Inhomogeneous Dielectric Materials Research Articles

Appearance estimation and reconstruction of glossy object surfaces based on the dichromatic reflection model

AbstractWe propose an approach for estimating and reconstructing the material appearance of objects based on the spectral image data acquired in complex illumination environments with multiple light sources. The object appearance can be constructed with various material properties such as spectral reflectance, glossiness, and matteness under different geometric and spectral illumination conditions. The objects are assumed to be made of an inhomogeneous dielectric material with gloss or specularity. The color signals from the object surface are described by the standard dichromatic reflection model, which consists of diffuse and specular reflections, where the specular component has the same spectral composition as the illuminant. The overall appearance of objects is determined by a combination of chromatic factors, based on the reflectance and illuminant spectra, and shading terms, which represent the surface geometries of the surface illumination. Therefore, the appearance of a novel object can be reconstructed by modifying the chromatic factors and shading terms. The method for appearance estimation and reconstruction comprises four steps: (1) illuminant estimation, (2) spectral reflectance estimation, (3) shading term estimation and region segmentation, and (4) appearance reconstruction based on the reflection model. The proposed approach is validated in an experiment in which objects of different materials are illuminated using different light sources. We demonstrate typical reconstruction results with novel object appearances.

Prepreg and Core Dielectric Permittivity (ϵr ) Extraction for Fabricated Striplines’ Far-End Crosstalk Modeling

As the data rate and density of digital high-speed systems are getting higher, far-end crosstalk (FEXT) noise becomes one of the major issues that limit signal integrity performance. It was commonly believed that FEXT would be eliminated for striplines routed in a homogeneous dielectric, but in reality, FEXT can always be measured in striplines on the fabricated printed circuit boards. A slightly different dielectric permittivity (<inline-formula><tex-math notation="LaTeX">${{\boldsymbol{\varepsilon }}_{\boldsymbol{r}}}$</tex-math></inline-formula>) of prepreg and core may be one of the major contributors to the FEXT. This article is focusing on providing a practical FEXT modeling methodology for striplines by introducing an approach to extract <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{\varepsilon }}_{\boldsymbol{r}}}$</tex-math></inline-formula> of prepreg and core. Using the known cross-sectional geometry and measured <i>S</i>-parameters of the coupled stripline, the capacitance components in prepreg and core are separated using a two-dimensional solver, and the <inline-formula><tex-math notation="LaTeX">${{\boldsymbol{\varepsilon }}_{\boldsymbol{r}}}$</tex-math></inline-formula> of prepreg and core is determined. A more comprehensive FEXT modeling approach is proposed by applying extracted inhomogeneous dielectric material information.

Spectral-Reflectance Estimation under Multiple Light Sources

We describe a comprehensive method for estimating the surface-spectral reflectance from the image data of objects acquired under multiple light sources. This study uses the objects made of an inhomogeneous dielectric material with specular highlights. A spectral camera is used as an imaging system. The overall appearance of objects in a scene results from the chromatic factors such as reflectance and illuminant and the shading terms such as surface geometry and position. We first describe the method of estimating the illuminant spectra of multiple light sources based on detecting highlights appearing on object surfaces. The highlight candidates are detected first, and then some appropriate highlight areas are interactively selected among the candidates. Next, we estimate the spectral reflectance from a wide area selected from an object's surface. The color signals observed from the selected area are described using the estimated illuminant spectra, the surfacespectral reflectance, and the shading terms. This estimation utilizes the fact that the definition domains of reflectance and shading terms are different in each other. We develop an iterative algorithm for estimating the reflectance and the shading terms in two steps repeatedly. Finally, the feasibility of the proposed method is confirmed in an experiment using everyday objects under the illumination environment with multiple light sources.

Inhomogeneous dielectrics: conformal mapping and finite-element models

Abstract Field singularities in electrostatic and magnetostatic fields require special attention in field calculations, and today finite element methods are normally used, both in homogeneous and in inhomogeneous dielectric cases. Conformal mappings are a traditional tool in the homogeneous case, but two-stage Schwarz-Christoffel + Finite Difference procedures have been proposed for a long time to solve problems in case of inhomogeneous dielectric materials too. This allowed to overcome accuracy problems caused by convex corners in the domain boundary and relevant field singularities, and to easily apply finite difference (FD) solvers in rectangular domains. In this paper, compound procedures Schwarz-Christoffel + Finite Elements Method procedures are suggested, to improve both the accuracy and the speed of second stage calculations. The results are compared to Schwarz-Christoffel + Finite Difference and to direct finite-element calculations, and the small differences analyzed considering a well know case study geometry, i.e., a shielded dielectric-supported stripline geometry.

Analysis of EM scattering from composite conducting-dielectric objects by time domain non-conformal VSIE

To analyze the transient electromagnetic (EM) scattering from the composite structure containing inhomogeneous dielectric volumes and perfect electrically conducting (PEC) bodies efficiently and flexibly, a marching-on-in-time (MOT) based time domain non-conformal volume surface integral equations (TD-VSIE) method is proposed. The non-conformal volume integral equation scheme and surface integral equation discontinuous Galerkin (IEDG) method are combined to realize the non-conformal meshes discretization for composite objects. For some composite objects containing fine structure or inhomogeneous dielectric materials, notable reduction in the number of the unknowns can be obtained without sacrificing accuracy. Moreover, a hybrid mesh scheme is introduced to further improve the efficiency. Several numerical results are proposed to demonstrate the validity and flexibility of the proposed scheme.

Volume Integral Equation-Based Diakoptic Method for Electromagnetic Modeling

A novel diakoptic method based on volume integral equation (VIE) modeling of subsystems is proposed for 3-D electromagnetic analysis. The theoretical foundation of the method is the surface and volume equivalence principles, as it combines the VIE and surface integral equation (SIE) formulations, in conjunction with the method of moments (MoM). The method breaks the original structure into a number of nonoverlapping closed-region subsystems that contain inhomogeneous dielectric materials and an open-region subsystem. Each subsystem is analyzed completely independently applying the double higher order large-domain Galerkin generalized MoM-VIE-SIE (VSIE) or MoM-SIE solvers. The final solution is obtained from diakoptic matrices expressing linear relations between the electric and magnetic equivalent surface current coefficients on diakoptic surfaces. The proposed VSIE-diakoptic method is validated, evaluated, and discussed in several characteristic examples. The examples demonstrate that the diakoptic method substantially increases the efficiency of the conventional MoM-VIE approach. When compared with the pure MoM-VIE double higher order technique, the diakoptic approach enables very considerable accelerations and memory savings, while fully preserving the accuracy of the analysis.

Analysis of Scattering From Composite Conducting Dispersive Dielectric Objects by Time-Domain Volume-Surface Integral Equation

A marching-on-in-time (MOT)-based volume-surface integral equation (VSIE) method is introduced to analyze transient electromagnetic scattering from the composite structures comprising perfect electrically conducting (PEC) bodies and inhomogeneous dispersive dielectric materials. A recursive convolution scheme is employed to deal with dispersive materials. The plane-wave time-domain (PWTD) algorithm is incorporated to accelerate the MOT scheme. In our examples, Debye, Lorentz, and Drude models are used to analyze the dielectric materials of the composite objects, respectively. Numerical results are given to demonstrate the accuracy and efficiency of the proposed scheme.

Dynamic wave field synthesis: enabling the generation of field distributions with a large space-bandwidth product.

We present a novel approach for the design and fabrication of multiplexed computer generated volume holograms (CGVH) which allow for a dynamic synthesis of arbitrary wave field distributions. To achieve this goal, we developed a hybrid system that consists of a CGVH as a static element and an electronically addressed spatial light modulator as the dynamic element. We thereby derived a new model for describing the scattering process within the inhomogeneous dielectric material of the hologram. This model is based on the linearization of the scattering process within the Rytov approximation and incorporates physical constraints that account for voxel based laser-lithography using micro-fabrication of the holograms in a nonlinear optical material. In this article we demonstrate that this system basically facilitates a high angular Bragg selectivity on the order of 1°. Additionally, it allows for a qualitatively low cross-talk dynamic synthesis of predefined wave fields with a much larger space-bandwidth product (SBWP ≥ 8.7 × 10(6)) as compared to the current state of the art in computer generated holography.

Lagrange‐type modeling of continuous dielectric permittivity variation in double‐higher‐order volume integral equation method

AbstractA novel double‐higher‐order entire‐domain volume integral equation (VIE) technique for efficient analysis of electromagnetic structures with continuously inhomogeneous dielectric materials is presented. The technique takes advantage of large curved hexahedral discretization elements—enabled by double‐higher‐order modeling (higher‐order modeling of both the geometry and the current)—in applications involving highly inhomogeneous dielectric bodies. Lagrange‐type modeling of an arbitrary continuous variation of the equivalent complex permittivity of the dielectric throughout each VIE geometrical element is implemented, in place of piecewise homogeneous approximate models of the inhomogeneous structures. The technique combines the features of the previous double‐higher‐order piecewise homogeneous VIE method and continuously inhomogeneous finite element method (FEM). This appears to be the first implementation and demonstration of a VIE method with double‐higher‐order discretization elements and conformal modeling of inhomogeneous dielectric materials embedded within elements that are also higher (arbitrary) order (with arbitrary material‐representation orders within each curved and large VIE element). The new technique is validated and evaluated by comparisons with a continuously inhomogeneous double‐higher‐order FEM technique, a piecewise homogeneous version of the double‐higher‐order VIE technique, and a commercial piecewise homogeneous FEM code. The examples include two real‐world applications involving continuously inhomogeneous permittivity profiles: scattering from an egg‐shaped melting hailstone and near‐field analysis of a Luneburg lens, illuminated by a corrugated horn antenna. The results show that the new technique is more efficient and ensures considerable reductions in the number of unknowns and computational time when compared to the three alternative approaches.

Regularized 1-D Dielectric Profile Inversion in a Uniform Metallic Waveguide by Measurement and Simulation

An iterative technique for the reconstruction of longitudinally inhomogeneous lossy dielectric material loaded in a uniform metallic waveguide is addressed in this paper. The problem is first formulated as an inverse scattering one based on an integral equation in terms of the unknown complex permittivity. By using knowledge of scattering parameters, the Gauss-Newton technique is employed to solve the inverse problem with both the Tikhonov regularization and multiplicative regularization. In order to show the effectiveness of the method, it is tested against numerical and experimental data at X- and K-bands and satisfactory reconstructions are obtained. Experimental results show that the inverse algorithm with multiplicative regularization can be used for the characterization of multilayered structures in a waveguide without needing a priori information.

A spectral invariant representation of spectral reflectance

Spectral image acquisition as well as color image is affected by several illumination factors such as shading, gloss, and specular highlight. Spectral invariant representations for these factors were proposed for the standard dichromatic reflection model of inhomogeneous dielectric materials. However, these representations are inadequate for other characteristic materials like metal. This paper proposes a more general spectral invariant representation for obtaining reliable spectral reflectance images. Our invariant representation is derived from the standard dichromatic reflection model for dielectric materials and the extended dichromatic reflection model for metals. We proof that the invariant formulas for spectral images of natural objects preserve spectral information and are invariant to highlights, shading, surface geometry, and illumination intensity. It is proved that the conventional spectral invariant technique can be applied to metals in addition to dielectric objects. Experimental results show that the proposed spectral invariant representation is effective for image segmentation.

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere of multilayers

Electromagnetic scattering by an inhomogeneous plasma anisotropic sphere is formulated and obtained, where the inhomogeneous plasma anisotropic sphere is divided into (s-1) homogeneous anisotropic spherical layers. The electromagnetic fields in the inner spherical multilayers and outer free space of the inhomogeneous plasma anisotropic spherical structure can be expanded in terms of the spherical vector wave functions in plasma anisotropic medium and in isotropic medium, respectively. By applying the continuous boundary conditions of electromagnetic fields on the spherical interfaces of the (s-1)-layered homogeneous anisotropic plasma medium, the unknown expansion coefficients of fields in the multilayered plasma spherical structure are obtained, and then the electromagnetic field distributions are calculated. Numerical results for the very general inhomogeneous plasma dielectric material sphere are given and the data in a special case are obtained using the present method and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach and compared to each other to verify the correctness and applicability of the present analysis.

Efficient Analysis of Periodic Structures with Arbitrary Shape Using Volume-surface Integral Equation Method

A coupled volume-surface integral equation method is presented for analyzing arbitrarily shaped periodic structure of mixed dielectric and conducting objects. Free space periodic Green’s function is used in the formulation of both integral equations. In the method of moments solution to the integral equations, the target is discretized using triangular patches for conducting surfaces and tetrahedral cells for dielectric volume. Ewald’s method is used to accelerate the convergence of computing each element in the impedance matrix. Numerical results are presented to demonstrate the accuracy and efficiency of the technique. I. Introduction Electromagnetic analysis of periodic structures has a wide range of application. The spectral method of moments is a power tool in analyzing periodic structures [1]. To improve the flexibility in modeling various geometries, the Rao-Wilton-Gillison (RWG) [2] triangular discretization was reported in [3]. In this paper, the coupled volume-surface integral equation method [4] is presented for the electromagnetic wave scattering from arbitrarily shaped periodic structures composed of dielectrics and conducting objects. Free space periodic Green’s function is used in the formulation of both integral equations. The triangular patches and tetrahedral elements are used to mesh the dielectric and conducting objects, respectively. The coupled integral equations are solved by the method of moments (MoM) [5] with surface RWG and volume SWG basis functions [6] discretization. To rapidly generate the impedance elements, Ewald’s method [7] is used to speed the computation of the periodic Green function due to the fact that the periodic Green function, which is a summation of series, converges very slowly. The proposed technique can also be extensively applied to analyze the periodic structure consisted of inhomogeneous dielectric material and conducting body. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed technique for analyzing the scattering problem of arbitrarily shaped periodic structure.

Refractive index estimation and color image rendering

A method is described for estimating the refractive index of the material of an object surface with convex shape in natural scenes. The refractive index is an optical constant that is inherent to the surface material. This optical parameter is not only useful for identifying the material of an object surface, but also important for creating realistic images of the object. It is difficult to measure the refractive index of any material in natural scenes, except for transparent materials. In this paper, we consider estimation of the refractive index for relatively smooth surfaces of inhomogeneous dielectric materials by using a calibrated CCD camera. First, we show how the appearance of an image including specular highlights changes with the refractive index. This parameter is then estimated from the camera data of specular highlights of an object surface at different directions of illumination and viewing. The estimation algorithm is based on histogram analysis using the Torrance-Sparrow reflection model. The estimated refractive index is compared with direct measurements using a refractometer. Moreover the feasibility of the proposed method is demonstrated in computer graphics images created by using the estimated reflection parameters.

Inhomogeneous Dielectric Media: Wave Propagation and Dielectric Permittivity Reconstruction in the Case of a Rectangular Waveguide

In this paper we study the theoretical part of a novel non-destructive testing method for the reconstruction of the dielectric profile of an inhomogeneous dielectric material. We consider the inhomogeneity to be described by a polynomial of third order, i.e., εr(z)= ε0 + ε1z2 + ε3z3 and we utilize a system of three rectangular waveguides to solve the direct and the inverse problem. We apply Frobenius method to solve the underlying differential equations. We give special attention to the first cut-off frequency on the main mode TE10 and we propose a good estimation of it by using the mean value of the dielectric profile.

Tapered stripline embedded in inhomogeneous media as microwave matching line

A novel design method for a stripline microwave matching line is developed in this paper. Striplines considered have a tapered inner conductor embedded in an inhomogeneous dielectric material with continuous spatial variation of the relative permittivity. The employment of this kind of waveguide, as it is shown in this paper, ensures good matching properties in a wide frequency range. These matching properties can be controlled by means of two different factors: the taper of the stripline inner conductor and the relative permittivity spatial variation of the dielectric material filling the stripline. Starting from the nonuniform transmission-line theory, a novel closed analytical form for the input reflection coefficient of such lines is derived, and design formulas for the matching line are carried out. Finally, several applications that show the capability, flexibility, and fastness of the developed synthesis method are presented.

Inhomogeneous Dielectric Media: Wave Propagation and Dielectric Permittivity Reconstruction

In this paper we study the propagation of electromagnetic waves in a waveguide completely filled with a inhomogeneous dielectric material. The material is inhomogeneous in the longitudinal direction, i.e., the dielectric permittivity is described by a function ε = ε0εr(z). We first solve the direct problem; then we develop a computational procedure for solving the inverse problem and apply the procedure to the estimation of an unknown dielectric permittivity profile. An important feature of our approach is the expansion of the unknown εr(z) into a power series. The dielectric permittivity profile estimation consists in determining the unknown coefficients through error function minimization. We test our method by numerical experiments utilizing a genetic algorithm and obtain very accurate results.

A New Stripline High Pass Filter Layout

A new kind of stripline microwave high pass filter is proposed in this paper. Striplines here used have a tapered inner conductor and are filled by inhomogeneous dielectric materials with continuous spatial variation of the refraction index. Thus, filtering properties of such components can be controlled by means of two different keys: the inner conductor taper and the refraction index spatial variation of the dielectric material filling the stripline. A design method for such a filter is carried out starting from the generalized nonuniform transmission line theory by which a novel closed analytical form for the input reflection coefficient is derived. This closed form allows to obtain straightforwardly the design formulas for the high pass filters. Finally, some applications that show the capability of the new filter here proposed and the fastness of the developed synthesis method are presented.

Estimating reflection parameters from a single color image

This article proposes a method for estimating various parameters of a reflection model from a single color image of an object. We used an RGB charge-coupled device (CCD) camera for imaging and parameter estimation. We assumed the object surface is composed of an inhomogeneous dielectric material and used the Phong model to describe the surface's dichromatic reflection. This approach also generalizes to objects with smooth convex surfaces.

Characterization of dielectric materials with the finite-element method

A technique to characterize homogeneous and inhomogeneous dielectric materials based on measurements and computations is presented. The first step of the method proposed consists of measuring the resonant frequencies of an arbitrarily shaped cavity containing an arbitrarily shaped sample of the material under test. In the second step, the measured data are used in two different algorithms, both based on the finite-element method, to solve for the dielectric constant.