Open-Ended Rectangular Waveguide for Nondestructive Thickness Measurement and Variation Detection of Lossy Dielectric Slabs Backed by a Conducting Plate

Solutions of fields inside a slab of a generally lossy dielectric medium backed by a conducting plate, placed outside a waveguide-fed rectangular aperture, are evoked in the application to 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 then solved to extract the slab thickness from 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 to describe 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 realtime applications. Experiments were conducted to verify the theoretical findings. Good agreement was obtained between the theoretical and experimental results. Multiple thicknesses of two different dielectric samples were estimated in this way

A Novel Numerical Technique for Dielectric Measurement of Generally Lossy Dielectrics

A method for determining the dielectric properties of infinite half-space of generally lossy dielectric materials is described. This method utilizes the measurement of the admittance of a rectangular waveguide radiating into such dielectrics. It is shown that the real part of the admittance is relatively insensitive to the variations of the imaginary part of the dielectric constant. Subsequently, a numerical procedure is initiated which provides a simple and fast-converging approach for calculating the dielectric properties. This numerical procedure lends itself to implementation by personal computers--a major advantage over the existing computational schemes. The theoretical formulation for the expression of the admittance of an open-ended waveguide and the numerical procedure are discussed in detail. Results of several measurements of freespace and lossy dielectric samples (rubber with carbon black) to verify the theory and the numerical scheme are given. The results give good agreement with other measurement schemes. Comments on the accuracy of the results are also provided

Analysis of Radiation from an Open-Ended Coaxial Line into Stratified Dielectrics

Radiation from an open-ended coaxial transmission line into an N-layer dielectric medium is studied in application to nondestructive evaluation of materials. Explicit formulations for two cases of layered media, one terminated into an infinite half-space and the other into a conducting sheet are addressed in general form. In the theoretical derivations it is assumed that only the fundamental TEM mode propagates inside the coaxial line. The terminating admittance of the line is then formulated using the continuity of the power flow across the aperture. The admittance expressions for specific cases of two-layer dielectric composite with generally lossy dielectric properties, and a two-layer composite backed by a conducting sheet are presented and inspected explicitly. The numerical results of the aperture admittance formulation are discussed and compared with the available infinite half-space model which had been experimentally verified

Detection Optimization of Disbond in Layered Composites with Varying Thicknesses using an Open-Ended Rectangular Waveguide

The detection of air disbond in layered dielectric composite, which is an important practical issue in many industries, is studied both theoretically and experimentally. Sensitivity of disbond detection depends on certain parameters, like the frequency of operation, the distance between the sensor and the first dielectric layer, and the layered composite geometry (conductor backed or terminated by an infinite half-space of air). The impact of all these parameters is investigated theoretically and then verified experimentally

Measurement Parameter Optimization for Surface Crack Detection in Metals using an Open-Ended Waveguide Probe

Fatigue and stress induced surface crack detection in metals is an important practical issue. A newly developed microwave inspection approach, using an open-ended rectangular waveguide, has proved to be an effective tool for detecting such cracks. This novel microwave approach overcomes some of the limitations associated with the standard detection methods for surface crack detection. In addition, this approach is applicable to exposed, filled (with a dielectric such as dirt, rust, etc.) and cracks under dielectric coatings such as paint. This paper presents the basic foundation of this surface crack detection methodology along with the ways by which measurement parameters may be optimized for increased detection sensitivity

Microwave Detection Optimization of Disbond in Layered Dielectrics with Varying Thickness

The detection sensitivity optimization of air disbond in layered dielectric composites, using an open-ended rectangular waveguide, is studied both theoretically and experimentally. The sensitivity of the disbond detection is strongly influenced by the proper choice of parameters such as the operating frequency and the layered composite geometry (conductor backed or terminated by an infinite half-space of air). The capability of optimizing the measurement system parameters to detect and estimate the thickness of a disbonded layer independent of some changes in the thickness of the dielectric coating is also demonstrated. The impact of the parameters influencing detection optimization is theoretically investigated and then experimentally verified

Modeling of Surface Hairline-Crack Detection in Metals under Coatings using an Open-Ended Rectangular Waveguide

A surface-breaking hairline crack or a narrow slot in a metallic specimen when scanned by an open-ended rectangular waveguide probe influences the reflection-coefficient properties of the incident dominant mode. Subsequent recording of a change in the standing-wave pattern while scanning such a surface results in what is known as the crack characteristic signal. Since microwave signals penetrate inside dielectric materials, this methodology is capable of detecting cracks under dielectric coatings of various electrical thicknesses as well. To electromagnetically model the interaction of an open-ended rectangular waveguide with a surface-breaking hairline crack under a dielectric coating, the dielectric-coating layer is modeled as a waveguide with a large cross section. Thus, the problem is reduced to a system of three waveguides interacting with each other while the location of the crack is continuously changing relative to the probing waveguide aperture (a dynamic scanning problem). An analysis of modeling the dielectric-coating layer as a dielectric-filled waveguide with a large cross section is given, and its comparison with radiation into an unbounded medium is presented. For obtaining the reflection coefficients of the dominant and higher order modes, the electromagnetic properties of the probing waveguide-dielectriccoating layer junction and the dielectric-coating layer-crack junction are separately analyzed. For each junction, a magneticcurrent density M is introduced over the common aperture. Subsequently, the junction formed by the two respective waveguide sections is separated into two systems. A numerical solution employing the method of moments is obtained, and the properties of the junctions are expressed by their respective generalized scattering matrices. Consequently, the generalized scattering matrix for the total system can be evaluated. The convergence behavior of the system is studied to determine an optimal set of basis functions and the optimal number of higher order modes for a fast and accurate solution. Finally, the theoretical and measured crack characteristic signals are compared

Calibration and Measurement of Dielectric Properties of Finite Thickness 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

Microwave Noncontact Examination of Disbond and Thickness Variation in Stratified Composite Media

Numerical and experimental results of a microwave noncontact, nondestructive detection and evaluation of disbonds and thickness variations in stratified composite media are presented. The aperture admittance characteristics of a flange mounted rectangular waveguide radiating into a layered, generally lossy dielectric media backed or unbacked by a conducting sheet is modeled. The theoretical implementation is based on a Fourier transform boundary matching technique to construct the field components in each medium, coupled with a stationary form of the terminating aperture admittance of the waveguide. The model can serve as a reliable test bed for real-time examination of layered composite media. Experimental results for several cases are presented which show good agreement with the theoretical findings. This is a versatile technique for near-field in situ interrogation of stratified composite media which provides for high resolution measurements

Analysis of the Crack Characteristic Signal using a Generalized Scattering Matrix Representation

Electromagnetic properties of a system formed by an open-ended rectangular waveguide and a surface crack/slot in a metallic specimen are described in this paper. Scanning a crack on a metal surface changes the reflection coefficient of the incident dominant mode. A model as a function of relative crack location within the waveguide aperture (i.e., crack moving with respect to the waveguide aperture) is desired to describe and optimize practical crack detection applications. Hence, the change in the reflection coefficient for a generalized system encompassing empty, filled, and finite cracks located at an arbitrary position inside the waveguide aperture, is evaluated. A moment solution approach is employed, and a magnetic current density M is introduced over the common aperture formed by the waveguide and the crack. Subsequently, the junction formed by the waveguide and the cracked metallic surface is separated into two systems. A numerical solution employing the method of moments is obtained, and the reflection coefficient at the waveguide aperture is expressed in terms of the generalized scattering matrix. The convergence behavior is studied to determine an optimized set of basis functions and the optimal number of higher order modes for a fast and accurate solution. Numerical results presented in this paper include the evaluation of the field distribution over the waveguide aperture. Finally, the theoretical and measured crack characteristic signals are compared