Light Scattering Reviews: Single and Multiple Light Scattering

509 Pages·2006·6.023 MB·English

by  Olga Muñoz, Hester Volten (auth.), Dr Alexander A. Kokhanovsky (eds.)

Light Scattering Reviews
SingleandMultipleLightScattering
Alexander A. Kokhanovsky (Editor)
Light Scattering
Reviews
Single and Multiple Light Scattering
Published inassociationwith
PPrraaxxiiss PPuubblliisshhiinngg
Chichester, UK
Editor
Dr Alexander A. Kokhanovsky
Institute of Environmental Physics
University of Bremen
Bremen
Germany
SPRINGER–PRAXIS BOOKS IN ENVIRONMENTAL SCIENCES
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Contents
List of contributors .............................................. XI
Notes on the contributors .......................................XIII
Preface ..........................................................XXI
Part I Single Light Scattering
1 Experimental light scattering matrices from the Amsterdam
Light Scattering Database
Olga Mun˜oz and Hester Volten ...................................... 3
1.1 Introduction.................................................. 3
1.2 Light scattering theory ........................................ 4
1.3 Experimental method ......................................... 4
1.3.1 Calibration measurements............................... 7
1.4 Database .................................................... 9
1.4.1 Samples .............................................. 9
1.4.2 Scanning electron microscope images ..................... 9
1.4.3 Particle composition and refractive indices ................ 10
1.4.4 Size distributions ...................................... 10
1.4.5 Measurements ......................................... 12
1.5 Applications and examples ..................................... 14
1.5.1 Mineral aerosol particles with moderate refractive indices ... 15
1.5.2 Shape effect ........................................... 20
1.5.3 Size effect............................................. 21
1.5.4 Color effect ........................................... 24
1.6 Conclusions .................................................. 26
References ........................................................ 26
2 Light scattering and absorption by nonspherical ice crystals
Ping Yang and Kuo-Nan Liou ....................................... 31
2.1 Introduction.................................................. 31
2.2 Geometric optics for light scattering by large ice crystals........... 33
2.3 The finite-difference time domain method ........................ 47
2.4 Numerical examples ........................................... 53
2.5 Summary .................................................... 61
References ........................................................ 64
VI Contents
3 Light scattering and absorption characteristics of optically
soft particles
Subodh K. Sharma ................................................. 73
3.1 Introduction.................................................. 73
3.2 Small phase shifts............................................. 73
3.2.1 Rayleigh–Gans-Debye approximation ..................... 73
3.2.2 Modified RGDA ....................................... 76
3.2.3 Quasistatic approximation .............................. 76
3.2.4 Shifrin and Ston approximation.......................... 77
3.2.5 Walstra approximation ................................. 77
3.3 Potential scattering ........................................... 77
3.4 Arbitrary phase shifts ......................................... 80
3.4.1 Straight line approximations............................. 81
3.4.2 Perelman approximation ............................... 95
3.4.3 Hart and Montroll approximation ....................... 99
3.4.4 Evans and Fournier approximation ....................... 100
3.4.5 Bohren and Nevitt approximation........................ 101
3.4.6 Numerical comparisons ................................. 103
3.5 Nonspherical scatterers ........................................ 105
3.6 Applications.................................................. 113
References ........................................................ 116
4 Single light scattering: computational methods
Victor G. Farafonov and Vladimir B. Il’in ............................ 125
4.1 Introduction.................................................. 125
4.2 Light scattering problem....................................... 126
4.2.1 Maxwell equations ..................................... 126
4.2.2 Hertz vectors and scalar potentials ....................... 126
4.2.3 Light scattering problem for a small particle............... 127
4.2.4 Methods of solving the problem using field expansions ...... 128
4.2.5 Selected bibliography................................... 131
4.2.6 Specific approach for axisymmetric scatterers.............. 133
4.3 Solutions using the spherical wave functions ...................... 134
4.3.1 Potential expansions.................................... 135
4.3.2 Boundary conditions ................................... 136
4.3.3 Methods to determine the expansion coefficients ........... 138
4.3.4 Applicability of the methods based on the spherical basis ... 145
4.4 Solutions using the spheroidal wave functions..................... 150
4.4.1 Features of the problem formulation...................... 151
4.4.2 Some details of the methods............................. 156
4.4.3 Applicability of the methods based on the spheroidal basis .. 162
4.5 Solution using the ellipsoidal wave functions...................... 166
4.5.1 Ellipsoidal coordinates.................................. 166
4.5.2 Scalar potentials and the separation of variables ........... 167
4.5.3 Ellipsoidal wave functions............................... 167
4.5.4 Potential expansions.................................... 168
Contents VII
4.5.5 Determination of the expansion coefficients................ 169
4.5.6 Comparison with a solution based on the spheroidal basis ... 170
4.6 Concluding remarks ........................................... 170
References ........................................................ 171
Part II Multiple Light Scattering
5 Multiple scattering of short waves by uncorrelated and
correlated scatterers
Anatoli G. Borovoi................................................. 181
5.1 Waves in free space ........................................... 182
5.1.1 General equations...................................... 182
5.1.2 Chain of wave equations ................................ 183
5.1.3 Corpuscular treatment of short waves..................... 185
5.1.4 Equations for quadratic values........................... 187
5.1.5 Energy conservation law ................................ 190
5.2 Wave scattering............................................... 193
5.2.1 Scatterers............................................. 193
5.2.2 General wave scattering equation ........................ 195
5.2.3 Scattered field in the wave zone.......................... 196
5.2.4 Optical theorem ....................................... 197
5.2.5 Scattering of waves by small scatterers.................... 199
5.2.6 Large scatterers........................................ 200
5.3 Multiple scattering of waves .................................... 210
5.3.1 General equations...................................... 210
5.3.2 Two limiting cases for multiple scattering of waves ......... 213
5.4 Multiple scattering by uncorrelated scatterers .................... 215
5.4.1 Uncorrelated scatterers ................................. 215
5.4.2 Average or coherent field................................ 216
5.4.3 Multiple scattering of short and long waves................ 219
5.4.4 Exponential extinction law .............................. 221
5.4.5 Radiative transfer equation.............................. 224
5.4.6 Assessment of remaining diagrams ....................... 229
5.4.7 Spatial coherence function for random media
with large scatterers.................................... 230
5.4.8 Small-angle radiative transfer equation ................... 233
5.5 Multiple scattering by correlated scatterers....................... 236
5.5.1 Correlated scatterers ................................... 236
5.5.2 General equations...................................... 238
5.5.3 Transparency for ensembles of correlated scatterers......... 239
5.5.4 Transparency of monolayers ............................. 242
5.5.5 Transparency of random media in the framework
of the stochastic radiative transfer theory ................. 248
Bibliographic comments ............................................ 251
VIII Contents
6 Asymptotic radiative transfer
A.A. Kokhanovsky ................................................. 253
6.1 Introduction.................................................. 253
6.2 Radiative transfer equation..................................... 254
6.3 Reflection and transmission functions............................ 256
6.4 Asymptotic theory ............................................ 259
6.4.1 Auxiliary functions and relationships ..................... 259
6.4.2 Asymptotic equations .................................. 266
6.4.3 Weak absorption....................................... 267
6.4.4 Nonabsorbing media.................................... 276
6.5 Exponential approximation..................................... 280
6.5.1 Semi-infinite light scattering media....................... 280
6.5.2 Optically thick light scattering layers ..................... 283
6.6 Conclusion ................................................... 286
References ........................................................ 287
7 Multiple scattering of polarized light in turbid media with
large particles
Evgenii E. Gorodnichev, Alexander I. Kuzovlev, and Dmitrii B. Rogozkin . 291
7.1 Introduction.................................................. 291
7.2 General relations.............................................. 292
7.3 Polarization mode approximation ............................... 296
7.4 Diffusive propagation.......................................... 304
7.5 Small-angle multiple scattering ................................. 310
7.5.1 Unpolarized light ...................................... 310
7.5.2 Circularly polarized light................................ 316
7.5.3 Linearly polarized light ................................. 319
7.6 A narrow beam of linearly polarized light ........................ 325
7.7 Discussion ................................................... 331
References ........................................................ 334
8 Adjoint radiative transfer equation and inverse problems
Vladimir V. Rozanov ............................................... 339
8.1 Introduction.................................................. 339
8.2 Instrument response function and the mathematical model of the
ideal measurement ............................................ 341
8.3 Linearization and the variational derivative....................... 343
8.4 Standard and generalized forms of the vector RTE ................ 346
8.4.1 Standard form of the vector RTE ........................ 347
8.4.2 Operator form of the direct VRTE ....................... 349
8.4.3 Generalized form of the direct VRTE..................... 350
8.5 Generalized form of the adjoint radiative transfer operator ......... 351
8.6 Adjoint radiative transfer equation .............................. 354
8.7 General expression for the weighting function..................... 357
8.7.1 Linearization of the direct VRTE with respect to the
variation of optical and surface parameters ................ 357
Contents IX
8.7.2 Adjoint approach and the weighting function .............. 360
8.8 Weighting functions for main optical and surface parameters ....... 361
8.9 Other representations for weighting functions..................... 365
8.9.1 Separation of the total adjoint intensity in the diffuse and
direct components ..................................... 366
8.9.2 Representation of weighting functions for the total forward
and diffuse adjoint intensity (TD representation)........... 369
8.9.3 Representationofweightingfunctionsforthediffuseforward
and diffuse adjoint intensity (DT and DD representation) ... 370
8.9.4 Using the formal solution of the direct VRTE for the
weighting function derivation ............................ 372
8.10 Comparison with previous results ............................... 376
8.11 Conclusion ................................................... 382
Appendix A: Derivation of t(τ,µ) and b(τ,µ) .......................... 384
Appendix B: Adjoint modified differential operator..................... 386
References ........................................................ 388
Part III Applications
9 Light scattering in combustion
Alan R. Jones ..................................................... 393
9.1 Introduction.................................................. 393
9.2 Soot and other nanoparticles ................................... 394
9.3 Liquid fuel sprays and pulverised fuel (PF)....................... 414
9.4 Numerical inversion ........................................... 432
9.5 Inclusions.................................................... 433
9.6 Conclusions .................................................. 437
9.7 Symbols ..................................................... 438
References ........................................................ 439
10 Absorption and scattering of light in natural waters
Vladimir I. Haltrin................................................. 445
10.1 Introduction.................................................. 445
10.2 Absorption of light in natural water ............................. 447
10.3 Elastic scattering of light in natural water........................ 450
10.3.1 Rayleigh scattering in pure water ........................ 450
10.3.2 Petzold experimental volume scattering functions .......... 451
10.3.3 Mankovsky experimental volume scattering functions ....... 451
10.3.4 Lee experimental volume scattering functions.............. 451
10.3.5 Relationships between integral properties of experimental
light scattering phase functions .......................... 459
10.4 Raman scattering of light in natural water ....................... 463
10.5 Chlorophyll fluorescence in natural water ........................ 466
10.6 Yellow substance (Gelbstoff, DOM or CDOM) fluorescence in
natural water................................................. 466
X Contents
10.7 Diffuse reflection coefficient .................................... 468
10.8 Diffuse reflection coefficient of a water basin illuminated by direct
solar light and diffuse light of the sky............................ 472
10.9 Diffuse reflection coefficient of
shallow water body illuminated by diffuse light ................... 474
10.10Diffuse attenuation coefficient .................................. 475
10.11Optical models of scattering and absorption of light in natural water 476
10.11.1 The Kopelevich physical model of elastic scattering......... 476
10.11.2 Chlorophyll-based model of elastic scattering and absorption 477
10.11.3 Empirical model of inherent optical properties ............. 478
10.12Conclusion ................................................... 480
References ........................................................ 480
Appendix: Notation and definitions.............................. 487
Index............................................................491