A Data Engineering Approach to Wave Scattering Analysis with Applications in Radar, Sonar, Medical Diagnostics, Structural Flaw Detection and Intelligent Robotics

About the Author xi

Preface xiii

Acknowledgments xv

Introduction xvii

1 Background 1

1.1 Some History 1

1.1.1 The Titanic Disaster 1

1.1.2 Das Unterseeboot 2

1.1.3 Aircraft Detection 4

1.1.4 Medical Ultrasonography and NDE 6

1.2 Ultrasound Immersion Tank Scans 9

1.3 A-, B-, C-Scans, M-Mode 14

1.4 Monostatic, Bistatic, Doppler 19

1.5 Didey Wagon vs. War Wagon 21

1.6 Acoustic Parametric Arrays 28

1.7 Forward to Scattering 30

References 31

2 Field Equations 35

2.1 Index Notation 35

2.2 Stress Is Force per Unit Area 37

2.2.1 Two-Question Pop Quiz, Pass–Fail 37

2.3 Strain Is Dimensionless 42

2.4 Stress Is Proportional to Strain 45

2.5 Elastic Waves 47

2.6 Electromagnetic Waves 50

2.7 Acoustic Waves 52

2.8 Anisotropic Elastic Solids 53

2.9 Summary 57

3 Boundary Conditions: Continuous and Discretized 61

3.1 Boundary Conditions for E&M 61

3.2 Boundary Conditions for Acoustics 62

3.3 Boundary Conditions for Elastodynamics 65

3.4 Finite Difference Time Domain 67

3.5 Elastodynamic Simulations 79

3.6 The Acoustic Parametric Array 82

References 87

4 Reflection and Refraction 93

4.1 Reflection from a Free Surface 101

4.2 Surface Waves 105

4.3 Acoustic Microscopy 109

4.3.1 V(z) Curves 112

4.3.2 Wave Model of Acoustic Microscopy 115

4.3.3 Detecting Cracks in Teeth 118

4.3.4 Inspection of V22 Hydraulic Lines 121

References 122

5 Guided Waves 125

5.1 Guided Waves in Plates 127

5.2 Cylindrical Guided Waves 135

5.2.1 Torsional Modes in a Rod 139

5.2.2 Longitudinal Waves in a Rod 139

5.2.3 Flexural Waves in a Rod 140

5.3 Guided Waves in Pipes 142

5.4 Data Engineering for Tomography 144

5.4.1 Tomography Overview 148

5.4.2 Fan Beam Tomography 149

5.4.3 Double Crosshole Tomography 150

5.4.4 Arrival Time Determination 153

5.4.5 Curvilinear SIRT 160

References 163

6 Scattering from Spheres 167

6.1 Clebsch–Mie Scattering 167

6.2 Acoustic Scattering from a Sphere 181

6.3 Elastic Wave Sphere Scattering 192

6.4 Incident Transverse Wave 199

6.5 Scattering from Spherical Shells 204

References 207

7 Scattering from Cylinders 209

7.1 Electromagnetic Wave Scattering 209

7.1.1 Incident E-Field Parallel to the xz-Plane 212

7.1.2 Incident E-Field Perpendicular to the xz-Plane 214

7.2 Elastic Wave Scattering 217

7.2.1 Scattering Due to an Incident L-Wave 220

7.2.2 Scattering of Acoustic Waves from an Elastic Cylinder 224

7.2.3 Scattering Due to an Incident T-Wave 227

7.2.3.1 Scattering from an Acoustic Cylinder 231

7.2.4 Limiting Cases 233

7.3 Plate Wave Scattering 237

7.3.1 Flexural Wave Scattering from Cylinders 240

7.3.2 Dilatational Wave Scattering 242

7.4 Thermal “Wave” Scattering 246

7.5 Scattering from a Semicircular Gap in a Ground Plane 248

References 256

8 Scattering from Spheroids and Elliptic Cylinders 259

8.1 Scalar Wave Equation in Elliptic Cylinder Coordinates 260

8.1.1 Separation of Variables 263

8.2 Scattering from a Perfectly-Conducting Elliptic Cylinder 264

8.3 Scattering from a Dielectric Elliptic Cylinder 268

8.3.1 Important Tea About Orthogonality 269

8.3.2 Numerical Implementation of Mathieu Functions 276

8.4 Scattering of Elastic Waves by an Elliptic Cylindrical Inclusion 277

8.5 Scattering from Spheroids 281

References 288

9 Scattering from Parallelepipeds 289

9.1 Integral Equations 289

9.2 High Frequency Scattering and Diffraction Coefficients 295

9.3 Reflection/Transmission by a Slab 311

9.4 Reflection at Conducting Halfspace 314

9.5 Surface Plasmon Polaritons 317

References 321

10 Inverse Scattering 325

10.1 Wavelet Fingerprinting 329

10.2 Wavelet Fingerprints Applied 331

10.2.1 Roof Fall Detection 331

10.2.2 RF Scattering from a Food Truck 334

10.2.3 Time Domain Reflectometry 335

10.2.4 Counterfeit Routers 337

10.2.5 Bladder Distension Monitor 337

10.2.6 RF Occlusion by Building 339

10.3 Conclusions 341

Index 347