- A method for driving and terminating Holland–
Simpson based thin-wire models by arbitrary lumped-element
circuits is proposed. The approach uses the fact that these
thin-wire models result in modified Telegrapher’s equations,
and interfacing transmission lines and lumped-element circuits
is straightforward. The thin-wire voltage and current at a circuit/wire junction can be written in terms of circuit nodal voltages nd branch currents, permitting the circuit solution to act as a boundary condition for the thin-wire system. In this work, we provide
the circuit/wire interfacing conditions and combine circuits ith Edelvik’s Holland–Simpson model that permits thin-wires to be arbitrarily oriented within an unstructured mesh. Edelvik’s
work, previously implemented for finite-difference and finite-element

time-domain solvers is formulated for the finite-volume method. Numerical and experimental results for circuit-driven thin-wire antennas are provided to validate the method.

[**JP50**] C. Gilmore, A. Zakaria, P. Mojabi, M. OstadRahimi, S. Pistorius, J. LoVetri, "The University of Manitoba Microwave Imaging Repository: A Two-Dimensional Microwave Scattering Database for Testing Inversion and Calibration Algorithms," [Measurements Corner], *IEEE Antennas and Propagation Magazine*,, Vol. 53, No.5, pp.126-133, Oct. 2011. (doi: 10.1109/MAP.2011.6138442)

- We present a repository of multi-static, near-field microwave scattering measurements. The data are presented both raw (uncalibrated), and calibrated with a scattered-field calibration. Measurements were taken with 24 co-resident Vivaldi antennas in a single plane, inside an air-filled microwave tomography system. The antennas were linearly polarized in the vertical direction, and we intended for the two-dimensional transverse magnetic (scalar) approximation to apply. Data are presented for seven targets, both metallic and dielectric, with varying geometrical complexity. Data from simple geometric targets, useful for calibration using analytic equations, are given. The repository is available from the Web site: http://www.ee.umanitoba.ca/~lovetri/EMILab/MWT_data.html.

[**JP49**] M. OstadRahimi, P. Mojabi, S. Noghanian, J. LoVetri, L.Shafai, "A Multiprobe per Collector Modulated Scatterer Technique for Microwave Tomography,"* IEEE Antennas and Wireless Propagation Letters*, Vol. 10, pp. 1445-1448, 2011.

- Scattering probes with collector antennas can be utilized for microwave tomography (MWT) applications based on the modulated scatterer technique. Using this technique, we previously demonstrated a novel tomography system that utilizes a single printed-wire probe in front of each collector of a multicollector MWT system. Each collector is implemented as a multilayer Vivaldi antenna. In this letter, the number of collector antennas is reduced while maintaining the number of probes. This results in a nonuniform distribution of probes with respect to the collectors and requires special calibration techniques to infer the scattered-field at the probe location. The advantages of using such a configuration for MWT are investigated. Image reconstructions for a number of targets using data collected from this system are shown and compared to results obtained from data collected using a standard MWT system that uses only the Vivaldi antennas. It is shown that the new configuration successfully extracts useful data at the locations of the probes, resulting in good tomographic constructions.

[**JP48**] OstadRahimi, M., Mojabi, P., Gilmore, C., Zakaria, A., Noghanian, S., Pistorius, S., LoVetri, J. "Analysis of Incident Field Modeling and Incident/Scattered Field Calibration Techniques in Microwave Tomography,"* IEEE Antennas and Wireless Propagation Letters*, Vol. 10, pp. 900-903, 2011.

- Imaging with microwave tomography systems requires both the incident field within the imaging domain as well as calibration factors that convert the collected data to corresponding data in the numerical model used for inversion. The numerical model makes various simplifying assumptions, e.g., 2-D versus 3-D wave propagation, which the calibration coefficients are meant to take into account. For an air-based microwave tomography system, we study two types of calibration techniques—incident and scattered field calibration—combined with two different incident field models: a 2-D line-source and an incident field from full-wave 3-D simulation of the tomography system. Although the 2-D line-source approximation does not accurately model incident field in our system, the use of scattered field calibration with the 2-D line-source provides similar or better images to incident and scattered field calibration with an accurate incident field. Thus, if scattered field calibration is used, a simple (but inaccurate) incident field is acceptable for our microwave tomography system. While not strictly generalizable, we expect our methodology to be applicable to most other microwave tomography systems.

[**JP47**] M. OstadRahimi, P. Mojabi, S. Noghanian, L. Shafai, S. Pistorius, J. LoVetri "A Novel Microwave Tomography System based on the Scattering Probe Technique," *IEEE Trans. on Instrumentation and Measurement*, Vol. 61, No. 2, pp. 379-390, Feb., 2012.

- In this paper, we introduce a novel microwave tomography system, which utilizes twenty-four double layered Vivaldi antennas, each of which is equipped with a diode-loaded printed-wire probe. By biasing probe’s diodes, the impedance of the probe is modified, allowing an indirect measurement of the electric field at the probe’s locations. Each printed-wire probe is loaded with five equally-spaced PIN diodes, in series. We show that the electric-field data collected in this way within the proposed tomography system can be used to reconstruct the dielectric properties of an object of interest. Reconstructions for various objects are shown. Although the results are still preliminary, sufficient experimentation has been done to delineate the advantages of such an indirect method of collecting scattered-field data for tomographic imaging purposes.

[**JP46**] P. Mojabi, J. LoVetri, L. Shafai "A Multiplicative Regularized Gauss-Newton Inversion for Shape and Location Reconstruction,"* IEEE Trans. on Antennas and Propagation*, Vol. 59, No. 12, December, pp. 4790-4802.

- A multiplicative regularized Gauss-Newton inversion
algorithm is proposed for shape and location reconstruction
of homogeneous targets with known permittivities. The data misfit
cost-functional is regularized with two different multiplicative
regularizers. The first regularizer is the weighted L2-norm total
variation which provides an edge-preserving regularization. The
second one imposes
*a priori*information about the permittivities of the objects being imaged. Using both synthetically and experimentally collected data sets, we show that the proposed algorithm is robust in reconstructing the shape and location of homogeneous targets.

[**JP45**] D. Isleifson, I. Jeffrey,L. Shafai, J. LoVetri, D.G. Barber "An Efficient Scattered-Field Formulation for Objects in Layered Media using the FVTD Method,"* IEEE Trans. on Antennas and Propagation*, Vol. 59, No. 11, Nov. 2011, pp. 4162-4170.

- A technique for efficiently simulating the scattering from objects in multi-layered media is presented. The efficiency of the formulation comes from the fact that the sources for the scattered-fields only occur at the inhomogeneities and therefore the scattered-fields impinging on the boundaries are more easily absorbed. To demonstrate the technique, a 1D-FDTD solution to the plane-wave propagation through a multi-layered medium is used as an incident-field source for a scattered-field formulation of the FVTD method. Practical aspects of the application are discussed and numerical examples for scattering from canonical objects are presented to show the validity of the proposed technique. The simulation scheme described herein can be used for simulations of geophysical media with appropriate specifications of the dielectric properties of the media and the inhomogeneities.

[**JP44**] A. Zakaria, J. LoVetri "Application of Multiplicative Regularization to the Finite-Element Contrast Source Inversion Method,"* IEEE Trans. on Antennas and Propagation*, Vol. 59, No. 9, pp. 3495-3489, 2011. [Link to IEEE Explorer]

- Multiplicative regularization is applied to the finite element contrast source inversion (FEM-CSI) algorithm recently developed for microwave tomography. It is described for the two dimensional (2D) transverse-magnetic (TM) case and tested by inverting experimental data where the fields can be approximated as TM. The unknown contrast, which is to be reconstructed, is represented using nodal variables and first-order basis functions on triangular elements; the same first-order basis functions used in the FEM solution of the accompanying field problem. This approach is different from other MR-CSI implementations where the contrast variables are located on a uniform grid of rectangular cells and represented using pulse basis functions. The linear basis function representation of the contrast makes it difficult to apply the weighted L2-norm total variation multiplicative regularization which requires that gradient and divergence operators be applied to the predicted contrast at each iteration of the inversion algorithm; the use of finite-difference operators for this purpose becomes unwieldy. Thus, a new technique is introduced to perform these operators on the triangular mesh.

[**JP43**] P. Mojabi, J. LoVetri "A Pre-Scaled Multiplicative Regularized Gauss-Newton Inversion," *IEEE Trans. on Antennas and Propagation*, Vol. 59, No. 8, pp. 2954-2963, August 2011.

[Link to IEEE Explorer]

- A prescaled multiplicative regularized Gauss-Newton inversion (GNI) algorithm is proposed which utilizes
*a priori*information about the expected ratio between the average magnitude of the real and imaginary parts of the true contrast as well as the expected ratio between the average magnitude of the gradient of the real and imaginary parts of the true contrast. Using both synthetically and experimentally collected data sets, we show that this prescaled inversion algorithm is successful in reconstructing both real and imaginary parts of the contrast when there is a large imbalance between the average magnitude of these two parts where the standard multiplicative regularized Gauss-Newton inversion algorithm fails. We further show that the proposed prescaled inversion algorithm is robust and does not require the*a priori*information to be exact.

[**JP42**] P. Mojabi, J. LoVetri "A Novel Microwave Tomography System Using a Rotatable Conductive Enclosure,"*IEEE Trans. on Antennas and Propagation*," Vol. 59, No. 5, pp. 1597-1605, May 2011.

[Link to IEEE Explorer]

- A novel microwave tomography (MWT) setup is proposed wherein a rotatable conductive enclosure is used to generate electromagnetic scattering data that are collected at each static position of the enclosure using a minimal antenna array having as few as only four co-resident elements. The antenna array remains fixed with respect to the target being imaged and only the boundary of the conductive enclosure is rotated. To show that non-redundant scattering data can be generated in this way several 2D transverse magnetic imaging examples are considered using single-frequency synthetic data. For each example, the reconstruction of the complex permittivity profile is compared to that obtained using a homogeneous openregion MWT setup having 16 co-resident antennas. The weighted L2-norm total variation multiplicative-regularized Gauss-Newton inversion (MR-GNI) is used for all inversions and for the new MWT setup the data collected at all positions of the conductive enclosure are inverted simultaneously. The quality of images obtained from the two systems is similar, but the advantage of the new configuration is its use of a fixed minimal antenna array which will put less of a burden on the numerical system model.

[**JP41**] A. Zakaria, C. Gilmore, J. LoVetri "Finite-element Contrast Source Inversion Method for Microwave
Imaging,"* Inverse Problems, *26 (2010) 115010. [Link to IOP]

- With respect to the microwave imaging of the dielectric properties in an imaging region, the full derivation of a new inversion algorithm based on the contrast source inversion (CSI) algorithm and a finite-element method (FEM) discretization of the Helmholtz differential operator formulation for the scattered electromagnetic field is presented. The unknown dielectric properties are represented as nodal values on a two-dimensional (2D) arbitrary triangular mesh using linear basis functions. The use of FEM to represent the Helmholtz operator allows for the flexibility of having an inhomogeneous background medium, as well as the ability to accurately model any boundary shape or type: both conducting and absorbing. The resulting sparse and symmetric FEM matrix equation can be solved efficiently, and it is shown how its solution can be used to calculate the gradient operators required in the conjugate-gradient CSI update without storing the inverse of the FEM matrix. The inversion algorithm is applied to conductive-enclosures of various shapes and unbounded-region microwave tomography configurations where the 2D transverse magnetic (TM) approximation can be applied.

[**JP40**] C. Gilmore, P. Mojabi, A. Zakaria, S. Pistorius, J. LoVetri "On Super-Resolution with an Experimental Microwave Tomography System,"* IEEE Antennas and Wireless Propagation Letters*, Vol. 9, pp. 393-396, 2010. [Link to IEEE Explorer]

- The resolution of an experimental microwave tomography (MWT) system is investigated. Using two cylindrical nylon targets and an operating frequency of 5 GHz, a separation resolution of 2 mm, or 1/30 of a wavelength, is achieved. While this resolution is among the highest reported in the literature, it is not a sufficiently robust indicator of the expected resolution obtainable for complex targets, and this is shown with further examples of more complicated targets. However, the basic separation resolution limit obtained is a good way of comparing various aspects of different MWT systems.

[**JP39**] M. OstadRahimi, S. Noghanian, L. Shafai, A. Zakaria, C. Kaye, J. LoVetri "Investigating a Double Layer Vivaldi Antenna Design for Fixed Array Field Measurement," *Int. J. Ultra Wideband Communications and Systems*, Vol. 1, No. 4, pp.282–290, 2010. [Link to Inderscience]

- Vivaldi antenna is widely known as a broadband antenna. In this paper, we investigate a modified Vivaldi antenna with improved cross polarisation working in the ultra-wideband (UWB) frequency range (3.1–10.6 GHz) to be used as multiple probes for microwave tomography system. Our study includes investigation of radiation characteristics of the antenna, antenna design steps, fabrication sensitivity effects on the antenna performance and proposing and implementing a twenty-four antenna element system for fast data acquisition, including a novel method for frequency selection in microwave tomography applications. We also studied the fidelity parameter of the antennas inside the twenty-four element setup. The mutual coupling of adjacent elements, in spite of close proximity, is less than –17dB and fidelity variations for the antennas located in front of transmitter are less than 10%.

[**JP38**] C. Gilmore, P. Mojabi, A. Zakaria, M. OstadRahimi, C. Kaye, S. Noghanian, L. Shafai, S. Pistorius, J. LoVetri, "A Wideband Microwave Tomography System with a Novel Frequency Selection Procedure," *IEEE Trans. on Biomedical Engineering*, Vol. 57, No. 4, pp. 894-904, April 2010.
[Link to IEEE Explorer]

- In this paper, we describe a 2-D wideband microwave
imaging system intended for biomedical imaging. The system is
capable of collecting data from 3 to 6 GHz, with 24 coresident
antenna elements connected to a vector network analyzer via a
2 × 24 port matrix switch. As one of the major sources of error
in the data collection process is a result of the strongly coupling
24 coresident antennas, we provide a novel method to avoid the
frequencies where the coupling is large enough to prevent successful
imaging. Through the use of two different nonlinear reconstruction
schemes, which are an enhanced version of the distorted
born iterative method and the multiplicative regularized contrast
source inversion method, we show imaging results from dielectric
phantoms in free space. The early inversion results show that with

the frequency selection procedure applied, the system is capable of quantitatively reconstructing dielectric objects, and show that the use of the wideband data improves the inversion results over single-frequency data.

[**JP37**] P. Mojabi, J. LoVetri, "Comparison of TE and TM Inversions in the Framework of the Gauss-Newton Method,"* IEEE Trans. on Antennas and Propagation*, Vol. 58, No. 4, pp. 1336-1348, 2010.
[Link to IEEE Explorer]

- The Gauss-Newton inversion method in conjunction with a regularized formulation of the inverse scattering problem is used to invert transverse electric (TE) and transverse magnetic (TM) data. The utilized data sets consist of experimental data provided by the Institut Fresnel as well as synthetic data. TheTE inversion outperformed the TM inversion when utilizing near-field scattering data collected using only a few transmitters and receivers. However, very little difference was found between TE and TM inversions when using far-field scattering data. It is conjectured that the reason for the better performance of the near-field TE result is that the near-field TE data contains more information than the near-field TM data at each receiver point. In all cases considered herein, the TE inversion required equal or fewer iterations than the TM inversion. The per-iteration computational complexity of both TE and TM inversions is discussed in the framework of the Gauss-Newton inversion method. Actual costs are consistent with the computational complexity analysis that is given.

[**JP36**] P. Mojabi, J. LoVetri, "Eigenfunction Contrast Source Inversion for Circular Metallic Enclosures," *Inverse problems*, Vol. 26, 025011 (23pp), Jan. 2010. [Link to IOP Inverse Problems]

- The microwave imaging problem is considered where an object of interest is surrounded by a circular metallic enclosure. A new contrast source inversion (CSI) algorithm which uses eigenfunction expansions of the unknowns is presented for the reconstruction of the complex dielectric profile. Orthonormal eigenfunction expansions associated with the Helmholtz operator for a homogeneous medium and Dirichlet boundary conditions are used for the unknown contrast source and the contrast functions in the CSI functional. These are also used to express the incident field, which is assumed known, as well as for expanding the inverse Helmholtz operator in the CSI functional. The imaging domain is taken to be the whole interior of the metallic enclosure. No prior information, other than keeping the permittivity profile physical, is used. Results are provided for synthetic as well as experimental data. Based on the number of eigenfunctions used, a theoretical limit to the reconstruction quality is defined. Normalized errors relative to this theoretical limit are provided for each of the synthetic data sets.

[**JP35**] C. Gilmore, J. LoVetri, "Corrigendum on 'Enhancement of microwave tomography through the use of electrically conducting enclosures'," *Inverse Problems*, Vol. 26, 019801 (7pp), Jan. 2010. [Link to IOP Inverse Problems]

- Corrigendum and comments on [JP28]

[**JP34**] P. Mojabi, J. LoVetri, "Enhancement of the Krylov Subspace Regularization for Microwave Biomedical Imaging," *IEEE Trans. on Medical Imaging*, Vol. 28, No. 12, pp. 2015-2019, Dec. 2009. [Link to IEEE Explorer]

- Although Krylov subspace methods provide fast regularization techniques for the microwave imaging problem, they cannot preserve the edges of the object being imaged and may result in an oscillatory reconstruction. To suppress these spurious oscillations and to provide an edge-preserving regularization, we use a multiplicative regularizer which improves the reconstruction results significantly while adding little computational complexity to the inversion algorithm. We show the inversion results for a real human forearm assuming the 2D transverse magnetic illumination and a cylindrical object assuming the 2D transverse electric illumination.

[**JP33**] P. Mojabi, J. LoVetri, "Overview and Classification of Some Regularization Techniques for the Gauss-Newton Inversion Method Applied to Inverse Scattering Problems," *IEEE Trans. on Antennas and Propagation*, Vol. 57, No. 9, pp. 2658-2665, 2009.

[Link to IEEE Explorer]

- Different regularization techniques used in conjunction with the Gauss-Newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories. The first category attempts to regularize the quadratic form of the nonlinear data misfit cost-functional at different iterations of the Gauss-Newton inversion method. This can be accomplished by utilizing penalty methods or projection methods. The second category tries to regularize the nonlinear data misfit cost-functional before applying the Gauss-Newton inversion method. This type of regularization may be applied via additive, multiplicative or additive-multiplicative terms. We show that these two regularization strategies can be viewed from a single consistent framework.

[**JP32**] P. Mojabi, J. LoVetri, "Microwave Biomedical Imaging Using the Multiplicatively Regularized Gauss–Newton Inversion Method," *IEEE Antennas and Wireless Propagation Letters*, Vol. 8, pp. 645-648, July 2009.

[Link to IEEE Explorer]

- The weighted
*L*2-norm total variation multiplicative regularized GaussNewton inversion method, recently developed for inversion of low-frequency deep electromagnetic geophysical measurements, is used for microwave biomedical imaging. This inversion algorithm automatically adjusts the regularization weight and provides edge-preserving characteristics. The accuracy of this method is demonstrated by inverting experimental data of a human forearm and synthetic data taken from brain and breast models, both assuming two-dimensional (2D) transverse magnetic illumination.

[**JP31**] C. Gilmore, P. Mojabi, J. LoVetri "Comparison of an Enhanced Distorted Born Iterative Method and the Multiplicative-Regularized Contrast Source Inversion Method," *IEEE Trans. on Antennas and Propagation*, Vol. 57, No. 8, pp. 2341-2351, August 2009.

[Link to IEEE Explorer]

- For 2D Transverse Magnetic (TM) microwave inversion, Multiplicative-Regularized Contrast Source Inversion (MR-CSI), and the Distorted Born Iterative Method (DBIM) are compared. The comparison is based on a computational resource analysis, inversion of synthetic data, and inversion of experimentally collected data from both the Fresnel and UPC Barcelona data sets. All inversion results are blind, but appropriate physical values for the reconstructed contrast are maintained. The data sets used to test the algorithms vary widely in terms of the background media, antennas, and far/near field considerations. To ensure that the comparison is replicable, an automatic regularization parameter selection method is used for the additive regularization within the DBIM, which utilizes a fast implementation of the
*L*-curve method and the Laplacian regularizer. While not used in the classical DBIM, we introduce an MR term to the DBIM in order to provide comparable results to MR-CSI. The introduction of this MR term requires only slight modifications to the classical DBIM algorithm, and adds little computational complexity. The results show that with the addition of the MR term in the DBIM, the two algorithms provide very similar inversion results, but with the MR-CSI method providing advantages for both computational resources and ease of implementation.

**[J30]** D.K. Firsov and J. LoVetri, "New Stability Criterion for Unstructured Mesh Upwinding FVTD Schemes for Maxwell’s Equations," *ACES Journal*, Vol. 23, No. 3, pp. 193-199, September 2008.

- A new stability criterion applicable to explicit upwind FVTD schemes for solving Maxwell’s equations on unstructured meshes is derived. This criterion is based on
*L2*-norm estimates of specially constructed matrices*Gi*for each finite volume*i*. Each such matrix is constructed using the scalar product of the eigenvectors corresponding to the unity eigenvalues of the fluxsplitting operators associated with the facets of volume*i*. The new stability criterion is obtained numerically once the grid is constructed using these matrices over the mesh and is therefore mesh dependent. The new criterion gives a time-step that is larger than the time-step calculated using previously published stability criteria. On structured meshes the new criterion gives the same time-step limit as the von Neumann analysis. The method incurs a small computational expense at the beginning of each run of the algorithm. The method is generalizable but the extent to which it can be generalized to other time-evolving physical phenomenon is not considered in this paper.

**[J29]** P. Mojabi and J. LoVetri, "Preliminary Investigation of the NCP Parameter-Choice Method for Inverse Scattering Problems Using BIM: 2-D TM Case," *ACES Journal*, Vol. 23, No. 3, pp. 207-214, September 2008.

- A new method of choosing the regularization parameter, originally developed for a general class of discrete ill-posed problems, is investigated for electromagnetic inverse scattering problems that are formulated using a penalty method. This so-called normalized cumulative periodogram (NCP) parameterchoice method uses more information available in the residual vector, as opposed to just its norm, and attempts to choose the largest regularization parameter that makes the residual resemble white noise. This is done by calculating the NCP of the residual for each choice of the regularization parameter, starting from large values and stopping at the first parameter which puts the NCP inside the Kolmogorov-Smirnov limits. The main advantage of this method, as compared, for example, to the
*L*-curve and Generalized Cross-Validation (GCV) techniques, is that it is computationally inexpensive and therefore makes it an appropriate technique for large-scale problems arising in inverse imaging. In this paper, we apply this technique to the general-form Tikhonovregularized functional arising in the 2-D/TM inverse electromagnetic problem, which is formulated via an integral equation and solved using the Born Iterative Method (BIM).

**[****J28****]** C. Gilmore and J. LoVetri, "Enhancement of microwave tomography through the use of electrically conducting enclosures,"* Inverse Problems*, vol. 24, issue 3 (21 pp), June 2008 (was online 8 April 2008)

- We consider microwave tomography (MWT) where the imaging region is surrounded by an electrically conducting surface. This surface acts as both a shield from outside interference, holding tank for any possiblematching media, and, in certain cases, serves to enhance the performance of electromagnetic (EM) inversion algorithms. For the 2D transverse magnetic (TM) case and where the surface consists of a perfect electrical conductor (PEC) in the shape of a circular cylinder, we formulate an appropriate Greens function which is amenable to implementation in the existing EM inversion codes. We utilize this Greens function in the multiplicative-regularized contrast source inversion (MR-CSI) method. Several different synthetic examples are used to test the performance of the inversion when the PEC surface is present and the results show that in many cases, the tomographic image is significantly improved. The reasons for the improved inversion results are an area of active research, but are likely to be due to the increased interrogation energy deposited into the imaging region. Results are also shown which demonstrate the problems which may arise if the unbounded domain Greens function is used in an MWT system that utilizes a matching medium of finite extent—a problem which is overcome by the inclusion of a PEC surface on the exterior of the MWT system.

**[****J27****]** P. Mojabi and J. LoVetri, "Adapting the Normalized Cumulative Periodogram Parameter-Choice Method to the Tikhonov Regularization of 2-D/Tm Electromagnetic Inverse Scattering Using Born Iterative Method,"* Progress In Electromagnetics Research M*, vol. 1, pp. 111-138, 2008.

- A new method of choosing the regularization parameter, originally developed for a general class of discrete ill-posed problems,is investigated for electromagnetic inverse scattering problems that are formulated using a penalty method. This so-called Normalized Cumulative Periodogram (NCP) parameter-choice method uses more than just the norm of the residual to determine the regularization parameter, and attempts to choose the largest regularization parameter that makes the residual resemble white noise. This is done by calculating the NCP of the residual vector for each choice of the regularization parameter, starting from large values and stopping at the first parameter which puts the NCP inside the Kolmogorov- Smirnov limits. The main advantage of this method, as compared, for example, to the
*L*-curve and Generalized Cross Validation (GCV) techniques, is that it is computationally inexpensive and therefore makes it an appropriate technique for large-scale problems arising in inverse imaging. In this paper, we apply this technique, with some modification, to the Tikhonov-regularized functional arising in the 2-D Transverse Magnetic (TM) inverse electromagnetic problem, which is formulated via an integral equation and solved using the Born iterative method (BIM).

**[****J26****]** B. Kordi, G.E. Bridges, J. LoVetri, and J.E. Nordstrom, "Full-wave Based Transmission-line Model for Lossy-substrate Multiconductor Interconnects," *Int. J. of Numerical Modelling: Electronic Networks, Devices and Fields* (Special Issue on Frontiers of Applied Computational Electromagnetics), vol. 21, no. 1-2, pp. 103-115, January-April 2008.

- A full-wave-based modal analysis is used for simulating a multiconductor coplanar waveguide (CPW) over a selectively etched lossy silicon substrate. Propagating modes, which are similar to the classic ‘common’ and ‘differential’ modes, are extracted, and circuit theory energy relationships are used for the determination of transmission-line model parameters. A time-frequency domain technique is employed for implementing the transmission-line model within a circuit simulator. The model is used to study the effect of etching the dielectric and the substrate for a two-conductor CPW line. The simulation results show that etching both the dielectric and the lossy substrate improves the loss and dispersion characteristics of the CPW line.

**[****J25****]** D.K. Firsov and J. LoVetri, "FVTD—Integral Equation Hybrid for Maxwell’s Equations," Int. J. of Numerical Modelling: Electronic Networks, Devices and Fields (Special Issue on Frontiers of Applied Computational Electromagnetics), vol. 21, no. 1-2, pp. 29-42, January-April 2008.

- A new hybrid finite-volume time-domain integral equation (FVTD/IE) algorithm for the solution of Maxwell’s Equations on unstructured meshes of arbitrary flat-faceted volume elements is presented. A time-domain IE-based numerical algorithm is applied on the boundary of the computational domain to determine the incoming fluxes for the boundary facets of the mesh. This method is a global grid-truncation technique similar to the method previously introduced for the finite-difference time-domain scheme by Ziolkowski et al. The three main advantages of this IE truncation method are that (1) it allows geometrical objects to be located (almost) arbitrarily close to the mesh boundaries without compromising the physics of the problem, (2) it couples the physics of unconnected meshes so that distant scatterers can be surrounded by their own local mesh, thus reducing total mesh size, and (3) the same IE formulation can be used to compute electromagnetic field values at points outside the mesh. Currently, the main disadvantage is that an acceleration scheme for performing the IE update, which requires integrating field components on an interior surface at a retarded time, is not available. Computational results are presented for the scattering from a perfectly electrical conducting sphere and compared numerically with the analytic time-domain solution as well as the solution obtained using a large spherical outer mesh boundary with local absorbing boundary conditions. Results are excellent and show almost no reflections from the mesh boundary even when the observation point is located close to the corner of the cubically shaped outside mesh boundary. Results are also presented and validated for the scattering from two objects that are contained inside their own unconnected meshes.

**[****J24****]** I. Jeffrey, V. Okhmatovski, J. LoVetri and C. Gilmore, "An Adaptive Basis Function Solution to the 1D and 2D Inverse Scattering Problems using the DBIM and the BIM," *ACES Journal*, vol. 22, no. 1, pp. 60-70, March 2007.

- We present the use of an adaptive set of basis functions used in conjunction with the MoM to solve the linearized scalar inverse electromagnetic scattering problem. The basis functions, which are whole-domain and harmonic, are selected to provide a perfectly conditioned solution under the first-order Born approximation when multiple frequency experiments are considered. In order to iteratively solve the full nonlinear problem by the Distorted Born Iterative Method (DBIM) and/or the Born Iterative Method (BIM), we introduce a single parameter into the basis function expansion to demonstrate that it is possible to maintain a well-conditioned linearized inverse problem by selecting the parameter value that minimizes the condition number of the discrete matrix operator. The proposed technique eliminates the need for Tikhonov regularization or equivalent regularization schemes commonly applied to the single-frequency, pulse-basis formulation of the linearized inverse scattering problem.

**[****J23****]** D. Firsov, J. LoVetri, I. Jeffrey, V. Okhmatovski, C. Gilmore, and W. Chamma, "High-Order FVTD on Unstructured Grids using an Object-Oriented Computational Engine," *ACES Journal*, vol. 22, no. 1, pp. 71-82, March 2007.

- An object-oriented implementation of a finite-volume time-domain (FVTD) engine for solving Maxwell’s equations is presented. The relevant aspects of the FVTD method are discussed from an objectoriented perspective and details of the object classes are given. Computational results obtained using the FVTD engine for solving Maxwell’s Equations on unstructured grids are also shown. The engine implements both MUSCL and polynomial interpolation methods to approximate the fluxes at the cell boundaries up to thirdorder accuracy. In addition, the engine has the capability of using a number of time-integration schemes. Results are presented for the transient scattering from a PEC sphere and a lossy dielectric cube. For the case of the sphere, almost perfect agreement with the analytic solution in the time-domain is achieved. The number of cells required as compared to FDTD is substantially reduced.

**[****J22****]** C. Gilmore, I. Jeffrey, and J. LoVetri, "Derivation and Comparison of SAR and Frequency-Wavenumber Migration Within aCommon Inverse Scalar Wave Problem Formulation," *IEEE Transactions on Geoscience and Remote Sensing*, vol. 44, no. 6, pp. 1454-1461, June 2006.

- Two common Fourier imaging algorithms used in ground penetrating radar (GPR), synthetic aperture radar (SAR), and frequency-wavenumber (F-K) migration, are reviewed and compared from a theoretical perspective. The two algorithms, while arising from seemingly different physical models: a point-scatterer model for SAR and the exploding source model for F-K migration, result in similar imaging equations. Both algorithms are derived from an integral equation formulation of the inverse scalar wave problem, which allows a clear understanding of the approximations being made in each algorithm and allows a direct comparison. This derivation brings out the similarities of the two techniques which are hidden by the traditional formulations based on physical scattering models. The comparison shows that the approximations required to derive each technique from the integral equation formulation of the inverse problem are nearly identical, and hence the two imaging algorithms and physical models are making similar assumptions about the solution to the inverse problem, thus clarifying why the imaging equations are so similar. Sample images of landmine-like targets buried in sand are obtained from experimental GPR data using both algorithms.

**[****J21****]** B. Kordi, J. LoVetri, and G. E. Bridges, "Finite-Difference Analysis of Dispersive Transmission Lines Within a Circuit Simulator," *IEEE Transactions on Power Delivery*, vol. 21, pp. 234-242, 2006.

- In this paper, a finite-difference time-domain (FDTD) analysis of the transmission line equations for a general circuit simulator is presented. A two-port circuit representation is derived for integrating a dispersive transmission line network within a circuit/system simulator. The circuit model consists of resistive elements and dependent current sources, which are updated at every time step by the FDTD algorithm. The frequency dependence of the conductors' parameters is taken care of by a recursive integration that employs the Vector Fitting algorithm. The application of this model is presented for several examples, such as nonuniform transmission lines, plane wave excitation of the line, and determination of overvoltages induced by a nearby lightning stroke.

**[****J20****]** I. Jeffrey, C. Gilmore, G. Siemens, and J. LoVetri, "Hardware invariant protocol disruptive interference for 100BaseTX Ethernet communications," *IEEE Transactions on Electromagnetic Compatibility*, vol. 46, pp. 412-422, 2004.

- In this paper, we introduce a new concept that we refer to as hardware invariant protocol disruptive interference (HIPDI). Such interference would pose a severe threat as intentional EMI to the corresponding protocol for which it was designed. In this paper, we consider only the 100BaseTX Ethernet protocol over UTP CAT-5 cable which is used extensively in local-area networks. We show that low power, narrowband, differential-mode voltage levels on a 100BaseTX Ethernet twisted-pair can seriously degrade network throughput independent of the physical features of the network or the protocol interpreter hardware. Moreover, we show that the required parameters of disruptive interference can be derived from the protocol itself using a concept we call hardware aperture. The experimental results reported herein indicate that creating such interference is practically feasible and therefore, is a possible threat to existing communication networks.

**[****J19****]** J. E. Makaran and J. LoVetri, "BLDC motor and drive conducted RFI simulation for automotive applications," *IEEE Transactions on Electromagnetic Compatibility*, vol. 45, pp. 316-329, 2003.

- In considering automotive conducted radio-frequency-interference (RFI) specifications applicable to motors and their associated drives, simulation of conducted RF emissions in the range from 150 kHz to 30 MHz is an area of interest from the product design perspective for several reasons. Traditionally, suppression of conducted noise in this frequency range of interest has been achieved through the use of bulk suppression elements such as capacitors and inductors. These elements consume valuable space within the motor, as well as add cost. The selection of bulk noise suppression elements, has, in the past, been predominately made through trial and error "brute force" methods. A method is presented whereby conducted RFI emissions can be simulated through the use of a high-fidelity virtual motor and drive model, as well as a virtual spectrum analyzer. Experimental validation of the model shows that accurate predictions can be made in the low-frequency range, below 10 MHz. Suggestions are made on how to improve the model at higher frequencies.

**[****J18****]** S. Primak, J. LoVetri, and J. Roy, "On the statistics of a sum of harmonic waveforms," *IEEE Transactions on Electromagnetic Compatibility*, vol. 44, pp. 266-271, 2002.

- In this paper, we address certain aspects of the problem of statistically characterizing the electromagnetic field inside an enclosure. The field that we are interested in describing is time-harmonic and a three-dimensional spatial vector; therefore, two random variables are required for each vector component at each location in the enclosure. We can describe either the magnitude (or intensity) and phase, or the real (in-phase) and imaginary (quadrature) parts, of each spatial component. It is the relationship between these two modes of description that is addressed in this paper. We show that this relationship is given by the Blanc-Lapierre transform and when there is a sum of more than one time-harmonic field, by equations first derived by Kluyver. The relationships are derived for any form of distribution taken on by any of the random variable. We also address issues related to the approximation of the probability density function (pdf) of the amplitude of an electromagnetic field given a known pdf of the intensity of this field. The work presented herein fills in some of the gaps which were left in some literature wherein the independence of the variables to each other was assumed, that is, the independence of the in-phase to the quadrature variables.

**[****J17****]** T. Lapohos and J. LoVetri, "Forcing term discretization techniques in the external field-to-MTL coupling problems," *International Journal of Numerical Modelling: Electronic Networks, Devices and Fields*, vol. 14, pp. 31-47, 2001.

- In this paper, two, under certain conditions, equivalent models of electromagnetic plane wave coupling to multiconductor transmission lines (MTLs) are described. The?frequency-to-time domain? (FTD) model incorporates the effect of the impinging electromagnetic waves by means of distributed voltage and current sources whose expressions are found through mathematical approximations made in the frequency domain followed by a transformation to the time domain. The approximations were made in order to gain an advantage in computation time in the discrete FTD (DFTD) model. In contrast to this approach, the same distributed sources of the?approximate analytic? (AA) model are derived by directly evaluating the corresponding integral formulas. It is shown that, although the same second-order-accurate discretization technique has been employed to create both the DFTD and the discrete AA (DAA) models, the simulation results are not the same. In the case of the DFTD model, significant numerical error can be seen in the simulation results, whereas the DAA model does not show such a behaviour. It is shown that time averaging of the forcing terms in the DFTD model helps to reduce the numerical errors significantly at no extra computational cost.

**[****J16****]** T. Lapohos, J. LoVetri, and J. Seregelyi, "External field coupling to MTL networks with nonlinear junctions: numerical modeling and experimental validation," *IEEE Transactions on Electromagnetic Compatibility*, vol. 42, pp. 16-28, 2000.

- The problem of predicting the voltages and currents induced on a printed circuit multiconductor transmission line (MTL) network by an impinging transient plane wave electromagnetic field is considered. The MTL network contains nonlinear circuit elements and test cases with various dielectric substrates are examined. Numerical predictions based on quasi-TEM models of the MTL and modified nodal analysis (MNA) models of the lumped element junctions are compared to experimental results obtained in the time domain using a GTEM cell. As has been done in the past, the effect of the incident plane wave is introduced as forcing functions in the MTL equations. The primary goal of this paper is to quantify the accuracy of the various commonly used quasi-TEM mathematical time-domain models. It is shown that when modeling the forcing function terms, it is important to take into account the perturbation of the incident plane wave due to the dielectric substrate. (The experimental-numerical comparisons herein are shown for the case of end-fire illumination since it best demonstrates this point.) Neglecting the dielectric effect on the incident transient pulse, even for substrates with low dielectric constant, produces poor results.

**[****J15****]** N. R. S. Simons, R. Siushansian, J. LoVetri, and M. Cuhaci, "Comparison of the transmission-line matrix and finite-difference time-domain methods for a problem containing a sharp metallic edge," *IEEE Transactions on Microwave Theory and Techniques*, vol. 47, pp. 2042-2045, 1999.

- We compare Yee's finite-difference time-domain (FDTD) and symmetric condensed node transmission-line matrix (SCN-TLM) solutions for a cavity containing a metallic fin. Differential equation-based numerical methods are known to produce inaccurate results for this type of problem due to the rapid spatial variation of the field distribution in the vicinity of the singularity at the edge of the metal fin. This problem is relevant to the analysis of structures of practical interest such as microstrip and coplanar waveguides. Based on simulations, it is determined that for identical discretizations, SCN-TLM is more accurate than FDTD for this problem. We interpret this result as an indication that the symmetric condensed representation of fields (used within the SCN-TLM) lends itself to a more accurate algorithm than the distributed representation used by Yee. We estimate that the FDTD method requires 3.33 times more cells for a given three-dimensional problem than the transmission-line matrix (TLM) method (1.49 times more cells per linear dimension of the problem) in order to achieve the same accuracy. If we consider the requirements to update and store a single TLM or FDTD cell, we find the SCN-TLM algorithm is more efficient than the Yee FDTD algorithm in terms of both computational effort and memory requirements. Our conclusions regarding computational effort and memory requirements are limited to problems with homogeneous material properties.

**[****J14****]** S. L. Primak, J. LoVetri, Z. Damjanschitz, and S. Kashyap, "Auto-regressive filter-based E-pulse discriminating scheme," *IEEE Transactions on Antennas and Propagation*, vol. 47, pp. 216-218, 1999.

- Ultrawide-band radar target discrimination schemes have been of great interest during the last two decades. One of the most used methods is the so-called E-pulse discrimination scheme, which is based on the late-time impulse response of a target. Traditional techniques to construct the proper E-pulses require the determination of the natural frequencies as an intermediate step. Here, we present a technique that allows us to obtain the required E-pulses directly. The approach suggested is applied to two simple three-dimensional (3D) targets: a rectangular cavity and a strip with a fin.

**[****J13****]** R. Siushansian and J. LoVetri, "Efficient evaluation of convolution integrals arising in FDTD formulations of electromagnetic dispersive media," *Journal of Electromagnetic Waves and Applications*, vol. 11, pp. 101, 1997.

- The Trapezoidal Recursive Convolution (TRC) scheme was previously used to model Nth order Lorentz type dispersive media. In this paper, the full derivation of this quasi-trapezoidal-based algorithm is presented and the derivation is expanded to include the Nth order Debye type dispersion as well as Sellmeyer's dispersion equation. In addition, the case of general convolution integrals is considered where any arbitrary integrand or the integral itself is represented as a sum of exponential functions, i.e. Prony's method. The technique is compared to several previously published schemes and it is shown that its performance equals or exceeds various other methods in terms of accuracy, robustness, and computational efficiency. A comparison to the exact application of trapezoidal numerical integration is made and it is shown that, for time increments encountered in typical FDTD analyses, the truncation error due to applying the quasi-trapezoidal approximation is negligible. Finally, it is shown how the skin effect phenomenon, as it applies to multiconductor transmission lines, can be modeled using a rational function approximation to the frequency dependency of the line resistance. This model is obtained by using Levy's method to curve fit the line resistance directly in the frequency domain and then the convolution integral is formulated in a form amenable to the TRC algorithm.

**[****J12****]** J. LoVetri and T. Lapohos, "Explicit upwind schemes for lossy MTLs with linear terminations," *IEEE Transactions on Electromagnetic Compatibility*, vol. 39, pp. 189-200, 1997.

- The time domain multiconductor transmission line (MTL) equations are written as a general first order system of partial differential equations and a characteristic decomposition is used to obtain first order and second order accurate upwind differencing schemes. Linear boundary conditions in the form of generalized Thevenin equivalent sources are incorporated into the scheme. These schemes are compared with the standard time-space centered second order accurate leapfrog scheme where the current and voltage variables are interlaced in space and time. For any general explicit numerical scheme, for a given MTL, only the fastest propagating TEM mode can be solved for at the Courant limit of the scheme. This causes the other slower modes to disperse. The results of our comparisons, show that at the Courant number both upwind schemes produce less numerical dispersion for the slower propagating modes than the standard leapfrog scheme under the same conditions. In addition, the Courant number of the second order upwind scheme is twice that of the leapfrog scheme. These advantages make the upwind schemes better tools to model inhomogeneous MTLs with linear terminations.

**[****J11****]** M. Rizvi and J. LoVetri, "Modeling and reduction of crosstalk on coupled microstrip line structures and multichip modules: an FDTD approach," *International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering*, vol. 6, pp. 58, 1996.

- The finite difference time domain modeling technique is used to model the near end and far end crosstalk on coupled microstrip structures used in multichip modules. The lines are terminated in lumped resistors which closely, but not exactly, match the lines. One line is excited by a Gaussian voltage pulse produced by a Thevenin equivalent voltage source. It is shown that adding dielectric strips in the substrate below the conducting lines will reduce the peak crosstalk by as much as 80%. Eight different configurations are modeled consisting of dielectric strips with different dielectric constant combinations. All configurations are modeled with and without a metal case in order to make sure that the crosstalk reduction persists when the structure is enclosed in a metallic enclosure (this would be the case for multichip modules). The results show that using dielectric strips with the smallest possible dielectric constant reduces crosstalk the most.

**[****J10****]** J. LoVetri, D. Mardare, and G. Soulodre, "Modeling of the seat dip effect using the finite-difference time-domain method," *The Journal of the Acoustical Society of America*, vol. 100, pp. 2204-2212, 1996.

- In this paper the use of the finite-difference time-domain technique for the modeling of the seat dip effect in concert halls is demonstrated. The linear time-domain acoustic partial differential equations are discretized using a finite-difference technique. The second-order accurate differencing scheme is time–space centered, and the velocity and pressure are solved on an interlaced mesh. First- and second-order Mur absorbing boundary conditions, originally formulated for electromagnetic problems, are adapted to the acoustics case and used to truncate the numerical grid. The technique is first verified by comparing the numerical results to the analytic solution of a simple point source. Results from computer simulations of the seat dip phenomena are compared with the findings of previous studies where measurements had been made on scale models and in real concert halls. The computer model successfully predicts the effects associated with the source–receiver distance, the height of the receiver, and the height of the source.

**[****J09****]** R. Siushansian and J. LoVetri, "A comparison of numerical techniques for modeling electromagnetic dispersive media," *IEEE Microwave and Guided Wave Letters*, vol. 5, pp. 426-428, 1995.

- A comparison of various time domain numerical techniques to model material dispersion is presented. Methods that model the material dispersion via a convolution integral as well as those that use a differential equation representation are considered. We have shown how the convolution integral arising in the electromagnetic constitutive relation can be approximated by the trapezoidal rule of numerical integration and implemented using a newly derived one-time-step recursion relation. The superiority of the new method, in terms of accuracy and computer resources, over four previously published techniques is demonstrated on the problem of a transient electromagnetic plane wave propagating in a dispersive media. All of the methods considered are easily incorporated into 3-D codes where the requirement for efficiency is very important.

**[****J08****]** D. Mardare and J. LoVetri, "The finite-difference time-domain solution of lossy MTL networks with nonlinear junctions," *IEEE Transactions on Electromagnetic Compatibility*, vol. 37, pp. 252-259, 1995.

- We describe a numerical technique to solve lossy multiconductor transmission line (MTL) networks, also known as tube/junction networks, which contain nonlinear lumped circuits in the junctions. The method is based on using a finite-difference technique to solve the time-domain MTL equations on the tubes, as well as the modified nodal analysis (MNA) formulation of the nonlinear lumped circuits in the junctions. The important consideration is the interface between the MTL and MNA regimes. This interface is accomplished via the first and last finite-difference current/voltage pair on each MTL of the network and, except for this, the two regimes are solved independently of each other. The advantage of the FDTD method is that the MTL equations may contain distributed source terms representing the coupling with an external field. We apply the method to previously published examples of multiconductor networks solved by other numerical methods, and the results agree exceptionally well. The case of an externally coupled field is also considered.

**[****J07****]** J. B. Ehrman and J. LoVetri, "Time-domain electromagnetic plane waves in static and dynamic conducting media. II," *IEEE Transactions on Electromagnetic Compatibility*, vol. 37, pp. 17-25, 1995.

- The electromagnetic field inside a lossy half-space for the case of a transient electromagnetic plane wave impinging on the half-space from free space is derived. The losses in the half-space are modeled by assuming either a static (J=σE) or a dynamic (τ∂J/∂t+J=σ0E) conducting medium. Solutions are derived directly from the first order system of partial differential equations, i.e. the Maxwell equations. Plots for the total fields at the half-space boundary are given and expressions for the fields anywhere inside the half-space based on these boundary fields are given. Asymptotic formulae for late and early times are derived for the case of a step function as well as a square pulse plane wave

**[****J06****]** M. Krumpholz, P. Russer, J. LoVetri, and N. R. S. Simons, "Comments on "A class of symmetrical condensed node TLM methods derived directly from Maxwell's equations"; [and reply]," *IEEE Transactions on Microwave Theory and Techniques*, vol. 42, pp. 1586, 1994.

- In the original paper, LoVetri and Simons [see ibid, vol.41, p. 1419-28,1993] derive the three-dimensional symmetrical condensed node TLM algorithm using a characteristic based field decomposition of Maxwell's equations. The goal and eventual result of the investigation was to present a mathematically sound method for deriving the TLM scattering and transfer events directly from Maxwell's equations (without recourse to the approximation of space by a mesh of transmission lines). The statement made by Krumpholz and Russer, that the original derivation is erroneous, is not valid and the two specific points they raise are considered

**[****J05****]** J. LoVetri and J. B. Ehrman, "Time-domain electromagnetic plane waves in static and dynamic conducting media. I," *IEEE Transactions on Electromagnetic Compatibility*, vol. 36, pp. 221-228, 1994.

- Solutions are derived for the time-domain Maxwell equations for static (J=σE) and dynamic (τ∂/∂t+J= σ0 E) conducting media where the field is assumed to vary with respect to only one spatial direction, i.e., plane-wave propagation. The plane wave is introduced into the media via the imposition of an electric field boundary condition at the plane boundary of a half-space and it is assumed that the fields inside the half-space are initially zero. Solutions are derived directly from the first-order system of partial differential equations and it is shown that once the electric field at the plane boundary is imposed, the magnetic field is automatically determined for causal solutions. It is shown that the form of the Maxwell equations, without a magnetic conductivity term added, is sufficient to allow well and uniquely defined solutions of this problem.

**[****J04****]** J. LoVetri and N. R. S. Simons, "A class of symmetrical condensed node TLM methods derived directly from Maxwell's equations," *IEEE Transactions on Microwave Theory and Techniques*, vol. 41, pp. 1419-1428, 1993.

- A series of general transmission line matrix (TLM)-type methods, which include the symmetrical condensed node method, are derived directly from Maxwell's curl equations without recourse to transmission line models. Written as a system of conservation laws, Maxwell's equations in 3-D plus time are decomposed along the orthogonal characteristic directions of a rectangular grid. The Riemann invariants in this method correspond to the voltage pulses of the TLM method. A new method of handling inhomogeneous media is proposed based on a new transfer event. The dispersive nature of these schemes is also investigated.

**[****J03****]** J. LoVetri and G. I. Costache, "Efficient implementation issues of finite difference time-domain codes for Maxwell's equations," *International Journal of Numerical Modelling: Electronic Networks, Devices and Fields*, vol. 6, pp. 195-206, 1993.

- The computer implementation of time-domain finite difference methods for the solution of Maxwell's equations is considered. As the basis of this analysis, Maxwell's equations are expressed as a system of hyperbolic conservation laws. It is shown that, in this form, all the well-known differencing schemes can be easily expressed, thus increasing the applicability of the implementation issues to be discussed. Practical issues, such as computational efficiency and memory requirements, are discussed for the implementation of the finite difference schemes. Advanced programming techniques in the C language are used to implement the finite difference schemes discussed. The example of the penetration of electromagnetic energy through a shield with a thick gap is used to check the performance of the methods. It is shown that, for cases where the disturbance remains localized in the computational mesh, these techniques result in memory and CPU time savings.

**[****J02****]** J. LoVetri and G. I. Costache, "An electromagnetic interaction modeling advisor," *IEEE Transactions on Electromagnetic Compatibility*, vol. 33, pp. 241-251, 1991.

- A knowledge-based approach for the modeling of electromagnetic (EM) interactions in a system is described. The purpose is to determine any unwanted EM effects that could jeopardize the safety and operation of the system. Modeling the interactions in a system requires the examination of the compounded and propagated effects of the EM fields. A useful EM modeling approach is one that is incremental and constraint-based. The approach taken here subdivides the modeling task into two parts: (a) the definition of the related EM topology and (b) the propagation of the EM constraints. A prototype of some of the EM constraints has been implemented in Quintus Prolog under NeWS on a Sun workstation. User interaction is through a topology drawing tool and a stack-based attribute interface similar to the HyperCard interface of the Apple Macintosh computer.

**[****J01****]** J. LoVetri and M. Hamid, "Coulomb wave functions in the theory of the circular paraboloidal waveguide," *Canadian Journal of Physics*, vol. 66, pp. 212, 1988.

- It is shown how Coulomb wave functions, commonly used in the description of a Coulomb field surrounding a nucleus, can be used in the description of electromagnetic fields that are symmetric with respect of phi inside a paraboloidal waveguide. The Abraham potentials Q and U, which are useful in describing fields with rational symmetry, are used to simplify the problem. It is shown that these potentials must satisfy a partial differential equation that when separated yields the Coulomb wave equation of order L=0. Electromagnetic fields due to simple source distributions inside the paraboloid are expanded in terms of these functions. Specifically, solutions for current-loop sources located in the focal plane of the paraboloid are obtained. The case where the wall of the paraboloidal waveguide is assumed to be perfectly conducting is treated as well as the case where the wall has finite impedance. The finite paraboloid is also considered, and the far field is formulated using Huygen's principle. It is found that for the finite surface-impedance case, the far-field pattern due to a current loop operating at 100 MHz in the focal plane of a paraboloidal reflector of 1 m focal length is different from the perfectly conducting case. Specifically, the pattern seems to be more omnidirectional for the impedance case than the perfectly conducting case. Numerical results are presented for relevant aspects of the problem.

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