© 2005 by CRC Press CRC PRESS Boca Raton London New York Washington, D.C. N. A. Armand and V. M. Polyakov Radio Propagation and Remote Sensing of the Environment © 2005 by CRC Press This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. 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Earth sciences—Remote sensing. I. Poliakov, Valerii Mikhailovich. II. Title. TK6553.A675 2004 621.36'78—dc22 2004047816 TF1710_book.fm Page 4 Thursday, September 30, 2004 1:43 PM Visit the CRC Press Web site at www.crcpress.com © 2005 by CRC Press Contents Chapter 1 Electromagnetic Field Equations 1 1.1 Maxwell’s Equations 1 1.2 Energetic Relationships 3 1.3 Solving Maxwell’s Equations for Free Space 4 1.4 Dipole Radiation 7 1.5 Lorentz’s Lemma 11 1.6 Integral Formulas 12 1.7 Approximation of Kirchhoff 17 1.8 Wave Equations for Inhomogeneous Media 18 1.9 The Field Excited by Surface Currents 19 1.10 Elements of Microwave Antennae Theory 22 1.11 Spatial Coherence 25 Chapter 2 Plane Wave Propagation 31 2.1 Plane Wave Definition 31 2.2 Plane Waves in Isotropic Homogeneous Media 32 2.3 Plane Waves in Anisotropic Media 35 2.4 Rotation of Polarization Plane (Faraday Effect) 39 2.5 General Characteristics of Polarization and Stokes Parameters 40 2.6 Signal Propagation in Dispersion Media 44 2.7 Doppler Effect 50 Chapter 3 Wave Propagation in Plane-Layered Media 53 3.1 Reflection and Refraction of Plane Waves at the Border of Two Media 53 3.2 Radiowave Propagation in Plane-Layered Media 59 3.3 Wave Reflection from a Homogeneous Layer 60 3.4 Wentzel–Kramers–Brillouin Method 67 3.5 Equation for the Reflective Coefficient 70 3.6 Epstein’s Layer 74 3.7 Weak Reflections 75 3.8 Strong Reflections 79 3.9 Integral Equation for Determining the Permittivity Depth Dependence 81 Chapter 4 Geometrical Optics Approximation 85 4.1 Equations of Geometrical Optics Approximation 85 4.2 Radiowave Propagation in the Atmosphere of Earth 92 TF1710_book.fm Page 5 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press 4.3 Numerical Estimations of Atmospheric Effects 97 4.4 Fluctuation Processes on Radiowave Propagation in a Turbulent Atmosphere 102 Chapter 5 Radiowave Scattering 111 5.1 Cross Section of Scattering 111 5.2 Scattering by Free Electrons 114 5.3 Optical Theorem 116 5.4 Scattering From a Thin Sheet 118 5.5 Wave Scattering by Small Bodies 120 5.6 Scattering by Bodies with Small Values of ε – 1 126 5.7 Mie Problem 127 5.8 Wave Scattering by Large Bodies 133 5.9 Scattering by the Assembly of Particles 141 5.10 Effective Dielectric Permittivity of Medium 145 5.11 The Acting Field 148 5.12 Incoherent Scattering by Electrons 150 5.13 Radiowave Scattering by Turbulent Inhomogeneities 152 5.14 Effect of Scatterer Motion 154 Chapter 6 Wave Scattering by Rough Surfaces 157 6.1 Statistical Characteristics of a Surface 157 6.2 Radiowave Scattering by Small Inhomogeneities and Consequent Approximation Series 161 6.3 The Second Approximation of the Perturbation Method 167 6.4 Wave Scattering by Large Inhomogeneities 171 6.5 Two-Scale Model 178 6.6 Impulse Distortion for Wave Scattering by Rough Surfaces 182 6.7 What Is Σ ? 187 6.8 The Effect of the Spherical Waveform on Scattering 192 6.9 Spatial Correlation of the Scattered Field 198 6.10 Radiowave Scattering by a Layer with Rough Boundaries 199 Chapter 7 Radiowave Propagation in a Turbulent Medium 211 7.1 Parabolic Equation for the Field in a Stochastic Medium 211 7.2 The Function of Mutual Coherence 215 7.3 Properties of the Function H 217 7.4 The Coherence Function of a Plane Wave 219 7.5 The Coherence Function of a Spherical Wave 220 Chapter 8 Radio Thermal Radiation 221 8.1 Extended Kirchhoff’s Law 221 TF1710_book.fm Page 6 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press 8.2 Radio Radiation of Semispace 224 8.3 Thermal Radiation of Bodies Limited in Size 231 8.4 Thermal Radiation of Bodies with Rough Boundaries 233 Chapter 9 Transfer Equation of Radiation 241 9.1 Ray Intensity 241 9.2 Radiation Transfer Equation 244 9.3 Transfer Equation for a Plane-Layered Medium 247 9.4 Eigenfunctions of the Transfer Equation 250 9.5 Eigenfunctions for a Half-Segment 255 9.6 Propagation of Radiation Generated on the Board 258 9.7 Radiation Propagation in a Finite Layer 259 9.8 Thermal Radiation of Scatterers 263 9.9 Anisotropic Scattering 264 9.10 Diffusion Approximation 268 9.11 Small-Angle Approximation 270 Chapter 10 General Problems of Remote Sensing 275 10.1 Formulation of Main Problem 276 10.1.1 Radar 277 10.1.2 Scatterometer 277 10.1.3 Radio Altimeter 278 10.1.4 Microwave Radiometer 278 10.2 Electromagnetic Waves Used for Remote Sensing of Environment 279 10.3 Basic Principles of Experimental Data Processing 281 10.3.1 Inverse Problems of Remote Sensing 295 Chapter 11 Radio Devices for Remote Sensing 303 11.1 Some Characteristics of Antenna Systems 303 11.2 Application of Radar Devices for Environmental Research 305 11.3 Radio Altimeters 306 11.4 Radar Systems for Remote Sensing of the Environment 308 11.5 Scatterometers 321 11.6 Radar for Subsurface Sounding 323 11.7 Microwave Radiometers 326 Chapter 12 Atmospheric Research by Microwave Radio Methods 335 12.1 Main A Priori Atmospheric Information 335 12.2 Atmospheric Research Using Radar 341 12.3 Atmospheric Research Using Radio Rays 347 12.4 Definition of Atmospheric Parameters by Thermal Radiation 356 TF1710_book.fm Page 7 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press Chapter 13 Remote Sensing of the Ionosphere 365 13.1 Incoherent Scattering 365 13.2 Researching Ionospheric Turbulence Using Radar 370 13.3 Radio Occultation Method 372 13.4 Polarization Plane Rotation Method 373 13.5 Phase and Group Delay Methods of Measurement 373 13.6 Frequency Method of Measurement 375 13.7 Ionosphere Tomography 376 Chapter 14 Water Surface Research by Radio Methods 377 14.1 General Problems of Water Surface Remote Sensing and Basic A Priori Information 377 14.2 Radar Research of the Water Surface State 387 14.3 Microwave Radiometry Technology and Oceanography 396 Chapter 15 Researching Land Cover by Radio Methods 405 15.1 General Status 405 15.2 Active Radio Methods 405 15.3 Passive Radio Methods 420 References 427 TF1710_book.fm Page 8 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press Introduction Airborne instruments designed for remote sensing of the surface of the Earth and its atmosphere are important sources of information regarding the processes occur- ring on Earth. This information is used widely in the fields of meteorology, geog- raphy, geology, and oceanology, among other branches of the sciences. Also, the data gained by satellite observation have been applied to an increasing number of other areas, such as cartography, land surveying, agriculture, forestry, building con- struction, and protection of the environment, to name a few. Most developed coun- tries have a space agency within their governmental organizations, a central task of which is development of remote sensing systems. Airborne and ground-based tech- nologies for remote sensing are developed along with the space systems. Recently, increased attention has been paid to development of microwave tech- nology for remote sensing, particularly synthetic aperture radars and microwave radiometers. This interest is due primarily to two circumstances. The first is con- nected with the fact that spectral channels other than optical are considered, thus providing a new way to obtain additional information on the natural processes of the Earth and its atmosphere. The second circumstance is the transparency of clouds for radiowaves, which allows effective operation of radio systems regardless of weather. In addition, radiowave devices for remote sensing do not require illumina- tion of the territory being observed so data can be collected at any moment of the day. The information gained from data collected by microwave instruments depends on the medium being studied. Interpretation of these data is impossible without analyzing the various mechanisms of interaction that may be present. Such mecha- nisms are the primary scientific basis for designing any device of remote sensing, particularly with regard to choosing the frequency band, polarization, dynamic range, and sensitivity. Stating remote sensing problems requires addressing the principles of radio propagation and such processes as absorption, reflection, scattering, and so on. The interpretation algorithms for remote sensing data are properly based on these processes. This book has generally been written in two parts based on the two circumstances just discussed. The first part describes the processes of radio propagation and the phenomena of absorption, refraction, reflection, and scattering. This discussion is intended to demonstrate determination of coupling between the radiowave parame- ters of amplitude, phase, frequency, and polarization and characteristics of the media (e.g., permittivity, shape). Solutions of well-posed problems provide a basis for estimation of the strength of various effects and demonstrate the importance of media parameters on the appearance of these effects, the possibility of detection of that or other effects against a background of noise and other masking phenomena, and so on. It is necessary to point out that only rather simple models can be analyzed; therefore, the numerical relations between the observed effects and parameters of a TF1710_book.fm Page 9 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press medium itself and radiowaves are of primary importance. Only rarely can natural media be described by simple models, and we must rely on experimental data when determining quantitative relations. It is necessary to keep this in mind with regard to the problems and solutions provided here. The second part of the book is dedicated to analysis of problems that used to be referred to as inverse problems . This analysis attempts to answer the question of how knowledge of radiowave properties allows us to estimate the parameters of the medium studied. Very often, inverse problems are ill posed; as a matter of fact, any measurement happens against a background of noise, and in all cases this concept of noise must be addressed sufficiently with regard to its additive interference with a signal. Inaccuracy of a model itself is also a factor to be considered. A typical peculiarity of ill-posed problems is their instability, manifested in the fact that a small error in the initial data (the data of measurement, in our case) can lead to a big error in the problem solution, in which case additional data must be inserted to remove the instability. These data are often referred to as a priori , and they bound possible solutions of the posed problem. The approximation of models of many natural media requires developing empir- ical methods to interpret remote sensing data. Some of these methods are described in this book, together with brief descriptions of the operational principles of micro- wave devices used in remote sensing. Here, the authors do not intend to delve deeply into either the details of device construction or the algorithms of their data process- ing, as it is very difficult to do so within the limited framework of this book; therefore, only the principal fundamentals are presented. The authors wish to thank the publisher for help in preparation of this book. TF1710_book.fm Page 10 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press 1 1 Electromagnetic Field Equations 1.1 MAXWELL’S EQUATIONS It is well known that the electromagnetic field is generally described by Maxwell’s equations as electric and magnetic fields E and H . Let us suppose the time depen- dence is e – i ω t . Such a notion of time dependence is especially convenient for narrow- band oscillations — that is, for such oscillations that have a spectrum close to the assigned frequency ω and often referred to as the carrier . In this case, the conditions of complex oscillation propagation are practically the same as the propagation conditions for the time-harmonic oscillation of the carrier frequency. This accepted supposition is also advantageous for broad-bandwidth oscillations. The time-har- monic oscillation should only be considered as one of the harmonic components of oscillation (Fourier’s theorem). Later on, magnetic media will not be involved, so permeability is equal to unity. On this basis, Maxwell’s equations may be written as: (1.1) in the Gaussian system of units. Here, k = ω / c = 2 π / λ is the wave number, where ω is the cyclic frequency and c = 3 ⋅ 10 8 cm/sec is the light velocity; D is the electric induction vector; and j is the external current density. The continuity equation resulted from Equation (1.1) is defined as: . (1.2) Material equations connecting E and D vectors are now introduced. In the case of an isotropic medium, this relation is given as: (1.3) where ε ( ω , r ) is the permittivity of the medium, which, in general, is a function of frequency ω and coordinates defined by vector r . This local dependence on the coordinates of r means that spatial dispersion is not taken into account. The permittivity is a complex value; that is, , (1.4) ∇ ×= ∇⋅ = ∇ ×=− + ∇⋅ =EH H H D j Dik ik c ,, ,0 4 4 π πρ iωρ = ∇⋅j Dr rEr () = ()() εω,, εω ε ω ε ω () = ′ () + ′′ () i TF1710_book.fm Page 1 Thursday, September 30, 2004 1:43 PM © 2005 by CRC Press 2 Radio Propagation and Remote Sensing of the Environment where the coordinate dependence is omitted. Here, ε″ ( ω ) describes Joule losses in the medium. In particular, if for static conductivity σ , the corresponding component of the imaginary part is: . (1.5) In an anisotropic medium (for example, in the ionosphere), due to the magnetic field of the Earth, a connection such as Equation (1.3) is substituted for the tensor: , (1.6) which is a summation over the repeating indexes. The tensor components ε αβ are complex functions of frequency (and coordinates in the general case). It is necessary to input boundary conditions at media boundaries. Let n be the unitary normal to the surface (referred to as the normal in this text). The boundary conditions usually described are the continuities of the tangential field components: . (1.7) Here, E 1 , E 2 , H 1 , and H 2 are field components on either side of the boundary. In some cases, we will come across problems when the tangential field components are broken due to the electric and magnetic surface currents of densities K e and K m ; that is, . (1.8) To the boundary conditions, as shown in Equation (1.7), we must add the conditions of radiation, and only divergent (going away) waves must equal infinity. Sometimes, it is more convenient to use gap-type boundary conditions: , (1.9) where ε 1 and ε 2 are the permittivities of media divided by the boundary concerned. They are equivalent to the conditions shown in Equation (1.7), and our use of them is only a matter of convenience. The maintenance conditions (Equations (1.7) and (1.9)) for field H are the equality magnetic fields on both sides of the boundary; that is, . (1.10) ′′ =ε πσ ω σ 4 DE ααββ ε= nEE nHH× −     =×−     =(), ( ) 12 1 2 00 nEE K nHH K 12 1 2 × −     = − × −     =() , ( ) 44ππ cc me nE E nHH 2 ⋅− () = ⋅− () =(),()εε 11 2 1 2 00 HH 12 = TF1710_book.fm Page 2 Thursday, September 30, 2004 1:43 PM [...]... Equations (1. 72) and (1. 73) are integral equations and rather often are the basis for numerical solution of diffraction problems © 2005 by CRC Press TF1 710 _book.fm Page 18 Thursday, September 30, 2004 1: 43 PM 18 Radio Propagation and Remote Sensing of the Environment The essence of Kirchhoff’s approximation is that the field is equal to zero on the reverse side of the screen (reverse according to the incident... as: q1 × E 1  = k H1 ,    q2 × E 2  = k H 2 ,    q1 × H1  = − k E 1 ,    q2 × H 2  = − ε k E 2 ,   ( q ⋅ E ) = ( q ⋅ H ) = 0, 1 (q 1 2 1 ) ( 1 ) ⋅ E 2 = q 2 ⋅ H 2 = 0 (1. 1 01) (1. 102) The last two equalities in Equations (1. 1 01) and (1. 102) reflect the conditions of transversality, defined by the electrical and magnetic field divergence being equal to zero in both media considered The boundary... (1. 66) TF1 710 _book.fm Page 12 Thursday, September 30, 2004 1: 43 PM 12 Radio Propagation and Remote Sensing of the Environment In the case of magnetic dipoles, analogous to Equation (1. 65), we have: ( ) ( ) m1 ⋅ H 2 r1 = m 2 ⋅ H1 r2 (1. 67) 1. 6 INTEGRAL FORMULAS In this part, we obtain an expression for the field inside secluded volume V restricted by S r′ surface S (Figure 1. 1) Let the components of V p... TF1 710 _book.fm Page 14 Thursday, September 30, 2004 1: 43 PM 14 Radio Propagation and Remote Sensing of the Environment We have written Equations (1. 72) and (1. 73) for the case when the observation point is inside the closed surface S These equations must be extended for the case when the point falls outside of the examined surface by using a synthetic method for a surface surrounded by a sphere of. .. (1. 109) TF1 710 _book.fm Page 22 Thursday, September 30, 2004 1: 43 PM 22 Radio Propagation and Remote Sensing of the Environment after some complicated calculations Let us substitute Equation (1. 108) here to obtain: ( γ 1 − γ 2 )E 2 = 4π  1 + γ2  q1 + ( γ 2 − γ 1 )e z  q1 ⋅ K e + − kK e +  c  k εγ 1 + γ 2   ( + γ 2 e z × K m  −   ( ε − 1) q + ( γ 1 ( ) 1 ) + ε γ 2 ez ε 1 + γ2 (q ⋅ e 1. .. z  ∫( ) (1. 135) Here, the function: () γ0 q = 1 4π 2 ∫ γ (s) e 0 − iq⋅s 2 ds (1. 136) is the normalized spatial spectrum of the sources field Index A under the integral in Equation (1. 135) indicates that the integration is carried out within the frame of the limited area (aperture) The expression obtained is the mathematical expression of the van Cittert–Zernike theorem ,11 confirming that the coherence... function of random sources © 2005 by CRC Press TF1 710 _book.fm Page 28 Thursday, September 30, 2004 1: 43 PM 28 Radio Propagation and Remote Sensing of the Environment of radiation is proportional to the Fourier transform of their spatial distribution intensity Equation (1. 135) is sometimes referred to as the generalized theorem of van Cittert–Zernike The theorem itself was proven primarily for the case... The half-power beamwidth is estimated by the value: ∆θ = 0. 512 λ λ = 1. 02 a 2a (1. 119 ) The result obtained corroborates the rule that the beamwidth of an antenna of size D has a value of the order λ/D Essentially, this rule is the result of the wave diffraction laws and follows from the principle of uncertainty typical of a Fourier transform This rule means, in particular, that the cross section of. .. ( ) 1 U 0 s1 U ∗ s 2 0 2 (1. 126) TF1 710 _book.fm Page 26 Thursday, September 30, 2004 1: 43 PM 26 Radio Propagation and Remote Sensing of the Environment Conceptually, we should have to calculate the real part of the defined coherence function and apply the corresponding equation for ReΓU; however, it is easier to employ the equation for the complex coherent function and to seek its real part in the. .. that: (e z π ) 1 (e ⋅ E ) − ε4ω (q ⋅ K ) ε ⋅E2 = z 1 1 (1. 106) e If we multiply Equation (1. 103) vectorially by ez and use the result, Equation (1. 106), we obtain: E 2 = E1 −  ε 1 4π  e z e z e z ⋅ E1 −  εk q1 ⋅ K e + e z × K m     ε c   ( ) ( ) (1. 107) Let us multiply this equation scalarly by q2 and use the equation of transversity and relation, Equation (1. 100), to obtain the equality: . Approximation 268 9 .11 Small-Angle Approximation 270 Chapter 10 General Problems of Remote Sensing 275 10 .1 Formulation of Main Problem 276 10 .1. 1 Radar 277 10 .1. 2 Scatterometer 277 10 .1. 3 Radio Altimeter. Remote Sensing 295 Chapter 11 Radio Devices for Remote Sensing 303 11 .1 Some Characteristics of Antenna Systems 303 11 .2 Application of Radar Devices for Environmental Research 305 11 .3 Radio. Cataloging-in-Publication Data Armand, N. A. Radio propagation and remote sensing of the environment / N.A. Armand, V.M. Polyakov. p. cm. Includes bibliographical references and index. ISBN 0-4 1 5-3 17 3 5-5