Ebook
Fundamentals of the Physical Theory of Diffraction, 2nd EditionISBN: 9781118848692
496 pages
April 2014, WileyIEEE Press

Description
Readers develop the skills to apply PTD to solve various scattering problems. The derived analytic expressions clearly illustrate the physical structure of the scattered field. They additionally describe all of the reflected and diffracted rays and beams, as well as the fields in the vicinity of caustics and foci. Shadow radiation, a fundamental component of PTD, is introduced and proven to contain half the total scattered power. The equivalence relationships between acoustic and electromagnetic diffracted waves are established and emphasized. Throughout the book, the author enables readers to master both the theory and its practical applications.
 Plotted numeric results supplement the theory and facilitate the visualization of individual contributions of distinct parts of the scattering objects to the total diffracted field
 Detailed comments help readers understand and implement all the critical steps of the analytic and numeric calculations
 Problem sets in each chapter give readers an opportunity to analyse and investigate the diffraction phenomena
Table of Contents
Foreword to the First Edition xv
Preface to the First Edition xix
Acknowledgments xxi
Introduction xxiii
1 Basic Notions in Acoustic and Electromagnetic Diffraction Problems 1
1.1 Formulation of the Diffraction Problem / 1
1.2 Scattered Field in the Far Zone / 3
1.3 Physical Optics / 7
1.3.1 Definition of Physical Optics / 7
1.3.2 Total Scattering CrossSection / 10
1.3.3 Optical Theorem / 11
1.3.4 Introducing Shadow Radiation / 12
1.3.5 Shadow Contour Theorem and the Total Scattering CrossSection / 17
1.3.6 Shadow Radiation and Reflected Field in the Far Zone / 20
1.3.7 Shadow Radiation and Reflection from Opaque Objects / 22
1.4 Electromagnetic Waves / 23
1.4.1 Basic Field Equations and PO Backscattering / 23
1.4.2 PO Field Components: Reflected Field and Shadow Radiation / 26
1.4.3 Electromagnetic Reflection and Shadow Radiation from Opaque Objects / 28
1.5 Physical Interpretations of Shadow Radiation / 31
1.5.1 Shadow Field and Transverse Diffusion / 31
1.5.2 Fresnel Diffraction and Forward Scattering / 32
1.6 Summary of Properties of Physical Optics Approximation / 32
1.7 Nonuniform Component of an Induced Surface Field / 33
Problems / 36
2 Wedge Diffraction: Exact Solution and Asymptotics 49
2.1 Classical Solutions / 49
2.2 Transition to Plane Wave Excitation / 55
2.3 Conversion of the Series Solution to the Sommerfeld Integrals / 57
2.4 The Sommerfeld Ray Asymptotics / 61
2.5 The Pauli Asymptotics / 63
2.6 Uniform Asymptotics: Extension of the Pauli Technique / 68
2.7 Fast Convergent Integrals and Uniform Asymptotics: The “Magic Zero” Procedure / 72
Problems / 76
3 Wedge Diffraction: The Physical Optics Field 87
3.1 Original PO Integrals / 87
3.2 Conversion of PO Integrals to the Canonical Form / 90
3.3 Fast Convergent Integrals and Asymptotics for the PO Diffracted Field / 94
Problems / 100
4 Wedge Diffraction: Radiation by Fringe Components of Surface Sources 103
4.1 Integrals and Asymptotics / 104
4.2 Integral Forms of Functions f (1) and g(1) / 112
4.3 Oblique Incidence of a Plane Wave at a Wedge / 114
4.3.1 Acoustic Waves / 114
4.3.2 Electromagnetic Waves / 118
Problems / 120
5 FirstOrder Diffraction at Strips and Polygonal Cylinders 123
5.1 Diffraction at a Strip / 124
5.1.1 Physical Optics Part of the Scattered Field / 124
5.1.2 Total Scattered Field / 128
5.1.3 Numerical Analysis of the Scattered Field / 132
5.1.4 FirstOrder PTD with Truncated Scattering Sources j(1) h / 135
5.2 Diffraction at a Triangular Cylinder / 140
5.2.1 Symmetric Scattering: PO Approximation / 141
5.2.2 Backscattering: PO Approximation / 143
5.2.3 Symmetric Scattering: FirstOrder PTD Approximation / 145
5.2.4 Backscattering: FirstOrder PTD Approximation / 148
5.2.5 Numerical Analysis of the Scattered Field / 150
Problems / 152
6 Axially Symmetric Scattering of AcousticWaves at Bodies of Revolution 157
6.1 Diffraction at a Canonical Conic Surface / 158
6.1.1 Integrals for the Scattered Field / 159
6.1.2 Ray Asymptotics / 160
6.1.3 Focal Fields / 166
6.1.4 Bessel Interpolations for the Field u(1) s,h / 167
6.2 Scattering at a Disk / 169
6.2.1 Physical Optics Approximation / 169
6.2.2 Relationships Between Acoustic and Electromagnetic PO Fields / 171
6.2.3 Field Generated by Fringe Scattering Sources / 172
6.2.4 Total Scattered Field / 173
6.3 Scattering at Cones: Focal Field / 176
6.3.1 Asymptotic Approximations for the Field / 176
6.3.2 Numerical Analysis of Backscattering / 179
6.4 Bodies of Revolution with Nonzero Gaussian Curvature: Backscattered Focal Fields / 183
6.4.1 PO Approximation / 184
6.4.2 Total Backscattered Focal Field: FirstOrder PTD Asymptotics / 186
6.4.3 Backscattering from Paraboloids / 186
6.4.4 Backscattering from Spherical Segments / 192
6.5 Bodies of Revolution with Nonzero Gaussian Curvature: Axially Symmetric Bistatic Scattering / 196
6.5.1 Ray Asymptotics for the PO Field / 196
6.5.2 Bessel Interpolations for the PO Field in the Region − ≤ ≤ / 200
6.5.3 Bessel Interpolations for the PTD Field in the Region − ≤ ≤ / 200
6.5.4 Asymptotics for the PTD Field in the Region 2 < ≤ − Away from the GO Boundary = 2 / 201
6.5.5 Uniform Approximations for the PO Field in the Ray Region 2 ≤ ≤ − , Including the GO Boundary = 2 / 202
6.5.6 Approximation of the PO Field in the Shadow Region for Reflected Rays / 205
Problems / 207
7 Elementary Acoustic and Electromagnetic Edge Waves 211
7.1 Elementary Strips on a Canonical Wedge / 212
7.2 Integrals for j(1) s,h on Elementary Strips / 213
7.3 Triple Integrals for Elementary Edge Waves / 217
7.4 Transformation of Triple Integrals into OneDimensional Integrals / 220
7.5 General Asymptotics for Elementary Edge Waves / 225
7.6 Analytic Properties of Elementary Edge Waves / 230
7.7 Numerical Calculations of Acoustic Elementary Fringe Waves / 234
7.8 Electromagnetic Elementary Edge Waves / 237
7.8.1 Electromagnetic EEWs on the Diffraction Cone Outside the Wedge / 241
7.8.2 Electromagnetic EEWs on the Diffraction Cone Inside the Wedge / 243
7.8.3 Numerical Calculations of Electromagnetic Elementary Fringe Waves / 245
7.9 Improved Theory of Elementary Edge Waves: Removal of the Grazing Singularity / 245
7.9.1 Acoustic EEWs / 248
7.9.2 Electromagnetic EEWs Generated by the Modified Nonuniform Current / 253
7.10 Some References Related to Elementary Edge Waves / 256
Problems / 257
8 Ray and Caustic Asymptotics for Edge Diffracted Waves 261
8.1 Ray Asymptotics / 261
8.1.1 Acoustic Waves / 261
8.1.2 Electromagnetic Waves / 266
8.1.3 Comments on Ray Asymptotics / 267
8.2 Caustic Asymptotics / 269
8.2.1 Acoustic waves / 269
8.2.2 Electromagnetic Waves / 274
8.3 Relationships between PTD and GTD / 275
Problems / 276
9 Multiple Diffraction of Edge Waves: Grazing Incidence and Slope Diffraction 285
9.1 Statement of the Problem and Related References / 285
9.2 Grazing Diffraction / 286
9.2.1 Acoustic Waves / 286
9.2.2 Electromagnetic Waves / 290
9.3 Slope Diffraction in Configuration of Figure 9.1 / 292
9.3.1 Acoustic Waves / 292
9.3.2 Electromagnetic Waves / 295
9.4 Slope Diffraction: General Case / 296
9.4.1 Acoustic Waves / 296
9.4.2 Electromagnetic Waves / 299
Problems / 302
10 Diffraction Interaction of Neighboring Edges on a Ruled Surface 305
10.1 Diffraction at an Acoustically Hard Surface / 306
10.2 Diffraction at an Acoustically Soft Surface / 309
10.3 Diffraction of Electromagnetic Waves / 312
10.4 Test Problem: Secondary Diffraction at a Strip / 314
10.4.1 Diffraction at a Hard Strip / 314
10.4.2 Diffraction at a Soft Strip / 317
Problems / 318
11 Focusing of Multiple Acoustic Edge Waves Diffracted at a Convex Body of Revolution with a Flat Base 325
11.1 Statement of the Problem and its Characteristic Features / 325
11.2 Multiple Hard Diffraction / 327
11.3 Multiple Soft Diffraction / 328
Problems / 330
12 Focusing of Multiple Edge Waves Diffracted at a Disk 333
12.1 Multiple Hard Diffraction / 334
12.2 Multiple Soft Diffraction / 336
12.3 Multiple Diffraction of Electromagnetic Waves / 340
Problems / 341
13 Backscattering at a FiniteLength Cylinder 343
13.1 Acoustic Waves / 343
13.1.1 PO Approximation / 343
13.1.2 Backscattering Produced by the Nonuniform Component j(1) / 347
13.1.3 Total Backscattered Field / 352
13.2 Electromagnetic Waves / 354
13.2.1 Epolarization / 354
13.2.2 Hpolarization / 360
Problems / 362
14 Bistatic Scattering at a FiniteLength Cylinder 365
14.1 Acoustic Waves / 365
14.1.1 PO Approximation / 366
14.1.2 Shadow Radiation as a Part of the Physical Optics Field / 368
14.1.3 PTD for Bistatic Scattering at a Hard Cylinder / 370
14.1.4 Beams and Rays of the Scattered Field / 376
14.1.5 PO ShootingThrough Rays and Their Cancellation by Fringe Rays / 381
14.1.6 Refined Asymptotics for the Specular Beam Reflected from the Lateral Surface / 382
14.2 Electromagnetic Waves / 386
14.2.1 EPolarization / 386
14.2.2 HPolarization / 388
14.2.3 Refined Asymptotics for the Specular Beam Reflected from the Lateral Surface / 390
Problems / 393
Conclusion 397
References 399
Appendix to Chapter 4: MATLAB Codes for TwoDimensional Fringe Waves and Figures (F. Hacivelioglu and L. Sevgi) 411
Appendix to Chapter 6: MATLAB Codes for Axial Backscattering at Bodies of Revolution (F. Hacivelioglu and L. Sevgi) 431
Appendix to Section 7.7: MATLAB Codes for Diffraction Coefficients of Acoustic Elementary Fringe Waves (F. Hacivelioglu and L. Sevgi) 439
Appendix to Section 7.8.3: MATLAB Codes for Diffraction Coefficients of Electromagnetic Elementary Fringe Waves (F. Hacivelioglu and L. Sevgi) 443
Appendix to Section 7.9.2: Field d⃗E (0) mod Radiated by Modified Uniform Currents ⃗J (0) mod Induced on Elementary Strips (P. Ya. Ufimtsev) 447
Index 451
Author Information
Pyotr Ya. Ufimtsev has been recognized for his outstanding work in the theory of diffraction and propagation of electromagnetic and acoustic waves. Dr. Ufimtsev has been affiliated with the Central Research Radio Engineering Institute of the USSR Defense Ministry, Moscow; the Institute of Radio Engineering and Electronics of the USSR Academy of Sciences, Moscow; the Moscow Aviation Institute; and the University of California at Los Angeles and Irvine. Among Dr. Ufimtsev’s many honors and awards are the USSR State Prize and the Leroy Randle Grumman Medal.