TOPICS FOR A STATISTICAL DESCRIPTION OF
RADAR CROSS SECTION
Andrew Lewis Maffett WlLEY
Jin Au Kong, Editor
Tsang, Kong, Shin THEORY OF MICROWAVE REMOTE SENSING
Hord REMOTE SENSING: METHODS AND APPLICATIONS
Elachi INTRODUCTION TO THE PHYSICS AND TECHNIQUES OF
REMOTE SENSING
Szekielda SATELLITE MONITORING OF THE EARTH
Maffett TOPICS FOR A STATISTICAL DESCRIPTION OF
RADAR CROSS SECTION
Asrar THEORY AND APPLICATIONS OF OPTICAL REMOTE
SENSING
Copyright 0 1989 by John Wiley & Sons, Inc
All rights reserved. Published simultaneously in Canada.
Reproduction or translation of any part of this work
beyond that permitted by Section 107 or 108 of the
1976 United States Copyright Act without the permission
of the copyright owner is unlawful. Requests for
permission or further information should be addressed to
the Permissions Department, John Wiley & Sons, Inc.
Library of Congress Cataloging in Publication Data:
Maffett, Andrew Lewis.
Topics for a statistical description of radar
cross section.
(Wiley series in remote sensing)
"A Wiley-Interscience publication."
Bibliography: p.
Includes index.
1. Radar-Statistical methods. 2. Radar-Mathematical
models. I. Title. 11. Series
TK6580.M34 1989 621 -3848 88-20698
ISBN 0-471-61357-6
Printed in the United States of America
CONTENTS
PREFACE
ACKNOWLEDGMENTS
HISTORICAL BACKGROUND AND PERSPECTIVE
PART l
FUNDAMENTALS
CHAPTER 1
DEFINITION OF FIELD QUANTITIES AND MAXWELL'S
EQUATIONS 9
1-1 Differential Operators 12
1-2 Flux Densities and Fields 14
1-3 Maxwell's Equations 15
1-4 Time-Harmonic Fields 17
1-5 Plane Waves 18
1-6 Polarization 20
CHAPTER 2
CONSTITUTIVE RELATIONS
2-1 Waves in Dissipative Media
2-2 Perfect Conductors
CHAPTER 3
BOUNDARY CONDITIONS AND SURFACE CURRENTS 31
3-1 Poynting's Theorem -
3-2 Reflection and Transmission at a Plane Boundary
CHAPTER 4
GREEN'S FUNCTIONS 4 1
4-1 Aside on the &Function and the Fourier Transform
4-2 Far Approximation
4-3 Hertzian Dipole
4-4 Duality
4-5 Uniqueness
4-6 Equivalent Source
4-7 Huygens's Principle
CHAPTER 5
RADAR CROSS SECTION (RCS)
5-1 Other Cross Sections
5-2 Two- and Three-Dimensional RCS
PART II
SCATTERING AND DIFFRACTION OF
ELECTROMAGNETIC WAVES
CHAPTER 6
DIFFRACTION OF A PLANE WAVE BY A PERFECTLY
ABSORBING HALF-PLANE 63
6-1 Some Details about the Path C 65
6-2 Integration by Stationary Phase and Steepest Descents Methods 68
CHAPTER 7
ASYMPTOTIC APPROXIMATION METHODS
7-1 Rayleigh Theory 71
7-2 Geometrical Optics 76
CHAPTER 8
DIFFRACTION APPROXIMATION METHODS
8-1 Physical Optics Approximation for Hs: The Bistatic Theorem 81
8-2 Method of Equivalent Currents (MEC)
8-3 ApplicBtion: A Composite Model for Sea Scattering
CHAPTER 9
NUMERICAL APPROXIMATIONS AND NUMERICAL
METHODS
9-1 A Numerical Approximation for Physical Optics
9-2 Integral Representations of Fields
9-3 Method of Moments (MOM)
9-4 Application of the MOMt o Sca-tt ering
9-5 PO Combo
9-6 Two-Dimensional Scatterers
9-7 Historical Perspective
CHAPTER 10
RCS MEASUREMENTS
10-1 Basic Principles of Electromagnetic Scattering Measurements
10-2 Far Field Criterion
10-3 Field Variation
10-4 Ground Plane Effects
10-5 Background
10-6 Power Relations
10-7 Antennas
10-8 Coordinate Systems and Transformations
10-9 Recording of Data
10-1 0 Scaling
10-1 1 The Compact Range
10-1 2 Near Field Measurements
10-13 Radar Ranges
PART Ill
PRACTICAL ASPECTS OF RCS
CHAPTER 11
RCS OF SIMPLE SHAPES
11 -1 Rayleigh Theory: A Different Viewpoint
1 1-2 Rayleigh RCS Shape Factor
11 -3 Asymptotic Evaluation of Scattering Integrals
11 -4 Interpretation of PO Integral-Truncated Elliptic Cone
1 1-5 Miscellaneous Simple Shapes
1 1-6 ' RCS of a Cavity
11 -7 Traveling Waves -
1 1-8 Creeping Waves
1 1-9 Two-Dimensional Scattering Examples
15-8 Detection Theory Using the @-Distributiono f Target RCS
15-9 -Example: 727 Over a North Carolina Forest
PART IV
CONSTITUTIVE PARAMETERS
CHAPTER 16
IMPEDANCE BOUNDARY CONDITION CHAPTER 12
RCS OF COMPLEX SHAPES
16-1 Thick, Thin, and Resonant Absorbers
16-2 Multiple Layers Over an Arbitrary Ground Plane
16-3 Salisbury Screen
16-4 Two Theorems of Weston
16-5 The Impedance Boundary Condition and Physical Optics
16-6 Two-Dimensional Coated Scatterers
12-1 First Order Statistics of RCS
12-2 Higher Order Statistics of RCS
12-3 Special Statistics of RCS
12-4 @-Parameters
12-5 Random Amplitudes
12-6 Allowable Regions
12-7 Statistics of RCS Scintillation: Lobe Structure
12-8 Glint CHAPTER 17
REFLECTION AND TRANSMISSION: A DIFFERENT
VIEWPOINT 31 1
CHAPTER 13
EXAMPLES: 727 AT 0.94 GHz; FIREBEE AT 9.0 GHz
13-1 The 727-1 00C
13-2 The Firebee
17-1 Phase Matching 31 1
17-2 k-Surfaces 313
17-3 Ray Vectors and Ray Surfaces 31 5
17-4 Phase Matching with k-Surfaces 316
CHAPTER 14 CHAPTER 18
A NEW METHOD FOR COMPARING EXPERIMENTAL STRATIFIED MEDIA [exp(jot)]
AND THEORETICAL DATA
18-1 Reflectivity
CHAPTER 15
ELEMENTS OF DETECTION THEQRY
CHAPTER 19
GYROELECTROMAGNETlC LAYERS
15-1 Example of Hypothesis Testing
15-2 Likelihood Ratio
15-3 Likelihood Ratio Example
15-4 Error Types: Probabilities of False Alarm (PFA) and Detection (PD)
15-5 Test Criteria
15-6 Multiple Samples
15-7 Radar Detection of Targets
19-1 Geometry of the Problem
19-2 Dispersion Relation for General Anisotropic Media
19-3 Particular Cases
19-4 Special Anisotropy
19-5 NASC That a Material Be Biaxial
19-6 Gyroelectromagnetic Layers
19-7 Chain Matrix Algorithm
19-8 Penetrable Backing
19-9 Numerical Results
CHAPTER 20
THE INVERSE PROBLEM FOR BlAXlAL MATERIALS
CONTENTS
20-1 The Boundary Value Problem
20-2 The Inverse Problem
20-3 Lossless Nondispersive Material
20-4 Lossy Dispersive Material
20-5 Measurement Procedure
20-6 Additional Comment
REFERENCES
AUTHOR INDEX
SUBJECT INDEX
PREFACE
This book treats the subject of radar cross section (RCS), with special
emphasis on the statistical aspects and applications thereof. To that
purpose, it is organized into four parts, of which the third part forms the
central core:
I. Fundamentals including notation, definitions, and formulas,
11. Scattering and diffraction of electromagnetic waves; approximations
from asymptotic and numerical methods,
111. Practical RCS analyses and applications using statistical methods,
and
IV. The role of constitutive parameters in RCS.
The material is arranged so that each part consists of five chapters, each
of which is designed to occupy a two-hour lecture period. Thus, the 20
chapters can be used for a standard 40-hour course of lectures. The material
has, in fact, been used twice in this manner for groups of working engineers;
so it has benefited considerably from constructive comment and criticism
offered by the listeners.
Chapters 1 through 5 review and establish the notation, the basic
definitions and theorems of electromagnetic theory. Chapters 6 through 10
present and discuss some results of asymptotic approximation theories as
well as numerical and measurement methods. In Chapters 11 through 15
these RCS estimation theories are combined with statistical ideas to show
that the RCS of a complex target is /?-distributed (Chapter 12). This salient
result is verified with measured data in Chapter 13 and is then applied, in
Chapter 15, to the subject of detection theory.
xiii
xiv PREFACE
All of Chapters 1 through 15 are develped under the assumptions that (1)
the medium of propagation is free space and (2) the scattering bodies are
perfect conductors (i.e., metallic). Chapters 16 through 20, in contrast, look
at the nature of results that can be established when assumptions 1 and 2 are
lifted.
Each chapter has its own equation and figure numbers beginning with
unity.
This work is aimed at RCS estimation for complex targets, based iargely
on statistical methods. Siegel, beginning in the 1950s, promoted the use of
first order statistics of RCS (mean and variance), described by Crispin and
Maffett (1965), to this purpose. In the 1980s, Follin used higher order
statistics of RCS to show that the RCS of a complex target can be described,
in the neighborhood of some fixed but arbitrary aspect, by a @-distribution;
this idea was further developed by Follin and Maffett (1981), and by Follin,
Paddison, and Maffett (1984) and is expanded with additional detail and
examples (especially as regards detection theory and the comparison of RCS
data) in Chapters 11 through 15 of this work.
Dexter, Michigan
November 1988
Radar Cross Section (RCS) measurements.
Topics For a Statistical Description Of Radar Cross Section: Topics For a Statistical Description Of Radar Cross Section.part01.rar
