Fundamentals of the physical theory of diffraction

348 Pages·2007·2.803 MB·English

by  Pyotr Ya. Ufimtsev

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Fundamentals of the
Physical Theory of
Diffraction
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Fundamentals of the
Physical Theory of
Diffraction
PyotrYa. Ufimtsev
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Copyright©2007byJohnWiley&Sons,Inc.Allrightsreserved
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LibraryofCongressCataloging-in-PublicationData.
Ufimstev,PyotrYakovlevich.
Fundamentalsofthephysicaltheoryofdiffraction / byPyotrUfimstev.
p. cm.
“AWiley–Intersciencepublication.”
Includesbibliographicalreferencesandindex.
ISBN:978-0-470-09771-7
1.Electromagneticwaves--Diffraction.2.Diffractivescattering.I.Title.
QC665.D5U352007
(cid:2)
621.3824--dc22 2006049684
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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Contents
Foreword xi
Preface xv
Acknowledgments xvii
Introduction 1
1. BasicNotionsinAcousticandElectromagneticDiffractionProblems 5
1.1 FormulationoftheDiffractionProblem 5
1.2 ScatteredFieldintheFarZone 7
1.3 PhysicalOptics 11
1.3.1 DefinitionofthePhysicalOptics 11
1.3.2 TotalScatteringCross-Section 13
1.3.3 Optical Theorem 15
1.3.4 IntroducingtheNotionof “ShadowRadiation” 16
1.3.5 ShadowContourTheoremandtheTotalScattering
Cross-Section 21
1.3.6 SummaryofPropertiesofPhysical
OpticsApproximation 24
1.4 NonuniformComponentofInducedSurfaceField 25
1.5 ElectromagneticWaves 27
Problems 31
2. WedgeDiffraction:ExactSolutionandAsymptotics 33
2.1 ClassicalSolutions 33
2.2 TransitiontothePlaneWaveExcitation 38
2.3 ConversionoftheSeriesSolutiontotheSommerfeldIntegrals 40
2.4 TheSommerfeldRayAsymptotics 44
2.5 ThePauliAsymptotics 47
2.6 UniformAsymptotics:ExtensionofthePauliTechnique 51
2.7 CommentsonAlternativeAsymptotics 55
Problems 56
v
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vi Contents
3. WedgeDiffraction:ThePhysicalOpticsField 59
3.1 OriginalPOIntegrals 59
3.2 ConversionofthePOIntegralstotheCanonicalForm 61
3.3 RayAsymptoticsforthePODiffractedField 67
Problems 68
4. WedgeDiffraction:RadiationbytheNonuniformComponent
ofSurfaceSources 71
4.1 IntegralsandAsymptotics 71
4.2 IntegralFormofFunctionsf (1)andg(1) 76
4.3 ObliqueIncidenceofaPlaneWaveataWedge 78
Problems 82
5. First-OrderDiffractionatStripsandPolygonalCylinders 83
5.1 DiffractionataStrip 83
5.1.1 PhysicalOpticsPartoftheScatteredField 85
5.1.2 TotalScatteredField 87
5.1.3 NumericalAnalysisoftheScatteredField 92
(1)
5.1.4 First-OrderPTDwithTruncatedScatteringSourcesj 95
h
5.2 DiffractionataTriangularCylinder 99
5.2.1 SymmetricScattering:POApproximation 101
5.2.2 Backscattering:POApproximation 102
5.2.3 SymmetricScattering:First-OrderPTDApproximation 104
5.2.4 Backscattering:First-OrderPTDApproximation 107
5.2.5 NumericalAnalysisoftheScatteredField 110
Problems 112
6. AxiallySymmetricScatteringofAcousticWavesat
BodiesofRevolution 115
6.1 DiffractionataCanonicalConicSurface 115
6.1.1 IntegralsfortheScatteredField 117
6.1.2 RayAsymptotics 118
6.1.3 FocalFields 124
(1)
6.1.4 BesselInterpolationsfortheFieldu 125
s,h
6.2 ScatteringataDisk 126
6.2.1 PhysicalOpticsApproximation 127
6.2.2 FieldGeneratedbyNonuniformScatteringSources 130
6.2.3 TotalScatteredField 132
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Contents vii
6.3 ScatteringatCones:FocalField 134
6.3.1 AsymptoticApproximationsfortheField 134
6.3.2 NumericalAnalysisofBackscattering 138
6.4 BodiesofRevolutionwithNonzeroGaussianCurvature:
BackscatteredFocalFields 141
6.4.1 POApproximation 143
6.4.2 TotalBackscatteredFocalField:First-OrderPTD
Asymptotics 145
6.4.3 BackscatteringfromParaboloids 145
6.4.4 BackscatteringfromSphericalSegments 151
6.5 BodiesofRevolutionwithNonzeroGaussianCurvature:
AxiallySymmetricBistaticScattering 155
6.5.1 RayAsymptoticsforthePOField 156
6.5.2 BesselInterpolationsforthePOFieldinthe
Regionπ−ω≤ϑ ≤π 159
6.5.3 BesselInterpolationsforthePTDFieldinthe
Regionπ−ω≤ϑ ≤π 160
6.5.4 AsymptoticsforthePTDFieldintheRegion
2ω<ϑ ≤π−ωawayfromtheGOBoundaryϑ =2ω 161
6.5.5 UniformApproximationsforthePOFieldintheRayRegion
2ω≤ϑ ≤π−ωIncludingtheGOBoundaryϑ =2ω 161
6.5.6 ApproximationforthePOFieldintheShadow
RegionforReflectedRays 165
Problems 166
7. ElementaryAcousticandElectromagneticEdgeWaves 169
7.1 ElementaryStripsonaCanonicalWedge 170
7.2 Integralsforj(1)onElementaryStrips 171
s,h
7.3 TripleIntegralsforElementaryEdgeWaves 175
7.4 TransformationofTripleIntegralsintoOne-DimensionalIntegrals 178
7.5 GeneralAsymptoticsforElementaryEdgeWaves 183
7.6 AnalyticPropertiesofElementaryEdgeWaves 187
7.7 NumericalCalculationsofElementaryEdgeWaves 191
7.8 ElectromagneticElementaryEdgeWaves 194
7.9 ImprovedTheoryofElementaryEdgeWaves 198
7.9.1 AcousticEEWs 199
7.9.2 ElectromagneticEEWs 203
7.10 SomeReferencesRelatedtoElementaryEdgeWaves 209
Problems 210
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viii Contents
8. RayandCausticsAsymptoticsforEdgeDiffractedWaves 213
8.1 RayAsymptotics 213
8.1.1 AcousticWaves 213
8.1.2 ElectromagneticWaves 218
8.1.3 CommentsonRayAsymptotics 219
8.2 CausticAsymptotics 220
8.2.1 AcousticWaves 221
8.2.2 ElectromagneticWaves 225
Problems 226
9. MultipleDiffractionofEdgeWaves:GrazingIncidenceandSlope
Diffraction 229
9.1 StatementoftheProblemandRelatedReferences 229
9.2 GrazingDiffraction 230
9.2.1 AcousticWaves 230
9.2.2 ElectromagneticWaves 234
9.3 SlopeDiffractionintheConfigurationofFigure9.1 236
9.3.1 AcousticWaves 236
9.3.2 ElectromagneticWaves 238
9.4 SlopeDiffraction:GeneralCase 240
9.4.1 AcousticWaves 240
9.4.2 ElectromagneticWaves 243
Problems 245
10.DiffractionInteractionofNeighboringEdgesonaRuledSurface 247
10.1 DiffractionatanAcousticallyHardSurface 248
10.2 DiffractionatanAcousticallySoftSurface 250
10.3 DiffractionofElectromagneticWaves 252
Problems 254
11.FocusingofMultipleAcousticEdgeWavesDiffractedataConvex
BodyofRevolutionwithaFlatBase 255
11.1 StatementoftheProblemanditsCharacteristicFeatures 255
11.2 MultipleHardDiffraction 256
11.3 MultipleSoftDiffraction 258
Problems 260
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Contents ix
12.FocusingofMultipleEdgeWavesDiffractedataDisk 261
12.1 MultipleHardDiffraction 261
12.2 MultipleSoftDiffraction 264
12.3 MultipleDiffractionofElectromagneticWaves 267
Problems 268
13.BackscatteringataFinite-LengthCylinder 269
13.1 AcousticWaves 269
13.1.1 POApproximation 269
13.1.2 BackscatteringProducedbytheNonuniform
Componentj(1) 273
13.1.3 TotalBackscatteredField 277
13.2 ElectromagneticWaves 279
13.2.1 E-Polarization 279
13.2.2 H-Polarization 283
Problems 285
14.BistaticScatteringataFinite-LengthCylinder 287
14.1 AcousticWaves 287
14.1.1 POApproximation 287
14.1.2 ShadowRadiationasaPartofthePhysicalOpticsField 289
14.1.3 PTDforBistaticScatteringataHardCylinder 290
14.1.4 BeamsandRaysoftheScatteredField 297
14.1.5 RefinedAsymptoticsfortheSpecularBeam 300
14.2 ElectromagneticWaves 304
14.2.1 E-Polarization 304
14.2.2 H-Polarization 306
14.2.3 RefinedAsymptoticsfortheSpecularBeamReflected
fromtheLateralSurface 308
Problems 311
Conclusion 313
References 315
Index 323
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