Electromagnetic Wave Scattering from Random Rough Surfaces: Asymptotic Models

162 Pages·2013·2.242 MB·English

by  Nicolas Pinel, Christophe Boulier

Electromagnetic Wave Scattering from
Random Rough Surfaces

FOCUS SERIES
Series Editor Joseph Saillard
Electromagnetic Wave
Scattering from
Random Rough Surfaces
Asymptotic Models
Nicolas Pinel
Christophe Bourlier
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Contents
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHAPTER 1. ELECTROMAGNETIC WAVE SCATTERING FROM RANDOM
ROUGHSURFACES: BASICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1.Maxwellequationsandboundaryconditions . . . . . . . . . . . . . 2
1.2.2.Propagationofaplanewave(Helmholtzequationandplanewave) 5
1.2.3.Incidentwaveataninterface: polarization . . . . . . . . . . . . . . 7
1.3.Randomroughsurfaces: statisticaldescriptionandelectromagnetic
roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.1.Statisticaldescriptionofrandomroughsurfaces . . . . . . . . . . . 12
1.3.2.Specificcaseofseasurfaces . . . . . . . . . . . . . . . . . . . . . . 19
1.3.3.ElectromagneticroughnessandRayleighroughnesscriterion . . . 21
1.4.Scatteringofelectromagneticwavesfromroughsurfaces: basics . . . . 28
1.4.1.Presentationoftheproblem(2D/3D). . . . . . . . . . . . . . . . . . 28
1.4.2.Huygens’principleandextinctiontheorem . . . . . . . . . . . . . . 30
1.4.3.Greenfunctions(2D/3D) . . . . . . . . . . . . . . . . . . . . . . . . 33
1.4.4.Scatteredpowersandscatteringcoefficients. . . . . . . . . . . . . . 36
CHAPTER2.DERIVATIONOFTHE SCATTERED FIELDUNDER
ASYMPTOTICMODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.1.Bibliographyonexistingmodels . . . . . . . . . . . . . . . . . . . . . . 42
2.1.1.Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.1.2.Rigorousmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.1.3.Asymptoticmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
vi ElectromagneticWaveScatteringfromRandomRoughSurfaces
2.1.4.Generalpropertiesofscattering. . . . . . . . . . . . . . . . . . . . . 52
2.1.5.AfewdetailsontheKAandtheGO . . . . . . . . . . . . . . . . . . 55
2.2.ScatteringinreflectionandtransmissionundertheKA
withshadowingeffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.2.1.KAinreflectionandtransmissionwithshadowing
effectfor2Dproblems. . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.2.2.ExtensionoftheKAmodelto3Dproblems. . . . . . . . . . . . . . 62
2.3.Scatteringinreflectionfor3Dproblemsundervarious
asymptoticmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.3.1.Contextandspecificnotations . . . . . . . . . . . . . . . . . . . . . 69
2.3.2.Thesmallperturbationmodel . . . . . . . . . . . . . . . . . . . . . . 71
2.3.3.TheKirchhoffapproximation–high-frequencyregime . . . . . . . . 73
2.3.4.Theweightedcurvatureapproximation . . . . . . . . . . . . . . . . 75
2.3.5.Thesmallslopeapproximation . . . . . . . . . . . . . . . . . . . . . 75
2.3.6.Thelocalcurvatureapproximation . . . . . . . . . . . . . . . . . . . 76
2.3.7.Theresonantcurvatureapproximation . . . . . . . . . . . . . . . . . 76
2.3.8.Validationofthedifferentasymptoticnumericalmodels
for2Dproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
CHAPTER3.DERIVATIONOFTHE NORMALIZED RADAR
CROSS-SECTIONUNDER ASYMPTOTICMODELS . . . . . . . . . . . . . . 81
3.1.Derivationofincoherentnormalizedradarcross-section
undertheGOfor2Dproblems . . . . . . . . . . . . . . . . . . . . . . . 82
3.1.1.IncoherentNRCSundertheGOwithshadowing
effectfor2Dproblems. . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.1.2.Calculationofthebistaticshadowingfunctionsin
reflectionandtransmission . . . . . . . . . . . . . . . . . . . . . . . 86
3.2.GeneralpropertiesandenergyconservationoftheGO
for2Dproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.2.1.GeneralpropertiesoftheGOfor2Dproblems . . . . . . . . . . . . 97
3.2.2.StudyofenergyconservationundertheGOfor2Dproblems . . . . 99
3.3.ScatteringcoefficientsundertheGOwithshadowing
effectfor3Dproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.4.EnergyconservationoftheGOmodelfor3Dproblems . . . . . . . . . 111
3.4.1.Caseofaperfectlyconductinglowermedium . . . . . . . . . . . . 112
3.4.2.Caseofalosslessdielectriclowermedium . . . . . . . . . . . . . . 115
3.5.Scatteringinreflectionfor3Dproblemsundervarious
asymptoticmodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
3.5.1.ExpressionoftheNRCSundertheSPM1 . . . . . . . . . . . . . . . 118
3.5.2.ExpressionoftheNRCSundertheGO . . . . . . . . . . . . . . . . 118
3.5.3.ExpressionoftheNRCSundertheSSA . . . . . . . . . . . . . . . . 119
3.5.4.Validationandcomparisonofthedifferentasymptotic
analyticalmodelsfor2Dproblems . . . . . . . . . . . . . . . . . . . 119
Contents vii
3.5.5.Comparisonbetweennumericalandanalyticalasymptotic
modelsfor3Dproblems . . . . . . . . . . . . . . . . . . . . . . . . . 121
APPENDIX1.FAR-FIELD SCATTERED FIELDSUNDERTHE METHODOF
STATIONARYPHASE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
APPENDIX 2. CALCULATION OF THE SCATTERING COEFFICIENTS
UNDERTHEGOFOR 3DPROBLEMS . . . . . . . . . . . . . . . . . . . . . . 131
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149