Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering

by Michael I. Mishchenko , Larry D. Travis , Andrew A. Lacis

• ISBN13: 9780521834902
• ISBN10: 0521834902
• Format: Hardcover
• Copyright: 2006-05-08
• Publisher: Cambridge University Press

Summary

This volume provides a thorough and up-to-date treatment of multiple scattering of light and other electromagnetic radiation in media composed of randomly and sparsely positioned particles. It systematically and consistently presents radiative transfer theory as a branch of classical macroscopic electromagnetics. After tracing the fundamental link between radiative transfer theory and the effect of coherent backscattering, the authors explain them in the context of a comprehensive hierarchy of electromagnetic scattering problems. Dedicated sections present a thorough discussion of the physical meaning and range of applicability of the radiative transfer equation and compare the self-consistent microphysical and the traditional phenomenological approaches to radiative transfer. This self-contained book will be valuable for science professionals, engineers, and graduate students working across a wide range of disciplines including optics, electromagnetics, remote sensing, atmospheric radiation, astrophysics, and biomedicine.

Table of Contents

Preface	xi
Dedication and acknowledgments	xv
Introduction	1	(19)
Electromagnetic scattering by a fixed finite object	1	(4)
Actual observables	5	(1)
Foldy--Lax equations	6	(1)
Dynamic and static scattering by random groups of particles	7	(2)
Ergodicity	9	(1)
Single scattering by random particles	10	(2)
Multiple scattering by a large random group of particles	12	(2)
Coherent backscattering	14	(2)
Classification of electromagnetic scattering problems	16	(2)
Notes and further reading	18	(2)
Maxwell equations, electromagnetic waves, and Stokes parameters	20	(46)
Maxwell equations and constitutive relations	20	(3)
Boundary conditions	23	(3)
Time-harmonic fields	26	(2)
The Poynting vector	28	(3)
Plane-wave solution	31	(6)
Coherency matrix and Stokes parameters	37	(4)
Ellipsometric interpretation of the Stokes parameters	41	(6)
Rotation transformation rule for the Stokes parameters	47	(1)
Quasi-monochromatic light	48	(6)
Measurement of the Stokes parameters	54	(4)
Spherical-wave solution	58	(4)
Coherency dyad of the electric field	62	(2)
Historical notes and further reading	64	(2)
Basic theory of electromagnetic scattering	66	(49)
Volume integral equation and Lippmann-Schwinger equation	67	(4)
Scattering in the far-field zone	71	(7)
Scattering dyadic and amplitude scattering matrix	78	(2)
Reciprocity	80	(4)
Scale invariance rule	84	(3)
Electromagnetic power and electromagnetic energy density	87	(6)
Phase matrix	93	(6)
Extinction matrix	99	(3)
Extinction, scattering, and absorption cross sections	102	(3)
Coherency dyad of the total electric field	105	(4)
Other types of illumination	109	(1)
Variable scatterers	110	(2)
Thermal emission	112	(2)
Historical notes and further reading	114	(1)
Scattering by a fixed multi-particle group	115	(8)
Vector form of the Foldy--Lax equations	115	(3)
Far-field version of the vector Foldy--Lax equations	118	(5)
Statistical averaging	123	(8)
Statistical averages	124	(2)
Configurational averaging	126	(1)
Averaging over particle states	126	(5)
Scattering by a single random particle	131	(9)
Scattering in the far-field zone of the trap volume	131	(5)
``Near-field'' scattering	136	(4)
Single scattering by a small random particle group	140	(25)
Single-scattering approximation for a fixed group of particles	141	(1)
Far-field single-scattering approximation for a fixed particle group	142	(3)
Far-field uncorrelated single-scattering approximation and modified uncorrelated single-scattering approximation	145	(2)
Forward-scattering interference	147	(4)
Energy conservation	151	(1)
Conditions of validity of the far-field modified uncorrelated single-scattering approximation	151	(7)
First-order-scattering approximation	158	(5)
Discussion	163	(2)
Radiative transfer equation	165	(62)
The Twersky approximation	166	(5)
The Twersky expansion of the coherent field	171	(2)
Coherent field	173	(7)
Transfer equation for the coherent field	180	(1)
Dyadic correlation function in the ladder approximation	181	(10)
Integral equation for the ladder specific coherency dyadic	191	(4)
Integro-differential equation for the diffuse specific coherency dyadic	195	(2)
Integral and integro-differential equations for the diffuse specific coherency matrix	197	(1)
Integral and integro-differential equations for the diffuse specific coherency column vector	198	(1)
Integral and integro-differential equations for the specific intensity column vector	199	(1)
Summary of assumptions and approximations	200	(3)
Physical meaning of the diffuse specific intensity column vector and the coherent Stokes column vector	203	(5)
Energy conservation	208	(1)
External observation points	209	(8)
Coherent field	210	(1)
Ladder coherency dyadic	211	(2)
Specific intensity column vector	213	(1)
Discussion	214	(2)
Illustrative example: first-order scattering	216	(1)
Other types of illumination	217	(1)
Phenomenological approach to radiative transfer	218	(6)
Scattering media with thermal emission	224	(1)
Historical notes and further reading	225	(2)
Calculations and measurements of single-particle characteristics	227	(13)
Exact theoretical techniques	227	(7)
Approximations	234	(3)
Measurement techniques	237	(2)
Further reading	239	(1)
Radiative transfer in plane-parallel scattering media	240	(21)
The standard problem	240	(3)
The propagator	243	(2)
The general problem	245	(2)
Adding equations	247	(8)
Invariant imbedding equations	255	(3)
Ambarzumian equation	258	(1)
Reciprocity relations for the reflection and transmission matrices	259	(1)
Notes and further reading	260	(1)
Macroscopically isotropic and mirror-symmetric scattering media	261	(41)
Symmetries of the Stokes scattering matrix	262	(3)
Macroscopically isotropic and mirror-symmetric scattering medium	265	(1)
Phase matrix	266	(4)
Forward-scattering direction and extinction matrix	270	(3)
Backward scattering	273	(2)
Scattering cross section and asymmetry parameter	275	(1)
Thermal emission	276	(1)
Spherically symmetric particles	277	(1)
Effects of nonsphericity and orientation	278	(1)
Normalized scattering and phase matrices	279	(3)
Expansion in generalized spherical functions	282	(4)
Circular-polarization representation	286	(5)
Illustrative examples	291	(11)
Radiative transfer in plane-parallel, macroscopically isotropic and mirror-symmetric scattering media	302	(22)
The standard problem	302	(2)
The general problem	304	(2)
Adding equations	306	(5)
Invariant imbedding and Ambarzumian equations	311	(2)
Successive orders of scattering	313	(2)
Symmetry relations	315	(3)
Phase matrix	315	(1)
Reflection and transmission matrices	316	(1)
Matrices describing the internal field	317	(1)
Perpendicular directions	317	(1)
Fourier decomposition	318	(3)
Fourier decomposition of the VRTE	318	(1)
Fourier components of the phase matrix	319	(2)
Scalar approximation	321	(1)
Notes and further reading	322	(2)
Illustrative applications of radiative transfer theory	324	(41)
Accuracy of the scalar approximation	324	(23)
Rayleigh-scattering slabs	325	(12)
Polydisperse spherical particles and spheroids	337	(10)
Directional reflectance and spherical and plane albedos	347	(10)
Polarization as an effect and as a particle characterization tool	357	(5)
Depolarization	362	(1)
Further reading	362	(3)
Coherent backscattering	365	(42)
Specific coherency dyadic	366	(5)
Reflected light	371	(2)
Exact backscattering direction	373	(6)
Other types of illumination	379	(1)
Photometric and polarimetric characteristics of coherent backscattering	380	(6)
Unpolarized incident light	380	(1)
Linearly polarized incident light	381	(1)
Circularly polarized incident light	382	(1)
General properties of the enhancement factors and polarization ratios	383	(2)
Spherically symmetric particles	385	(1)
Benchmark results for Rayleigh scattering	386	(1)
Numerical results for polydisperse spheres and polydisperse, randomly oriented spheroids	386	(9)
Angular profile of coherent backscattering	395	(7)
Further discussion of theoretical and practical aspects of coherent backscattering	402	(2)
Applications and further reading	404	(3)
Appendix A Dyads and dyadics	407	(2)
Appendix B Spherical wave expansion of a plane wave in the far-field zone	409	(2)
Appendix C Euler rotation angles	411	(2)
Appendix D Integration quadrature formulas	413	(3)
Appendix E Stationary phase evaluation of a double integral	416	(2)
Appendix F Wigner functions, Jacobi polynomials, and generalized spherical functions	418	(11)
Wigner d-functions	418	(4)
Jacobi polynomials	422	(1)
Orthogonality and completeness	422	(1)
Recurrence relations	423	(1)
Legendre polynomials and associated Legendre functions	424	(1)
Generalized spherical functions	425	(1)
Wigner D-functions, addition theorem, and unitarity	426	(2)
Further reading	428	(1)
Appendix G Systeme International units	429	(2)
Appendix H Abbreviations	431	(2)
Appendix I Glossary of symbols	433	(9)
References	442	(27)
Index	469