THE SCATTERING OF ELECTROMAGNETIC WAVES FROM ROUGH SURFACES

Transcription

1 THE SCATTERING OF ELECTROMAGNETIC WAVES FROM ROUGH SURFACES Petr Beckmann Andre Spizzichino

2 CONTENTS Part I-THEORY By PETR BECKMANN 1. INTRODUCTION 2. QUALITATIVE CONSIDERATIONS The Rayleigh Criterion The Location and Size of the Active Scattering Region THE GENERAL KIRCHHOFF SOLUTION FOR SCATTERING FROM ROUGH SURFACES General Solution for a Surface Rough in One Dimension General Solution for a Surface Rough in Both Dimensions Properties of the General Solution PERIODICALLY ROUGH SURFACES General Kirchhoff Solution of the Field Scattered by a Perfectly Conducting Periodic Surface The Rayleigh Method Application to Specific Profiles 47 A. Sinusoidal surfaces 47 B. Surfaces generated by superposition 57 С Saw-tooth profiles 58 D. Rectangular corrugations 59 E. Regular distributions of bosses on a plane Finite Conductivity RANDOM ROUGH SURFACES: I. SURFACES GENERATED BY RANDOM PROCESSES Classification of Approaches Rough Surfaces as Random Processes The Normally Distributed Surface Finite Conductivity RANDOM ROUGH SURFACES: II. OTHER MODELS Twersky: Bosses on a Conducting Plane Ament: Randomly Spaced Half-Planes Rice: A Randomized Rayleigh Method Beckmann: Facet Surface Generated by a Markov Chain Du Castel and Spizzichino: Surface of "Brilliant Points" Other Models A Guide to the Literature THE STATISTICAL DISTRIBUTION OF THE SCATTERED FIELD The Probability Distribution of the Sum of Arbitrary Random Coplanar Vectors The Statistical Distribution of the Amplitude of the Scattered Field Coherence and Incoherence of the Scattered Field 146 [v]

3 vi Contents 8. THE DEPOLARIZATION OF ELECTROMAGNETIC WAVES SCATTERED FROM A ROUGH SURFACE The Depolarization Factor Depolarization by a Smooth Plane Depolarization by a Rough Surface in the Plane of Incidence The Depolarization of Laterally Scattered Waves CONCLUSION 176 APPENDIX A A Note on the Helmholtz Integral 178 APPENDIX В Formulae from the Theory of Bessel Functions 182 APPENDIX С Formulae from Probability Theory 185 APPENDIX D The Distribution of Slopes of a Normally Distributed Surface 193 APPENDIX E Evaluation of an Integral 195 APPENDIX F Curves of the Scattered-Field Distribution 199 Part II -APPLICATION By ANDRE SPIZZICHINO {Translated by Petr Beckmann) 10. INTRODUCTION REFLECTION OF ELECTROMAGNETIC WAVES BY A PERFECTLY SMOOTH EARTH The Reflection Coefficient of a Perfectly Plane Earth Effect of the Earth's Curvature Interference of the Direct and Reflected Rays 224 Annex: Nomograms of quantities determining the reflection of electromagnetic waves by a smooth, spherical earth THE REFLECTION OF WAVES FROM IRREGULAR GROUND Qualitative Description of Scattering Phenomena: Criterions of Roughness Specular Reflection and Diffuse Scattering Quantitative Investigation of Specular Reflection in Radio Links Quantitative Investigation of Diffuse Scattering: Mean Value of the Scattered Field Theoretical foundations Practical Application Case I: Link between two points in the vicinity of the earth, "glistening surface" limited by the irregularities of the ground Case II: Terminals of the link near the earth, "glistening surface" bounded by the antenna patterns Case III: One terminal near the ground, the other at infinity The Statistical Distribution of the Scattered Field 277

4 Contents Vll Interference of the Direct Wave with the Diffusely Scattered Component The statistical distribution of the received field The radius of autocorrelation The Depolarization of the Diffusely Scattered Component 285 Annex: Practical determination of the first Fresnel ellipse in some special cases METHODS OF MEASUREMENT OF THE REFLECTION COEFFICIENTS OF THE EARTH; SEPARATION OF THE SPECULAR AND DIFFUSE COMPONENTS Measurement of the Specular Reflection Coefficient of the Earth (in the Absence of Diffuse Scattering) Separation of the reflected ray Interference of the direct with the reflected wave Measurement of the Diffuse-reflection Coefficient of the Earth (in the absence of specular reflection) Separation of the scattered wave Interference of the direct and scattered waves Separation of the Specular and Diffuse Components Separation of the reflected wave; goniometry Interference of the direct and reflected waves 305 Annex: Characteristics of some experimental radio paths used to measure the reflection coefficient of the earth's surface EXPERIMENTAL INVESTIGATION OF THE SPECULAR REFLECTION COEFFICIENT OF THE EARTH Parameters Determining the Reflection Coefficient Experimental Investigation of the Scattering Coefficient p s Dependence of the Reflection Coefficient on Frequency and on the Dimensions of the Irregularities Dependence on the Grazing Angle Dependence on Polarization Dependence on Meteorologie Conditions Very Irregular Terrain Multiple Reflections Fluctuations of the Resultant Field EXPERIMENTAL INVESTIGATION OF DIFFUSE SCATTERING FROM THE EARTH'S SURFACE Survey of the Cases to be Considered Results of Some Experiments Satisfying Conditions (a) to (f) Very Directional Antennae Effect of Vegetation Irregularities of the Ground Smaller than half the Space-wavelength: Diffuse Scattering Superimposed onto Strong Specular Reflection Irregularities Distributed along a Privileged Direction Vertically Polarized Waves Incident near the Brewster Angle Deflection of Antenna Beams: Dimensions of the "Glistening Surface" Depolarization Conclusions. The Rayleigh Criterion SPECULAR REFLECTION: PRACTICAL APPLICATIONS: LINE-OF-SIGHT PROPAGATION OF ULTRA-SHORT WAVES Fieldstrength in Line-of-Sight Links. Origin of Fadings 347

5 viii Contents Slow and Rapid Components of Fluctuations in Line-of-Sight Links Relative Importance of Specular Reflection and Other Components in Lineof-Sight Links Line-of-Sight Paths: Statistical Distribution of the Received Field Fading due to Specular Reflection Diversity Reception on Line-of-Sight Paths Radar Coverage Communication by Specular Reflection (without Visibility) 380 Annex: Characteristics of some experimental paths DIFFUSE SCATTERING: I. PRACTICAL APPLICATIONS Line-of-Sight Paths Communication by Diffuse Ground Reflections without Direct Visibility Scattering of Solar Radiation by the Earth Albedo DIFFUSE SCATTERING: II. APPLICATION TO BACK-SCATTERING BY THE EARTH'S SURFACE The Back-scattering Cross-Section ст Back-Scatter by the Sea at Large Grazing Angles Back-Scatter by Terrain at Large Grazing Angles Back-scattering by the Sea at Small Grazing Angles SCATTERING BY ATMOSPHERIC SHEETS Some Data on the Structure of the Troposphere Theory of Reflection by Tropospheric Sheets Tropospheric Scatter Propagation the Mean Field beyond the Horizon Tropospheric Scatter Propagation Fieldstrength Fluctuations, Bandwidth Limitations, Diversity Effects Some Experimental Verifications Ionospheric and Exospheric Sheets REFLECTION OF RADIO WAVES BY THE MOON AND THE PLANETS Problems Posed by the Reflection of Radio Waves by the Moon Reflections by the Rough Surface of the Moon Theory Reflections by the Rough Surface of the Moon Experimental investigations Reflections of Radio Waves from Venus and from the Sun 469 Annex: Tables of data on experiments with moon reflections quoted in Chapter CONCLUSION 474 BIBLIOGRAPHY 476 AUTHOR INDEX 493 SUBJECT INDEX 497