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Multiple Scattering of Light by Particles
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Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering
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MultipleScatteringofLightbyParticles:
RadiativeTransferandCoherentBackscattering
Book·January2006
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Radiative Transfer and
Coherent Backscattering
Michael I. Mishchenko
Larry D. Travis
Andrew A. Lacis
NASA Goddard Institute for Space Studies, New York
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
CAMBRIDGE UNIVERSITY PRESS
The Edinburgh Building, Cambridge CB2 2RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521834902
© NASA 2006
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 2006
Printed in the United Kingdom at the University Press, Cambridge
A catalog record for this publication is available from the British Library
ISBN-13 978-0-521-83490-2 hardback
ISBN-10 0-521-83490-2 hardback
Cambridge University Press has no responsibility for the persistence
or accuracy of URLs for external or third-party internet websites referred to in
this publication, and does not guarantee that any content on such websites is, or will
remain, accurate or appropriate.
v
Contents
Preface xi
Dedication and acknowledgments xv
Chapter 1 Introduction 1
1.1 Electromagnetic scattering by a fixed finite object 1
1.2 Actual observables 5
1.3 Foldy–Lax equations 6
1.4 Dynamic and static scattering by random groups of particles 7
1.5 Ergodicity 9
1.6 Single scattering by random particles 10
1.7 Multiple scattering by a large random group of particles 12
1.8 Coherent backscattering 14
1.9 Classification of electromagnetic scattering problems 16
1.10 Notes and further reading 18
Chapter 2 Maxwell equations, electromagnetic waves, and Stokes
parameters 20
2.1 Maxwell equations and constitutive relations 20
2.2 Boundary conditions 23
2.3 Time-harmonic fields 26
2.4 The Poynting vector 28
2.5 Plane-wave solution 31
2.6 Coherency matrix and Stokes parameters 37
2.7 Ellipsometric interpretation of the Stokes parameters 41
Multiple Scattering of Light by Particlesvi
2.8 Rotation transformation rule for the Stokes parameters 47
2.9 Quasi-monochromatic light 48
2.10 Measurement of the Stokes parameters 54
2.11 Spherical-wave solution 58
2.12 Coherency dyad of the electric field 62
2.13 Historical notes and further reading 64
Chapter 3 Basic theory of electromagnetic scattering 66
3.1 Volume integral equation and Lippmann–Schwinger equation 67
3.2 Scattering in the far-field zone 71
3.3 Scattering dyadic and amplitude scattering matrix 78
3.4 Reciprocity 80
3.5 Scale invariance rule 84
3.6 Electromagnetic power and electromagnetic energy density 87
3.7 Phase matrix 93
3.8 Extinction matrix 99
3.9 Extinction, scattering, and absorption cross sections 102
3.10 Coherency dyad of the total electric field 105
3.11 Other types of illumination 109
3.12 Variable scatterers 110
3.13 Thermal emission 112
3.14 Historical notes and further reading 114
Chapter 4 Scattering by a fixed multi-particle group 115
4.1 Vector form of the Foldy–Lax equations 115
4.2 Far-field version of the vector Foldy–Lax equations 118
Chapter 5 Statistical averaging 123
5.1 Statistical averages 124
5.2 Configurational averaging 126
5.3 Averaging over particle states 126
Chapter 6 Scattering by a single random particle 131
6.1 Scattering in the far-field zone of the trap volume 131
6.2 “Near-field” scattering 136
Chapter 7 Single scattering by a small random particle group 140
7.1 Single-scattering approximation for a fixed group of particles 141
7.2 Far-field single-scattering approximation for a fixed particle
group 142
7.3 Far-field uncorrelated single-scattering approximation and modified
uncorrelated single-scattering approximation 145
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