Microwave NDT
Front cover

Microwave NDT
Back cover

Microwave Nondestructive Testing

    Microwave testing has been paid only scant attention in the literature as a method for nondestructive testing of materials, yet it offers some attractive features, especially for the testing of composites and other nonmetallic materials.
    Microwave techniques have been used in a large number of  applications that can be classified as nondestructive testing applications, ranging from large scale remote sensing to detection of tumors in the body. This volume describes a unified approach  to microwave nondestructive testing by presenting the three essential components of testing: theory, practice, and modeling.     
    While recognizing  that each of these subjects is wide enough to justify a volume of its own, the presentation of the three topics together shows that they are interrelated and should be practiced together. While few will argue against a good theoretical background, modeling and simulation of the testing environment is seldom part of the NDT training in any method,  but particularly so in microwave testing. The text is divided into four parts. The first part presents the field theory background necessary for understanding the microwave domain. This includes chapter 1, 2 and 3. The second part treats microwave measurements as well as devices and sources and includes chapter 4 and 5.
    Chapter 6, 7, and 8 discuss practical tests applicable to a variety of materials and geometries. The fourth part discusses modeling of microwave testing and consists of chapter 9, 10 and 11. Each chapter contains a bibliography intended to expand on the material given and, in particular, to point to subjects which could  not be  covered either as not appropriate or for lack of space. Audience: engineers, appliedphysicists,materials scientists.

Kluwer Publishing Company, Amsterdam

Nov. 1992, 394 pages
ISBN 0-7923-2007-7

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1. The Microwave Domain 
2. Historical
3. Advantages and Disadvantagesof Microwaves for Testing
4. Energy Associated with Microwaves
5. Properties of Fields at HighFrequencies
6. A Note on References and Bibliography
7. References

Part I. Electromagnetic Field Theory

Chapter 1
The Electromagnetic Field Equationsand Theoretical Aspects
1.1. Introduction:  The Electromagnetic Field Equations
1.2. Maxwell's Equations in Differential Form 
   1.2.1. The Time Harmonic Equation 
   1.2.2. The Source Free Equations
1.3. Maxwell's Equations in IntegralForm
1.4. Material Properties and Constitutive Relations
   1.4.1. Conductivity 
   1.4.2. Complex Permittivity
   1.4.3. Complex Permeability 
   1.4.4. AnisotropicMaterials 
1.5. The Poynting Theorem 
   1.5.1. The Complex Poynting Vector
1.6. Potential Functions
   1.6.1. The Electric Scalar Potential
   1.6.2. The Magnetic Scalar Potential
   1.6.3. The MagneticVector Potential
1.7. The Field Equations in Termsof Potential Functions
   1.7.1. Vector Potentials
   1.7.2. Scalar Potentials 
   1.7.3. Gauge Conditions
1.8. The General, Time Dependent Wave Equation
   1.8.1. The Time-Harmonic Wave Equation
   1.8.2. The Helmholtz Equations
1.9. Propagation of Waves PlaneWaves
1.10. Propagation of Plane Wavesin Lossy Media
   1.10.1. Losses in Materials
   1.10.2. Propagationof Waves in Lossy Dielectrics
   1.10.3. Propagationof Waves in Low Loss Dielectrics
   1.10.4. Propagationof Waves in Conductors
1.11. Electromagnetic Boundary Conditions
   1.11.1. Interface Conditions
   1.11.2. Interface Conditions for The Magnetic Field
   1.11.3. Interface Conditions Between Two Lossless
   1.11.4. Interface Betweena Dielectric and a Conductor
   1.11.5. Other Interface Conditions 
1.12. Bibliography

Chapter 2
Transmission Lines, Waveguides,and Resonant Cavities
2.1. Transmission Lines
   2.1.1. The LosslessTransmission Line
   2.1.2. Reflection onTransmission Lines and the Reflection 
   2.1.3. The Transmission Coefficient 
   2.1.4. Power Relationsin a Lossy Transmission Line 
   2.1.5. Standing Waves
   2.1.6. Line Impedance
   2.1.7. Impedance Matching 
   2.1.8. Stub Matching 
   2.1.9. Quarter Wavelength Transformer
2.2. Waveguides 
   2.2.1. TM and TE Modes 
   2.2.2. Rectangular Waveguides 
   2.2.3. TM Modes in Rectangular Waveguides 
   2.2.4. TE Modes in Rectangular Waveguides 
   2.2.5. Cylindrical Waveguides
   2.2.6. TM Modes in Cylindrical Waveguides
   2.2.7. TE Modes in Cylindrical Waveguides
2.3. Cavity Resonators
   2.3.1. TM and TE Modesin Cavity Resonators
   2.3.2. TE Modes in a Rectangular Cavity Resonator
   2.3.3. Cylindrical Cavity Resonators
   2.3.4. Energy in a Cavity Resonator
   2.3.5. Quality Factor of a Cavity Resonator
   2.3.6. Coupling to Cavities
2.4. Perturbation Techniques
   2.4.1. Volume Perturbation 
   2.4.2. Material Perturbation 
   2.4.3. Perturbation by Material Insertion 
2.5. Bibliography 

Chapter 3
Reflection, Transmission, andScattering of Waves
3.1. Introduction 
3.2. Polarization of Plane Waves
   3.2.1. Linear Polarization
   3.2.2. Elliptical 
3.3. Reflection and Transmissionof Plane Waves
   3.3.1. Reflection andTransmission at a General Dielectric
             Interface:  Normal Incidence
   3.3.2. Reflection andTransmission at a Lossy Dielectric 
   3.3.3. Reflection andTransmission at a Lossless Dielectric 
   3.3.4. Reflection andTransmission at an Air Conductor
             Interface: Normal Incidence
   3.3.5. Reflection andTransmission at an Interface: Oblique
   3.3.6. Oblique Incidenceon a Conducting Interface: 
             Perpendicular  Polarization
   3.3.7. Oblique Incidenceon a Conducting Interface:
             Parallel Polarization
   3.3.8. Oblique Incidenceon a Dielectric Interface: 
             Perpendicular Polarization
   3.3.9. Oblique Incidenceon a Dielectric Interface:
             Parallel Polarization 
3.4. Brewster Angle
   3.4.1. Total Reflection
   3.4.2. Surface Waves 
3.5. Reflection and Transmissionfor Layered Materials at 
      Normal Incidence 
   3.5.1. Reflection andTransmission for a Dielectric Slab at 
             Normal Incidence
   3.5.2. Reflection andTransmission for a Low Loss Dielectric
             Slab at Normal  Incidence
   3.5.3. Reflection andTransmission for a High Loss Dielectric 
             Slab at Normal Incidence
   3.5.3. Reflection andTransmission for a Lossless Dielectric
             Slab Backed by a  Perfect Conductor: Normal
3.6. Reflection and Transmissionfor Layered Dielectrics
   3.6.1. Oblique Incidenceon N Dielectric Layers:
             Perpendicular Polarization 
   3.6.2. Oblique Incidenceon N Dielectric Layers: Parallel
3.7. Scattering 
3.8. Bibliography

Part II. Microwave Techniques and Devices

Chapter 4
Microwave Measurement Techniques
4.1. Introduction
4.2. Power Measurements 
   4.2.1. Definition ofPower
   4.2.2. Methods of Measurement
   4.2.3. Thermo-ResistiveMethods 
   4.2.4. ThermocoupleMeasurements
   4.2.5. Measurementof Power Density
4.3. Frequency Measurements 
   4.3.1. Frequency Counting 
   4.3.2. Heterodyne FrequencyMeasurement 
   4.3.3. Wavemeters 
4.4. Q Measurements
4.5. Attenuation Measurements
4.6. Standing Wave Ratio and ReflectionCoefficient 
4.7. Microwave Microscopy
4.8. An example of Test Setup: TheBalanced Microwave 
4.9. Bibliography 

Chapter 5
Microwave Sources, Sensors, andDevices
5.1. Introduction 
5.2. Generation of Microwave Fields:Microwave Tubes 
   5.2.1. The Magnetronand M Tubes
5.3. Microwave Liner-Beam Tubes 
   5.3.1. The Klystron
   5.3.2. The TravelingWave Tube
5.4. Solid State Microwave Devices
   5.4.1. The Tunnel Diode
   5.4.2. The Gunn Diode 
   5.4.3. The AvalancheDiode
   5.4.4. The BARITT Diode
   5.4.5. The PIN Diode
5.5. Microwave Circuits
   5.5.1. The NegativeResistance Oscillator
   5.5.2. Transistor Oscillators
   5.5.3. Amplifiers 
5.6. Coupling of Microwaves
5.7. Microwave Probes 
   5.7.1. The Thermocouple
   5.7.2. The Thermistor 
   5.7.3. Diode Detectors
5.8. Waveguide Probes
5.9. Antennas
   5.9.1. The Horn Antenna
   5.9.2. Microstrip orPatch Antennas
   5.9.3. Spiral Antennas
   5.9.4. Slot Antennas
5.10. Open Waveguides
   5.10.1. The Small Loop 
5.11. Passive Microwave Devices
   5.11.1. Waveguides,Waveguide Sections, and Cavity
   5.11.2. The Magic THybrid Junction 
   5.11.3. DirectionalCouplers
   5.11.4. Isolators 
   5.11.5. Attenuators
5.12. Bibliography

Part III. Testing

Chapter 6
Dimensional Testing
6.1. Introduction: Testing withMicrowaves
   6.1.1. Reflection Tests
   6.1.2. TransmissionTest
   6.1.3. Scattering Test 
   6.1.4. Resonant Tests 
   6.1.5. Testing Parameters
6.2. Thickness Gaging
   6.2.1. Reflectometry 
6.3. Transmission and AttenuationTests in Dielectrics and
      Lossy Dielectrics
6.4. Standing Wave Measurements 
6.5. Phase Measurements 
6.6. Frequency Measurements
6.7. Measurement of Coated Conductors 
6.8 Bibliography 

Chapter 7
Testing for Discontinuities
7.1. Introduction
7.2. Scattering Methods of FlawDetection 
7.3. Location of flaws
7.4. Scanning Measurements 
7.5. Automatic Testing
7.6. Bibliography 

Chapter 8
Testing by Monitoring MaterialProperties
8.1. Introduction 
8.2. Transmission Tests 
8.3. Reflection and AttenuationTests
8.4. Resonant Methods
   8.4.1. TransmissionLine Methods 
   8.4.2. Density Test 
8.5. Scattering Methods
8.6. Bibliography 
Part IV. Modeling of the TestingEnvironment

Chapter 9
Methods of Modeling
9.1. Introduction 
9.2. Purpose and Scope of Modeling
9.3. General Approach to Modeling:Numerical 
9.4. The Finite Difference Method
   9.4.1. The Finite DifferenceRepresentation 
   9.4.2. Finite DifferenceFormulation For the 1-D Wave
9.5. Finite Element Methods
   9.5.1. The Finite ElementFormulation
   9.5.2. Energy Functional 
   9.5.3. Finite ElementDiscretization
   9.5.4. Finite ElementFormulation 
   9.5.5. QuadrilateralIsoparametric Elements 
   9.5.6. Functional Minimization
   9.5.7. Boundary Conditions 
9.6. Boundary Integral Methods:The Method of Moments 
   9.6.1. The Method ofMoment
   9.6.2. SubsectionalBases
   9.6.3. The Method ofMoments for Integral Operators
   9.6.4. Method of Momentsfor Current Distributions
   9.6.5. Formulation
9.7. Bibliography 

Chapter 10
Modeling of the Time-DependentWave Equation
10.1. Introduction
10.2. Formulation 
   10.2.1. The Time DependentEquations
   10.2.2. AlternativeFormulation: TE and TMRepresentation
10.3. The Axi-Symmetric Formulation
10.4. Radiation Boundary Conditions 
10.5. Finite Difference Implementation
   10.5.1. Two-DimensionalApplications
   10.5.2. Axi-SymmetricApplications
10.6. Examples
   10.6.1. Scatteringby Embedded Cylinders
   10.6.2. Waves Due toa Small Loop
10.8. 3-D Formulation With the FiniteDifference 
10.9. Bibliography 

Chapter 11
Modeling of the Time-HarmonicWave Equation
11.1. Introduction 
11.2 The Time Harmonic Wave Equations 
   11.2.1. The Wave Equation
   11.2.2. The GeneralizedQuasi-Static Equation
   11.2.3. Formulationof the Two-DimensionalHelmholtz
   11.2.4. Formulationof the Three-Dimensional Helmholtz
   11.2.5. Formulationof the Modified Eddy Current Equation: 
               2-D Case
   11.2.6. Formulationof the Modified Eddy Current Equation:
               3-D Case
11.3. The Weak Form 
11.4. Examples
   11.4.1. Resonant Frequencyof a Cubic Cavity 
   11.4.2. Modes in RectangularWaveguides
   11.4.3. Modes in aLoaded Cavity Resonator
11.5. Bibliography 

Part V. Miscellaneous Topics

Chapter 12
Miscellaneous Topics
12.1. Tables of Material Properties
12.2. Hyperbolic and ExponentialFunctions 
12.3. Euler's Equation

Appendix A
Vector Relations
A.1. The Gradient, Divergence, andCurl 
   A.1.1. The ? Operator 
   A.1.2. The Gradient 
   A.1.3. The Divergence
   A.1.4. The Curl 
A.2. Vector Theorems
   A.2.1. The DivergenceTheorem 
   A.2.2. Stokes' Theorem 
   A.2.3. Helmholtz'sTheorem
A.3. Vector Identities
A.4. The Laplacian 
A.5. Expressions in Cartesian, Cylindricaland Spherical 

Subject Index


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