Open-ended rectangular waveguide for nondestructive thicknessmeasurement and variation detection of lossy dielectric slabs backed bya conducting plate

Solutions for fields inside a slab of a generally lossy dielectric medium backed by a conducting plate, placed outside a waveguide-fed rectangular aperture, are used for the microwave nondestructive thickness measurement of such dielectric slabs. Upon construction of the waveguide terminating admittance expression from its variational form, an inverse problem is solved to extract the slab thickness form the conductance and susceptance in a recursive manner. A comparison between the experimental and theoretical results showed that the significance of higher order modes is minimal; hence, the dominant mode assumption is, in general, valid for describing the aperture field distribution. The validity of this assumption has led to the construction of a simple integral solution which is fast converging for generally lossy dielectric slabs, and may easily be implemented for real-time applications. Good agreement was obtained between the theoretical and experimental results. Multiple thicknesses of two different dielectric samples were estimated in this way     

A general formulation for admittance of an open-ended rectangular waveguide radiating into stratified dielectrics

A general approach is presented for calculating the aperture admittance of a rectangular waveguide radiating into layered dielectric media. The two specific geometries of stratified, lossy dielectric media that are addressed terminate into either an infinite half-space or a perfectly conducting surface. The geometries describe two prevalent categories of layered dielectric composites and coatings that often are encountered in practical microwave nondestructive evaluation applications. Solutions are found initially by constructing a complete set of field components and subsequently enforcing the continuity of power flow across the aperture interface of the waveguide. Final results are presented as a superposition of transverse electric and magnetic components of the aperture admittance. The solutions presented allow the systematic calculation of admittance in the presence of arbitrary multilayer media, which in turn may be related to experimentaly measurable quantities of interest. With the practical assumption of dominant mode incidence on the aperture, the final expressions may be implemented without intense computational power, which often is desirable in practice where inaccuracies due to random errors and instrumentation sensitivity render incorporation of more rigorous solutions inefficient. Numerically simulated data also are presented to verify and interpret the results.     

A General Formulation for Admittance of an Open-Ended Rectangular Waveguide Radiating into Stratified Dielectrics

Abstract

A general approach is presented for calculating the aperture admittance of a rectangular waveguide radiating into layered dielectric media. The two specific geometries of stratified, lossy dielectric media that are addressed terminate into either an infinite half-space or a perfectly conducting surface. The geometries describe two prevalent categories of layered dielectric composites and coatings that often are encountered in practical microwave nondestructive evaluation applications. Solutions are found initially by constructing a complete set of field components and subsequently enforcing the continuity of power flow across the aperture interface of the waveguide. Final results are presented as a superposition of transverse electric and magnetic components of the aperture admittance. The solutions presented allow the systematic calculation of admittance in the presence of arbitrary multilayer media, which in turn may be related to experimentaly measurable quantities of interest. With the practical assumption of dominant mode incidence on the aperture, the final expressions may be implemented without intense computational power, which often is desirable in practice where inaccuracies due to random errors and instrumentation sensitivity render incorporation of more rigorous solutions inefficient. Numerically simulated data also are presented to verify and interpret the results.     

A Resonant Cavity Approach for the Nondestructive Determination of Complex Permittivity at Microwave Frequencies

A nondestructive microwave cavity approach for measuring complex permittivities of materials in sheet form is described. The resonant cavity is a section of a rectangular waveguide terminated by a thin rigid and large flange containing a small rectangular iris opening. The iris is placed in firm contact with one side of the dielectric sample while the other side is backed with a highly conducting plate. Variations of the cavity resonant frequency and Q-factor caused by the dielectric can be related to its complex permittivity through the consideration of equivalent admittance of this open-ended dielectricloaded aperture at resonance. Experimental determination of aperture admittance of a loaded iris is made and the results compared with theoretical calculations. The validity of this technique is confirmed by evaluating the resonant cavity characteristics by loading it with dielectrics of known permittivities and comparing the results with theoretical results. The permittivity of a lossy dielectric slab is measured and the value obtained by this method is compared with those found by other techniques. In all these cases the agreement between theory and measurements is satisfactory. Utility of this technique in evaluating the local inhomogeneities of permittivity of sheets is demonstrated. Measurement errors and limitations of this technique are pointed out.     

Nondestructive Measurement of Materials Using a Waveguide-Fed Series Slot Array

The reflection from an array of narrow series slots on the broad face of a rectangular waveguide is used to determine the permittivity of lossy materials. The theoretical study of the electromagnetic field in the vicinity of the slots yields a system of integral equations which takes into account the internal and external coupling between slots. The numerical solution is discussed and an optimization procedure for the array is presented, which provides a simple relationship linking the reflection coefficient to the complex permittivity over a specified range. Computed results are compared to experimental values for air and a lossy dielectric at 10 GHz, showing good agreement. Interpolation from computed data is provided by a polynomial expansion: this allows one to determine the complex permittivity once the reflection factor has been measured.     

Lossy multilayer channel optical waveguides analyzed by the transmission line matrix method

We demonstrate that the three-dimensional vectorial transmission line matrix (TLM) method is applicable to the analysis of lossy multilayer optical waveguiding structures. Any lossy multilayer waveguide geometry, including sharp discontinuities in the transverse plane, can be treated taking into account the coupling between all optical field components. The complex propagation constants (propagation constants and the attenuation coefficients) for the fundamental TE-like and TM-like modes can be determined. These parameters of the fundamental TM-like mode of a typical lossy multilayer rib dielectric waveguide are obtained as functions of free-space wavelength. Calculation of the electric-field pattern is also included. Numerical comparisons with the argument principle method (for the case of lossy multilayer slab waveguides) and the spectral-index technique (for the case of lossy multilayer rib waveguides) are also included, and it is shown that the application of the TLM method to lossy multilayer optical waveguides is accurate.     

Impact of Waveguide Filling Material on Near-Field Microwave Inspection of Carbon-Loaded Composites

The advent of carbon loaded composite materials gave a boost to many industries. This is because of their light weight, durability and strength. As new structures utilizing carbon loaded composites are built, the need for a reliable nondestructive testing technique increases. A carbon-loaded composite testing poses a challenge to most nondestructive testing and evaluation (NDT&E) techniques. Microwave NDT&I techniques main challenge is the lossy nature of carbon, especially at high microwave frequencies. Lower frequencies penetrate deeper in carbon-loaded composites, however, to operate at lower frequencies the size of the waveguide probe increases significantly which degrades the resolution rapidly. Open-ended rectangular waveguide sensors filled with a dielectric material will be used to inspect carbon-loaded composites. The filling of the waveguide reduces the frequency of operation and keeps the small size of the waveguide (i.e. increases the penetration depth and maintains the resolution). However, varying the waveguide filling material dielectric properties will have an impact on the measurement parameters optimization process and consequently on the detection sensitivity. In this paper, the use of the waveguide filling material as an optimization parameter will be investigated. Carbon-loaded composites with disbonds will be inspected and the variation of the dielectric properties of the loading material of rectangular waveguide probes for carbon loaded composites inspection will be assessed.     

A methodology for determining complex permittivity of construction materials based on transmission-only coherent,wide-bandwidth free-space measurements

An integrated methodology for determining the unique combination of complex permittivity based on measured transmission coefficient and time difference of arrival (TDOA) information in free-space measurements is proposed. The methodology consists of an estimation procedure of the real part of complex permittivity based on TDOA, and a root-searching procedure based on parametric system identification (SI) together with an error sum of squares (SSE) criterion. Generally, non-unique combinations of dielectric constant and loss factor are encountered when lossy or low-loss materials are measured and the proposed methodology is aimed at the determination of unique combinations of dielectric constant and loss factor for such materials. The proposed methodology is validated by measurements of several materials with known dielectric properties. The estimated complex permittivity values for Teflon, Lexan, Bakelite, and concrete are in good agreement with those reported in the literature. The method has potential for in-situ measurement of dielectric properties for construction materials. Applicability and limitations of the methodology are discussed.     

材料固有损耗对压电振子谐振特性及参数测量的影响

本从考虑损耗时压电振子的阻抗（或导纳）议程出发,详细分析了材料固有损耗对压电振子的频率特性及参数测量的影响。分析结果表明：谐振（或反谐振）频率与理想无损时的相应值的偏差随损耗的增大而增大、随谐序的增大而减小。中还进一步分析了机械损耗对压电振子几种常用参数测量结果的影响。     

Standard-independent estimation of dielectric permittivity with microdielectric fringe-effect sensors

Microdielectric spectroscopy with planar fringe-effect (FE) interdigital sensors is a useful method for noninvasive characterization of the interfacial properties of the materials. Unfortunately, obtaining an accurate dielectric spectrum is difficult because of the complexity of the probing electrical field created by the FE sensor and the contribution of the sensor substrate and stray elements to the overall measurements. Previously, quantitative microdielectric spectroscopy required the calibration of the FE sensor with standard materials that are known to be dielectrically similar to an unknown sample of interest. This limitation complicates the application of microdielectric spectroscopy, particularly in cases where the monitored sample undergoes a transformation that changes its dielectric permittivity. A standard-independent method for quantitative FE microdielectric measurements is proposed in this paper. The developed method is based on comparison of the theoretically predicted admittance of the FE sensor with the sample of known dielectric properties and the measured sensor admittance. Comparison of the theoretical predictions with the admittance measurements reveals the contribution of the unknown stray elements. The measurements with an unknown sample are then adjusted for the strays. The contribution of the sensor substrate to the sensor measurements is removed using the theoretical model derived from the electroquasistatic approximation of Maxwell equations. The dielectric permittivity of the material being tested is calculated by successively solving the system of complex nonlinear equations for each frequency at which the sensor admittance is measured. The developed method is illustrated by applying it to the dielectric measurements of several dissimilar samples. The results are in excellent agreement with those obtained using the gold standard parallel-plate measurement method over the entire range of frequencies.     

A Two Coupler Method for Measurement of Complex Permittivity of Dielectric Materials at Microwave Frequencies

This paper describes two coupler method for measurement of dielectric properties of materials, at microwave frequencies. Two waveguide sections, fed from a common source, are coupling power into a waveguide filled with dielectric. The phase and attenuation constants are computed from the values of phase and attenuation adjustment required for cancellation of the signal in the dielectric filled waveguide. The two coupler method is particularly applicable for measurements of dielectric properties of aerosols and gases.     

Calibration and measurement of dielectric properties of finitethickness composite sheets with open-ended coaxial sensors

The application of open-ended coaxial sensors for dielectric measurement of finite thickness composite sheets is studied. Expressions for calculation of the complex aperture admittance for two geometries are presented. These expressions are used to calculate the dielectric constant of infinite half-space as well as finite thickness slabs. A more efficient method of such calculations, using a personal computer, for low to medium loss dielectrics is demonstrated. The question of when a dielectric layer may be considered as infinitely thick is also addressed, and examples are presented. A different calibration technique (compared to the conventional ones) is described and successfully implemented. This calibration technique utilizes a dielectric sheet with known dielectric properties and thickness. Measurements for different airgaps between the open-ended coaxial line and the dielectric sheet are used to perform and enhance the calibration. The results of this calibration technique and several subsequent measurements are presented and discussed     

一种新的复介电常数自由空间测量技术研究

提出了一种新的复介电常数的自由空间测量方法,该方法将介质周期结构引入到复介电常数的测量中。运用多模网络理论与严格的模匹配技术,系统分析了加损耗样品层的介质周期结构的散射特性,详细研究了样品复介电常数对反射峰幅度和中心频率的影响。该测量方法不仅克服了传统自由空间法的不稳定性和相位模糊性问题,而且具有谐振法可以对低损耗介质精确测量且测量过程简单的优点,为复介电常数的精确测量提供了一种新的测量方法和重要的理论指导。     

Stable method for the calculation of layered dielectric and metal-dielectric waveguide structures with circular cross sections

A new method intended for the calculation of eigenmodes and leaky modes in layered dielectric and metal-dielectric waveguide structures possessing azimuthal symmetry is described. The proposed method generalizes the approach developed by Golant [1] for the analysis of planar layered structures. The numerical procedure is stable in application to the systems with wave tunneling or decay (instability) in radial directions. Possibilities of the proposed method are demonstrated in calculations of the Bragg optical fibers of various types.     

Microwave diagnosis of low-density fiberglass composites with resin binder

Dielectric properties of low-density fiberglass composites are studied at microwave frequencies and are related to the resin binder content and state of cure. A completely filled short-circuited waveguide method is used to study the dielectric properties of fresh and slightly cured resin binder (used in the production of low-density fiberglass composite materials) in the frequency range of 4–18 GHz. The preliminary results indicate that the dielectric properties of resin binder may be used to determine its state of cure. The same measurement approach is used to determine the dielectric properties of fiberglass materials containing uncured resin binder, no resin binder, and three different levels of resin binder. It is found that the dielectric properties of these low-permittivity and low-loss materials are very similar. Consequently, to distinguish among real fiberglass products with different resin binder levels, an open-ended rectangular waveguide measurement approach, is used. This technique allows for noncontact and on-line inspection. The standoff distance is utilized as an optimization parameter increasing the sensitivity of detection to slight dielectric property variations. Two microwave images, at 24 and 10 GHz of a panel containing five different fiberglass specimens are presented.     

Calibration of specific absorption rate (SAR) probes in waveguideat 900 MHz

The radiation safety tests for hand-held mobile phones require precise calibration of the small electric field probes used for the measurement of specific absorption rate (SAR) in phantoms simulating the human body. In this study, a calibration system based on a rectangular waveguide was developed for SAR calibrations at 900 MHz. The cross-sectional dimensions of the waveguide are a=190 mm and b=140 mm. The waveguide is loaded with a rectangular liquid slab where the dielectric parameters of the medium simulate human muscle and brain. The precise SAR reference is derived from the temperature rise during a short-term (10-15 s) microwave heating of the lossy slab by measuring with sensitive thermistor-type probes equipped with highly resistive lines. The thermistor probes are calibrated against a calibrated mercury thermometer. To improve the uniformity of the electric field at the calibration position, the thickness of the tissue equivalent slab was varied to adjust the standing wave pattern. This resulted in an almost threefold reduction in the positioning error of the E-field probe. The absolute uncertainty of the calibration is estimated to be ±5% (2σ) not including the uncertainty of the conductivity. The difference between the thermally measured SAR and a value computed with the FDTD method was well within this limit of uncertainty. This kind of closed waveguide system is more compact and requires less microwave power than open field calibration systems. Moreover, no radio-frequency interference is generated     

Diffraction of electromagnetic waves by periodic arrays of rectangular cylinders

Reflection, transmission, and absorption of electromagnetic waves by periodic arrays of conducting or dielectric rectangular cylinders are studied by a finite-difference time-domain technique. Truncated gratings made of lossless and lossy conducting and dielectric elements are considered. Results for surface current density, transmission, and reflection coefficients are calculated and compared with corresponding results in the literature, which are obtained by approximate or rigorous methods applicable only to idealized infinite models. An excellent agreement is observed in all cases, which demonstrates the accuracy and efficacy of our proposed analysis technique. Additionally, this numerical method easily analyzes practical gratings that contain a finite number of elements made of lossless, lossy, or even inhomogeneous materials. The results rapidly approach those for the idealized infinite arrays as the number of elements is increased. The method can also solve nested gratings, stacked gratings, and holographic gratings with little analytical or computational effort.     

Analysis of electromagnetic scattering from dielectric objects above a lossy half-space by multiresolution preconditioned multilevel fast multipole algorithm

In this study, a synthesis of the multilevel fast multipole algorithm (MLFMA) and the multiresolution (MR) preconditioning technique is presented for the analysis of scattering from homogeneous dielectric targets above a lossy half-space. The Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation and the MLFMA are used for efficient analysis of scattering problems in half-space. The MR preconditioning technique is used to speed up the convergence rate of the iterative solver. The numerical results are presented to demonstrate that the proposed method is efficient for the scattering from homogeneous dielectric objects above a lossy half-space.     

A technique for dielectric measurement of cylindrical objects in arectangular waveguide

In this paper, the inverse scattering problem of a homogeneous dielectric post in a rectangular waveguide is considered. A novel inversion algorithm, based on the method of moments and eigen analysis, for computation of the dielectric constant of the post (ϵ) from the measured voltage reflection coefficient is introduced. In this method the integral equation for the polarization current induced in the dielectric post is cast into a matrix equation, and then the contribution of ϵ to the resulting reflection coefficient is expressed explicitly using the eigen analysis. It is shown that the dielectric constant can be obtained from the solution of a complex polynomial function which in turn can be obtained numerically using the conjugate gradient method. Practical aspects of dielectric measurement using this technique are discussed. The HP-8510 network analyzer is used to measure the reflection coefficient of dielectric posts in an X-band waveguide sample holder. Metallic and known dielectric posts are used to determine the accuracy of the dielectric measurement technique     

A grounded coplanar waveguide technique for microwave measurement of complex permittivity and permeability

We present a method for extracting the complex permittivity and permeability of dielectric/magnetic thin films in a grounded coplanar waveguide configuration. The technique is applicable for extraction of these material parameters for lossy and lossless materials over a broad frequency range with high accuracy. For validation, we extracted complex permittivity and permeability, using the scattering parameters obtained from the full-wave electromagnetic simulation for two test cases over a frequency range of 5 to 15 GHz. Accuracy for both dielectric as well as magnetic materials is within 2% error.