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2012-06-25
PIER B
Vol. 41, 419-439, 2012
download: 162
High Frequency Electromagnetic Field Modeling and Experimental Validation of the Microwave Drying of Wheat Seeds
Vasile Darie Soproni Simina Maria Vicas Teodor Leuca Mircea N. Arion Francisc Ioan Hathazi Carmen Otilia Molnar
The aim of this study is to determine the effects of the thermal treatment with microwaves on the germination of wheat seeds, type Apache × Renan for different processing parameters. With the experimental data we intend to find out the optimum balance between applied energy and material humidity so that the material can be dried without its structure being adversely affected. From the analyze of experiments regarding wheat seeds drying with the aim of obtaining a quality product we mention that the best results are referring to the situation of using the microwave power of 0.3 W/g combined with hot air stream and having the measured temperature in the seed bed below the value of 75°C.
HIGH FREQUENCY ELECTROMAGNETIC FIELD MODELING AND EXPERIMENTAL VALIDATION OF THE MICROWAVE DRYING OF WHEAT SEEDS
2012-06-24
PIER B
Vol. 41, 397-417, 2012
download: 122
Gyrotropic-Nihility in Ferrite-Semiconductor Composite in Faraday Geometry
Vladimir Tuz Oleg D. Batrakov Yu Zheng
The reflection, transmission spectra and the polarization transformation of linearly polarized waves in the ferrite-semiconductor multilayer structure are considered. In the long-wavelength limit, the effective medium theory is applied to describe the studied structure as a uniaxial anisotropic homogeneous medium defined by the effective permittivity and effective permeability tensors. The investigations are carried out in the frequency band where the real parts of the diagonal elements of both the effective permittivity and permeability tensors are close to zero. In this frequency band the studied structure is referred to a gyrotropic-nihility medium. An enhancement of polarization rotation, impedance matching, backward propagation are revealed.
GYROTROPIC-NIHILITY IN FERRITE-SEMICONDUCTOR COMPOSITE IN FARADAY GEOMETRY
2012-06-22
PIER B
Vol. 41, 377-396, 2012
download: 250
Inductance and Force Calculation for Axisymmetric Coil Systems Including an Iron Core of Finite Length
Thierry Lubin Kevin Berger Abderrezak Rezzoug
This paper presents new semi-analytical expressions to calculate the selfinductance and the electromagnetic force for a ferromagnetic cylinder of finite length placed inside a circular coil of rectangular cross section. The proposed analytical model is based on boundary value problems with Fourier analysis. Laplace's and Poisson's equations are solved in each region by using the separation of variables method. The boundary and continuity conditions between the different regions yield to the global solution. Moreover, the iron cylinder is assumed to be infinitely permeable. Magnetic field distribution, self-inductance and electromagnetic force obtained with the proposed analytical model are compared with those obtained from finite-element.
INDUCTANCE AND FORCE CALCULATION FOR AXISYMMETRIC COIL SYSTEMS INCLUDING AN IRON CORE OF FINITE LENGTH
2012-06-20
PIER B
Vol. 41, 357-375, 2012
download: 114
Efficient Adaptive Detection Threshold Optimization for Tracking Maneuvering Targets in Clutter
Jian-Tao Wang Hong-Qiang Wang Yu-Liang Qin Zhaowen Zhuang
In this paper, we focus on the adaptive prior detection threshold setting problem to optimize the overall performance of the joint detection-tracking system for maneuvering target tracking in clutter. It is shown that our problem can be reduced to the information reduction factor (IRF) maximization by Gaussian fitting of maneuvering target Markovian switching dynamics via moment matching, even for the case with the nonlinear measurement equation. Our proposed adaptive threshold setting method outperforms the conventional threshold setting approaches greatly and also exhibits a mildly improvement in comparison with the earlier method for this problem in terms of tracking performance, especially in track loss percentage (TLP). However the computational burden of our method is reduced significantly because in our method generally only one IRF corresponding to the common validation region, not the every IRF corresponding to the individual model-conditioned validation region, is needed for threshold optimization at each time step and an approximate closed-form solution can also be obtained for the special case of the Neyman-Pearson (NP) detector.
EFFICIENT ADAPTIVE DETECTION THRESHOLD OPTIMIZATION FOR TRACKING MANEUVERING TARGETS IN CLUTTER
2012-06-16
PIER B
Vol. 41, 333-356, 2012
download: 165
Marginal Moment Generating Function Based Analysis of Channel Capacity Over Correlated Nakagami-m Fading with Maximal-Ratio Combining Diversity
Vivek K. Dwivedi Ghanshyam Singh
In this paper, we have investigated the marginal moment generating function (MMGF) for the correlated Nakagami-m fading channel by using maximal-ratio combining (MRC) diversity scheme at receiver for the computation of the channel capacity for various adaptive transmission schemes such as: 1) optimal simultaneous power and rate adaptation, 2) optimal rate adaptation with constant transmit power, 3) channel inversion with fixed rate, and 4) truncated channel inversion with fixed rate. The effects of diversity receiver as well as correlation coefficients on all these transmission schemes are discussed and the channel capacity obtained by this proposed approach for all schemes is compared with reported literature.
MARGINAL MOMENT GENERATING FUNCTION BASED ANALYSIS OF CHANNEL CAPACITY OVER CORRELATED NAKAGAMI-M FADING WITH MAXIMAL-RATIO COMBINING DIVERSITY
2012-06-13
PIER B
Vol. 41, 307-332, 2012
download: 114
Higher-Order Statistics for Stochastic Electromagnetic Interactions: Applications to a Thin-Wire Frame
Ousmane Oumar Sy Martijn Constant van Beurden Bastiaan L. Michielsen Jean-Pierre A. H. M. Vaessen Antonius G. Tijhuis
Uncertainties in an electromagnetic observable, that arise from uncertainties in geometric and electromagnetic parameters of an interaction configuration, are here characterized by combining computable higher-order moments of the observable with higher-order Chebychev inequalities. This allows for the estimation of the range of the observable by rigorous confidence intervals. The estimated range is then combined with the maximum-entropy principle to arrive at an efficient and reliable estimation of the probability density function of the observable. The procedure is demonstrated for the case of the induced voltage of a thin-wire frame that has a random geometry, is connected to a random load, and is illuminated by a random incident field.
HIGHER-ORDER STATISTICS FOR STOCHASTIC ELECTROMAGNETIC INTERACTIONS: APPLICATIONS TO A THIN-WIRE FRAME
2012-06-11
PIER B
Vol. 41, 285-305, 2012
download: 107
ISAR Imaging of Non-Uniform Rotation Targets with Limited Pulses via Compressed Sensing
Jihong Liu Xiang Li Shaokun Xu Zhaowen Zhuang
This research introduces compressed sensing (CS) principle into inverse synthetic aperture radar (ISAR) imaging of non-uniform rotation targets, and high azimuth resolution can be achieved with limited number of pulses. Firstly, the sparsity of the echoed signal of radar targets with non-uniform rotation in certain matching Fourier domain is analyzed. Then the restricted isometry property (RIP) and incoherence of partial matching Fourier matrices are checked, following which an ISAR imaging method based on CS for both random sparse aperture and short aperture cases is proposed. In particular, considering the dependence of the sparse dictionary on the relative rotation parameter, a parameter estimation method by the optimal search in fractional Fourier domain is presented. Simulation experiments verify the effectiveness as well as superiority of the proposed imaging method over traditional methods in terms of imaging performance.
ISAR IMAGING OF NON-UNIFORM ROTATION TARGETS WITH LIMITED PULSES VIA COMPRESSED SENSING
2012-06-11
PIER B
Vol. 41, 269-283, 2012
download: 220
All-Dielectric Frequency Selective Surfaces with Few Number of Periods
Jay H. Barton Raymond C. Rumpf Randall W. Smith Carrie L. Kozikowski Phillip A. Zellner
All-dielectric frequency selective surfaces (FSSs) can serve as an alternative to their metallic counterparts when they must operate at very high power, loss must be minimized, or when the surface itself must be low observable. When metals are avoided, there is a weaker interaction with electromagnetic waves and it becomes more difficult to achieve strong suppression in the stop band while also realizing compact size, wide field-of-view or broadband operation. One attractive approach utilizes guided-mode resonance (GMR) as the filtering mechanism, but this phenomenon exhibits several drawbacks that must be overcome for practical application at radio frequencies. This paper introduces the concept of guide-mode resonance for FSSs and describes how they can be made to operate with a dramatically fewer number of periods than conventional GMR devices.
ALL-DIELECTRIC FREQUENCY SELECTIVE SURFACES WITH FEW NUMBER OF PERIODS
2012-06-06
PIER B
Vol. 41, 251-268, 2012
download: 112
Performance Analysis of STAP Algorithms Based on Fast Sparse Recovery Techniques
Zhaocheng Yang Zhen Liu Xiang Li Lei Nie
In the field of space-time adaptive processing (STAP), spare recovery type STAP (SR-STAP) algorithms exploit formulation of the clutter estimation problem in terms of sparse representation of a small number of clutter positions among a much larger number of potential positions in the angle-Doppler plane, and provide an effective approach to suppress the clutter especially in very short snapshots. However, it differs from many situations encountered by other SR application fields in the following ways: (i) it does not require to obtain the exact solution; (ii) it highly requires low-complexity approaches. In this paper, we focus on the performance analysis and parameters setting of STAP algorithms based on five representative fast SR techniques, namely, the compressive sampling matching pursuit, the sparse reconstruction by separable approximation, the fast iterative shrinkage-thresholding algorithm, the focal underdetermined system solution and the smoothed l0 norm method.
PERFORMANCE ANALYSIS OF STAP ALGORITHMS BASED ON FAST SPARSE RECOVERY TECHNIQUES
2012-06-06
PIER B
Vol. 41, 231-249, 2012
download: 112
Rigorous Substantiation of the Method of Exact Absorbing Conditions in Time-Domain Analysis of Open Electrodynamic Structures
Olena Shafalyuk Paul Smith Lyudmyla Velychko
Exact absorbing conditions are used in computational electrodynamics of nonsine waves for truncating the domain of computation when replacing the original open initial boundary value problem by a modified problem formulated in a bounded domain. In this paper we prove the equivalency of these two problems.
RIGOROUS SUBSTANTIATION OF THE METHOD OF EXACT ABSORBING CONDITIONS IN TIME-DOMAIN ANALYSIS OF OPEN ELECTRODYNAMIC STRUCTURES
2012-06-04
PIER B
Vol. 41, 213-230, 2012
download: 98
A Multi-Dimensional Adaptive Sampling Method for Analysis and Design of Frequnecy Selective Surface with Arbitrary Element
Xin Ma Guobin Wan Wei Wan
A fast and efficient multi-dimensional adaptive sampling method (ASM) based on Stoer-Bulirsch (S-B) algorithm for frequency selective surface (FSS) analysis and design is presented in this paper. The multivariate rational function is established according to the functional relation of the scattering parameters with frequency and direction of incident wave, medium parameters and geometry dimensions of FSS structure, et al. In order to evaluate the values of the multivariate rational function fully automatically without determining the coefficients of the targeted rational interpolant, the one-dimensional S-B algorithm is expanded into multidimensional method. The sampling points in each dimension are chosen at the areas of maximum error in an adaptive way. The recursive interpolation results of one dimension are used as the initial values of next dimension in the recursive tabular until n-dimension recursive interpolation is accomplished. The initial values of recursive algorithm are calculated by spectral domain method of moments (MoM) at every sample point. The current distribution of FSS cell is predicted by Rao-Wilton-Glisson (RWG) subdomain basis functions which are applicable for arbitrarily shape elements. Four examples, including FSS with the eight-legged, cross and ring elements and FSS radome enclosed antennas, are considered to demonstrate the feasibility of applying the multi-dimensional ASM to analysis and optimal design of FSS. Numerical results show that the proposed method is superior in computation efficiency compared to the direct MoM. Good agreement between the proposed technique and the direct MoM is observed.
A MULTI-DIMENSIONAL ADAPTIVE SAMPLING METHOD FOR ANALYSIS AND DESIGN OF FREQUNECY SELECTIVE SURFACE WITH ARBITRARY ELEMENT
2012-06-04
PIER B
Vol. 41, 187-211, 2012
download: 161
Analysis of Coupled Microstrip Lines for Quad-Band Equal Power Dividers/Combiners
Ayman Mohamed Elsayed El-Tager Abdelrahman Mohamed El-Akhdar Hadia El-Hennawy
This paper presents a novel quad-band power divider with equal power division ratio. The proposed power divider is realized using two cascaded sections of dual-band transformers based on coupled microstrip lines. Limitations of using dual-band quarter-wavelength transformers based on coupled lines are studied through parametric analysis to obtain useful design guidelines related to available fabrication facilities. General closed-form expressions are used to calculate design parameters. To verify analysis and design methodologies, a prototype of quad-band equal power divider is proposed. Compared to conventional quad-band power dividers using sections of transmission line transformers the proposed power divider records a size reduction of about 20% and reduced parasitic effects at higher frequencies according to the usage of only two resistors instead of four with much smaller ohmic values. In addition, a quad-band power divider is proposed, fabricated and measured for 3G and 4G applications at 2.1, 2.5, 3.5, and 3.8 GHz frequencies. Measured and simulated data are in very good match which validates the novel design.
ANALYSIS OF COUPLED MICROSTRIP LINES FOR QUAD-BAND EQUAL POWER DIVIDERS/COMBINERS
2012-06-02
PIER B
Vol. 41, 153-185, 2012
download: 132
Human Head Interaction Over Ground Plane Booster Antenna Technology: Functional and Biological Analysis
Aurora Andujar Jaume Anguera Cristina Picher Carles Puente
Handset antennas strongly interact with the human body. When a user holds a handset during a phone call, the proximity of the human head considerably affects the antenna performance and eventually the quality of the wireless connection. Consequently, the assessment of the antenna parameters regarding free-space conditions is not enough to fully characterize the performance of handset antennas and a further analysis taking into account human head interaction is required. In this sense, this paper presents a study that deals with the human head interaction concerning two aspects: functional and biological. The first one analyzes the effect of the human head over the main antenna parameters (reflection coefficient, efficiency, and radiation pattern) whereas the second one evaluates the impact of the antenna over the human head in terms of Specific Absorption Rate (SAR). Four representative prototypes of radiating structures are measured in both conditions in order to compare their performance: a dual-band Planar Inverted F Antenna (PIFA), a hexa-band PIFA with a slotted ground plane, a set of coupled monopoles, and a new architecture referred as compact radiating system based on the excitation of the ground plane through a set of non-resonant ground plane boosters. A figure of merit that relates the antenna efficiency with the SAR values is proposed for comparison purposes. The results demonstrate that losses caused by the human head power absorption can be minimized if the antennas are placed in the edge located at a higher distance from the human cheek. Furthermore, the study reveals the robustness of the compact radiating system taking into account the human presence. This fact reinforces its position as an alternative solution to current handset antennas, capable of providing penta-band operation (GSM850/900, DCS, PCS, and UMTS) through ground plane boosters featured by their reduced volume of only 250 mm3.
HUMAN HEAD INTERACTION OVER GROUND PLANE BOOSTER ANTENNA TECHNOLOGY:  FUNCTIONAL AND BIOLOGICAL ANALYSIS
2012-05-31
PIER B
Vol. 41, 137-152, 2012
download: 102
A Novel Green Antenna Phase-Shift System with Data Acquisition Boards
Mohd Faizal Bin Jamlos Tharek Bin Abdul Rahman Muhammad Ramlee Kamarudin Mohd Aminudin Jamlos Mohd Asmi Romli Zahari Awang Ahmad Mohd Fareq Bin Abd Malek Muzammil Jusoh Nur Farhan Kahar Sharul Kamal Bin Abd Rahim
A novel green phase shifter system is proposed in this research. The system is developed by a combination of reconfigurable beam steering antennas and data acquisition (DAQ) boards. A combination of two reconfigurable beam steering antennas, located side-by-side, forms a spatial configuration structure with a fabricated `green' element plank of rice husk placed in between. The concept of a spatial configuration technique has been `mutated' by shifting the structure of spiral feed line and aperture slots of first beam steering antenna by as much as 45º. The PIN diode switches connected to the DAQ boards enable the intelligent capability of the spatial antennas. The activation of certain degree radiation patterns of either the first beam steering antenna or the second beam steering antenna depends on the memory of the DAQ boards --- Beam Manager. When an intruder comes from the cardinal angles of 0º/360º, 90º, 180º, or 270º, its range and angles' location will be automatically detected by the first antenna through the output ports of the 1st DAQ: P1.0, P1.1, P1.2, and P1.3. The second antenna is then activated by the output ports of the 2nd DAQ: P2.0 up to P2.3, to adaptively maneuver the beam towards four different ordinal directions of 45º, 135º, 225º, and 315º. As a result, this system collectively contributes to the development of eight angles of radiation patterns, which can be rotated in 45º steps within 0.01 ms and successfully cover 360º without any uncovered and overlapped angle; 0°/360°, 45º, 90°, 135º, 180°, 225º, 270°, and 315º. Moreover, a mutual coupling effect generated by the spatial configuration of both antennas is alleviated by the element plank of rice husk, whose width, length, and thickness are 45 mm, 150 mm, and 10 mm, respectively. Possessing the characteristics of an adaptive new phase shifter concept and assisted by the green element of a rice husk, this system is potentially an effective way to decrease the number of drop outs and lost connections, and provides larger coverage. It is a promising candidate for installation with a WiMAX application.
A NOVEL GREEN ANTENNA PHASE-SHIFT SYSTEM WITH DATA ACQUISITION BOARDS
2012-05-31
PIER B
Vol. 41, 121-136, 2012
download: 122
Mutual Coupling Analysis Using FDTD for Dielectric Resonator Antenna Reflectarray Radiation Prediction
Izyani Dzulkipli Mohd Haizal Jamaluddin Raphael Gillard Ronan Sauleau Razali Ngah Muhammad Ramlee Kamarudin Norhudah Seman Mohamad Kamal Abd Rahim
A simulation technique based on Finite-Difference Time-Domain (FDTD) is used to analyze mutual coupling effects in reflectarray environment. The neighbouring element method has the ability to analyze actual non-identical reflectarray unit-cell accurately compared to the traditional Floquet simulation which assumes all unit-cell is identical. It is also found that the nearest neighbouring unit-cell located in E-plane has a larger mutual coupling effects compared to the neighbouring unit-cell in H-plane. A good agreement is shown between simulation and measurement results. This technique presents a new prediction method for the radiation pattern of reflectarray antenna.
MUTUAL COUPLING ANALYSIS USING FDTD FOR DIELECTRIC RESONATOR ANTENNA REFLECTARRAY RADIATION PREDICTION
2012-05-29
PIER B
Vol. 41, 101-119, 2012
download: 113
Uncertainty Estimation in Complex Permittivity Measurements by Shielded Dielectric Resonator Technique Using the Monte Carlo Method
Eduardo Paez Marco A. Azpurua Ciro Tremola Roberto Cesare Callarotti
In this paper we estimate the uncertainty in complex permittivity measurements performed in a shielded dielectric resonator, by using the Monte Carlo method. We selected this approach since the theoretical expressions required to interpret the experimental results are highly non-linear. Furthermore the resonant frequency of the system and its quality factor are highly correlated. Thus we propose a model for the measurement process which considers the major sources of uncertainty previously reported in published experimental results. The proposed model combined with the Monte Carlo method was used to propagate the probability distributions of each uncertainty contribution, obtaining a) the approximate probability density function for the measured complex permittivity, and b) the estimated expanded uncertainty for the mode TE011. The results show that this procedure leads to small uncertainty intervals for the real part of the dielectric permittivity, while it is not very reliable in the loss tangent measurement. Additionally, for each input quantity, we calculated the standard deviation in the experimental results produced independently by each uncertainty contribution.
UNCERTAINTY ESTIMATION IN COMPLEX PERMITTIVITY MEASUREMENTS BY SHIELDED DIELECTRIC  RESONATOR TECHNIQUE USING THE MONTE CARLO METHOD
2012-05-28
PIER B
Vol. 41, 77-100, 2012
download: 173
Performance Analysis of Parallel Non-Orthogonal Peec-Based Solver for EMC Applications
Danesh Daroui Jonas Ekman
A parallel implementation of a quasi-static Partial Element Equivalent Circuit (PEEC)-based solver that can handle electromagnetic problems with non-orthogonal structures is presented in this paper. The solver has been written in C++ and employs GMM++ and ScaLAPACK computational libraries to make the solver fast, efficient, and adaptable to current parallel computer systems. The parallel PEEC-based solver has been tested and studied on high performance computing clusters and the correctness of the solver has been verified by doing comparisons between results from orthogonal routines and also another type of electromagnetic solver, namely FEKO. Two non-orthogonal numerical test cases have been analysed in the time and frequency domain. The results are given for solution time and memory consumption while bottlenecks are pointed out and discussed. The benchmarks show a good speedup which gets improved as the problem size is increased. With the capability of the presented solver, the non-orthogonal PEEC formulation is a viable tool for modelling geometrically complex problems.
PERFORMANCE ANALYSIS OF PARALLEL NON-ORTHOGONAL PEEC-BASED SOLVER FOR EMC APPLICATIONS
2012-05-27
PIER B
Vol. 41, 51-76, 2012
download: 160
A Circuit Model for Vertical Multilayer Transitions in Coplanar Waveguide Technology
Benito Lopez-Berrocal Enrique Marquez-Segura Inigo Molina-Fernandez Juan Carlos Gonzalez-Delgado
A circuit model for vertical transitions between different coplanar waveguide systems using via-holes is presented. The model is directly extracted from the geometry of the transition using closed expressions. Additionally, it can be used to find suitable initial dimensions for the transition in a circuit simulator, thereby greatly reducing the effort spent on subsequent electromagnetic simulations. To test the validity of the developed model, it is applied to a variety of situations involving a wide range of stack heights, dielectric constants, and transmission line geometry values. These situations cover most of the relevant broadband vertical transitions used in practical PCB and LTCC designs. Comparative analysis of the circuit model and electromagnetic simulations yields good agreement in all analyzed situations. Experimental assessment of the model is also provided for some of the transitions that were built and characterized in a back-to-back configuration.
A CIRCUIT MODEL FOR VERTICAL MULTILAYER TRANSITIONS IN COPLANAR WAVEGUIDE TECHNOLOGY
2012-05-18
PIER B
Vol. 41, 23-50, 2012
download: 142
Behavioral Model of Symmetrical Multi-Level T-Tree Interconnects
Blaise Ravelo
An accurate and behavioral modeling method of symmetrical T-tree interconnect network is successfully investigated in this paper. The T-tree network topology understudy is consisted of elementary lumped L-cells formed by series impedance and parallel admittance. It is demonstrated how the input-output signal paths of this single input multiple output (SIMO) tree network can be reduced to single input single output (SISO) network composed of L-cells in cascade. The literal expressions of the currents, the input impedances and the voltage transfer function of the T-tree electrical interconnect via elementary transfer matrix products are determined. Thus, the exact expression of the multi-level behavioral T-tree transfer function is established. The routine algorithm developed was implemented in Matlab programs. As application of the developed modeling method, the analysis of T-tree topology comprised of different and identical RLC-cells is conducted. To demonstrate the relevance of the model established, lumped RLC T-tree networks with different levels for the microelectronic interconnect application are designed and simulated. The work flow illustrating the guideline for the application of the routine algorithm summarizing the modeling method is proposed. Then, 3D-microstrip T-tree interconnects with width 0.1 μm and length 3 mm printed on FR4-substrate were considered. As results, very good agreement between the results from the reduced behavioral model proposed and SPICE-computations is found both in frequency- and time-domains by considering arbitrary binary sequence ''01001100" with 2 Gsym/s rate. The model proposed in this paper presents significant benefits in terms of flexibility and very less computation times. It can be used during the design process of the PCB and the microelectronic circuits for the signal integrity prediction. In the continuation of this work, the modeling of clock T-tree interconnects for packaging systems composed of distributed elements using an analogue process is in progress.
BEHAVIORAL MODEL OF SYMMETRICAL MULTI-LEVEL T-TREE INTERCONNECTS
2012-05-15
PIER B
Vol. 41, 1-22, 2012
download: 121
Determination of Closed-Form Expressions for Rayleigh Scattering of Polarized Light from Adsorbed Particles on OR Below a Substrate
Ray Simpkin
An integral equation formulation describing the scattered field from a distribution of optically small Rayleigh objects of arbitrary shape adsorbed onto a planar dielectric substrate is presented. When certain approximations are introduced concerning the scatterers' permittivity contrast and small size compared to the wavelength, simple closed-form expressions are obtained for the ellipticity ratio and reflectivity which can be readily related to the surface coverage and average height of the surface layer. The formulation is an alternative to thin-island film theory often used to describe electromagnetic scattering from such configurations. Results derived from the integral equation model are compared with previously published measurements of ellipticity ratio and reflectivity and are found to be in good agreement with observation.
DETERMINATION OF CLOSED-FORM EXPRESSIONS FOR RAYLEIGH SCATTERING OF POLARIZED LIGHT FROM ADSORBED PARTICLES ON OR BELOW A SUBSTRATE