Light Scattering Reviews 5

Single Light Scattering and Radiative Transfer
1. Auflage 2010
ISBN: 978-3-642-10336-0
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 549 Seiten

Light scattering by densely packed inhomogeneous media is a particularly ch- lenging optics problem. In most cases, only approximate methods are used for the calculations. However, in the case where only a small number of macroscopic sc- tering particles are in contact (clusters or aggregates) it is possible to obtain exact results solving Maxwell’s equations. Simulations are possible, however, only for a relativelysmallnumberofparticles,especiallyiftheirsizesarelargerthanthewa- length of incident light. The ?rst review chapter in PartI of this volume, prepared by Yasuhiko Okada, presents modern numerical techniques used for the simulation of optical characteristics of densely packed groups of spherical particles. In this case, Mie theory cannot provide accurate results because particles are located in the near ?eld of each other and strongly interact. As a matter of fact, Maxwell’s equations must be solved not for each particle separately but for the ensemble as a whole in this case. The author describes techniques for the generation of shapes of aggregates. The orientation averaging is performed by a numerical integration with respect to Euler angles. The numerical aspects of various techniques such as the T-matrix method, discrete dipole approximation, the ?nite di?erence time domain method, e?ective medium theory, and generalized multi-particle Mie so- tion are presented. Recent advances in numerical techniques such as the grouping and adding method and also numerical orientation averaging using a Monte Carlo method are discussed in great depth.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Contents;6
2;List of Contributors;14
3;Notes on the contributors;18
4;Preface;24
5;Part I Optical Properties of Small Particlesand their Aggregates;30
5.1;1 Numerical simulations of light scattering andabsorption characteristics of aggregates;31
5.1.1;1.1 Introduction;31
5.1.2;1.2 Properties of aggregates used in numerical simulations;32
5.1.2.1;1.2.1 Physical and light scattering properties;32
5.1.2.2;1.2.2 Shapes of aggregates;34
5.1.2.3;1.2.3 Aggregate orientation;35
5.1.3;1.3 Methods for numerical light scattering simulations;36
5.1.3.1;1.3.1 The DDA and FDTD;38
5.1.3.2;1.3.2 The CTM and GMM;39
5.1.3.3;1.3.3 The EMT;40
5.1.3.4;1.3.4 Future extensions of the numerical methods;40
5.1.4;1.4 Improved numerical simulations;41
5.1.4.1;1.4.1 Grouping and adding method (GAM);41
5.1.4.2;1.4.2 Numerical orientation averaging using a quasi-Monte-Carlomethod (QMC);44
5.1.4.3;1.4.3 Extended calculation of light scattering properties withnumerical orientation averaging;47
5.1.4.4;1.4.4 Scattering and absorption of BCCA composed of tensto thousands of monomers;50
5.1.4.5;1.4.5 Intensity and polarization of light scattered bysilicate aggregates;52
5.1.5;1.5 Summary;55
5.1.6;References;59
5.2;2 Application of scattering theories to thecharacterization of precipitation processes;64
5.2.1;2.1 Introduction;64
5.2.2;2.2 Aggregate formation;65
5.2.2.1;2.2.1 Precipitation and particle synthesis;65
5.2.2.2;2.2.2 Particle shapes during precipitation;66
5.2.2.3;2.2.3 Dynamics of precipitation: modelling;68
5.2.3;2.2.4 Particle sizing during precipitation;69
5.2.4;2.3 Approximations for non-spherical particles;71
5.2.4.1;2.3.1 Rayleigh approximation;71
5.2.4.2;2.3.2 Rayleigh–Gans–Debye approximation;71
5.2.4.3;2.3.3 Anomalous Diffraction approximation;73
5.2.5;2.4 Approximations for aggregate scattering cross-section;74
5.2.5.1;2.4.1 Exact theory for non-spherical particles and aggregates;74
5.2.5.2;2.4.2 Main features of the scattering properties of aggregates;77
5.2.5.3;2.4.3 Approximate methods (CS, BPK, AD, ERI) for aggregates;82
5.2.5.4;2.4.4 Application: turbidity versus time duringthe agglomeration process;88
5.2.6;2.5 Approximation for radiation pressure cross-section;91
5.2.6.1;2.5.1 Introduction;91
5.2.6.2;2.5.2 Main features of radiation pressure cross-section;92
5.2.6.3;2.5.3 Approximate methods for aggregates;95
5.2.6.4;2.5.4 Conclusion;97
5.2.7;2.6 Scattering properties versus geometrical parametersof aggregates;97
5.2.8;2.7 Conclusion;101
5.2.9;References;102
6;Part II Modern Methods in Radiative Transfer;106
6.1;3 Using a 3-D radiative transfer Monte–Carlomodel to assess radiative effects on polarizedreflectances above cloud scenes;107
6.1.1;3.1 Introduction;107
6.1.2;3.2 Including the polarization in a 3-D Monte–Carloatmospheric radiative transfer model;108
6.1.2.1;3.2.1 Description of radiation and single scattering:Stokes vector and phase matrix;108
6.1.2.2;3.2.2 Description of the radiative transfer model, 3DMCpol;113
6.1.3;3.3 Total and polarized reflectances in the caseof homogeneous clouds (1-D);117
6.1.3.1;3.3.1 Validation of the MC polarized model;117
6.1.3.2;3.3.2 Reflectances of homogeneous clouds as a functionof the optical thickness;120
6.1.4;3.4 Total and polarized reflectances in the caseof 3-D cloud fields;120
6.1.4.1;3.4.1 Description of the 3-D cloud fields used;120
6.1.4.2;3.4.2 Comparisons with SHDOM and time considerations;122
6.1.4.3;3.4.3 High spatial resolution (80 m): illumination and shadowing effects;124
6.1.4.4;3.4.4 Medium spatial resolution (10 km):sub-pixel heterogeneity effects;125
6.1.5;3.5 Conclusions and perspectives;127
6.1.6;References;128
6.2;4 Linearization of radiative transfer in sphericalgeometry: an application of the forward-adjointperturbation theory;131
6.2.1;4.1 Introduction;131
6.2.2;4.2 Forward-adjoint perturbation theoryin spherical geometry;134
6.2.2.1;4.2.1 The forward radiative transfer equation;134
6.2.2.2;4.2.2 The adjoint formulation of radiative transfer;137
6.2.2.3;4.2.3 Perturbation theory in spherical coordinates;140
6.2.3;4.3 Symmetry properties;141
6.2.4;4.4 Linearization of a radiative transfer model for aspherical shell atmosphere by the forward-adjointperturbation theory;143
6.2.4.1;4.4.1 Solution of the radiative transfer equationby a Picard iteration method;144
6.2.4.2;4.4.2 Solution of the pseudo-forward transfer equation;152
6.2.4.3;4.4.3 Verification of the adjoint radiation field;154
6.2.5;4.5 Linearization of the spherical radiative transfer model;158
6.2.6;4.6 Conclusions;165
6.2.7;Appendix A: Transformation of a volume source into asurface source;166
6.2.8;References;168
6.3;5 Convergence acceleration of radiativetransfer equation solution at stronglyanisotropic scattering;172
6.3.1;5.1 Introduction;172
6.3.2;5.2 Singularities of the solution of theradiative transfer equation;173
6.3.3;5.3 Small angle modification of thespherical harmonics method;177
6.3.4;5.4 Small angle approximation in transport theory;181
6.3.5;5.5 Determination of the solution of the regular partin a plane unidirectional source problem;185
6.3.6;5.6 Reflection and transmittance on the boundaryof two slabs;192
6.3.7;5.7 Generalization for the vectorial caseof polarized radiation;200
6.3.8;5.8 Evaluation of the vectorial regular part;206
6.3.9;5.9 MSH in arbitrary medium geometry;213
6.3.10;5.10 Regular part computationin arbitrary medium geometry;220
6.3.11;5.11 Conclusion;224
6.3.12;References;226
6.4;6 Code SHARM: fast and accurate radiativetransfer over spatially variable anisotropicsurfaces;229
6.4.1;6.1 The method of spherical harmonics:homogeneous surface;230
6.4.1.1;6.1.1 Solution for path radiance;233
6.4.1.2;6.1.2 Correction function of MSH;235
6.4.2;6.2 Code SHARM;236
6.4.2.1;6.2.1 Accuracy, convergence and speed of SHARM;238
6.4.3;6.3 Green’s function method and its applications;240
6.4.3.1;6.3.1 Formal solution with the Green’s function method;240
6.4.3.2;6.3.2 Practical considerations;243
6.4.3.3;6.3.3 Expression for TOA reflectance using LSRT BRF model;245
6.4.4;6.4 Green’s function solution for anisotropic inhomogeneoussurface;248
6.4.4.1;6.4.1 Operator solution of the 3-D radiative transfer problem;248
6.4.4.2;6.4.2 Linearized solution;251
6.4.4.3;6.4.3 Lambertian approximation;253
6.4.4.4;6.4.4 Numerical aspects;254
6.4.5;6.5 MSH solution for the optical transfer function;256
6.4.6;6.6 Similarity transformations;258
6.4.6.1;6.6.1 Singular value decomposition;260
6.4.6.2;6.6.2 Solution for moments;261
6.4.6.3;6.6.3 Solution for the OTF;261
6.4.7;6.7 Code SHARM-3D;264
6.4.8;6.7.1 Parameterized SHARM-3D solution;264
6.4.9;6.8 Discussion;266
6.4.10;References;268
6.5;7 General invariance relations reduction methodand its applications to solutions of radiativetransfer problems for turbid media of variousconfigurations;272
6.5.1;7.1 Introduction;272
6.5.2;7.2 Main statements of the general invariance relationsreduction method;275
6.5.2.1;7.2.1 Statement of boundary-value problems of the scalar radiativetransfer theory;275
6.5.2.2;7.2.2 Statement of the general invariance principle as applied toradiative transfer theory;283
6.5.2.3;7.2.3 General invariance relations and their physical interpretation;293
6.5.2.4;7.2.4 Scheme of using the general invariance principleand the general invariance relations;300
6.5.3;7.3 Some general examples of using the general invariancerelations reduction method;302
6.5.3.1;7.3.1 Doubling formulae;302
6.5.3.2;7.3.2 On the relationship between the volume Green functionsand the generalized reflection function;303
6.5.3.3;7.3.3 Analog of the Kirchhoff law for the case of non-equilibriumradiation in turbid media;305
6.5.3.4;7.3.4 General invariance relations for monochromatic radiation fluxes;307
6.5.3.5;7.3.5 Inequalities for monochromatic radiation fluxes and meanemission durations of turbid bodies;311
6.5.4;7.4 Strict, asymptotic and approximate analytical solutionsto boundary-value problems of the radiative transfertheory for turbid media of various configurations;317
6.5.4.1;7.4.1 Application of the general invariance relations reduction methodto the derivation of azimuth-averaged reflection function for amacroscopically homogeneous plane-parallel semi-infinite turbidmedium;317
6.5.4.2;7.4.2 Asymptotic and approximate analytical expressions formonochromatic radiation fluxes exiting macroscopicallyhomogeneous non-concave turbid bodies;324
6.5.4.3;7.4.3 On the depth regimes of radiation fields and on the derivation ofasymptotic expressions for mean emission durations of opticallythick, turbid bodies;332
6.5.5;7.5 Conclusion;336
6.5.6;Acknowledgment;337
6.5.7;Appendix A: Main mathematical notations, conceptions,and constructions used while stating the general invarianceprinciple and deriving the general invariance relations;337
6.5.8;References;341
7;Part III Optical Properties of Bright Surfaces andRegoliths;351
7.1;8 Theoretical and observational techniquesfor estimating light scattering in first-yearArctic sea ice;352
7.1.1;8.1 Introduction;352
7.1.2;8.2 Background;352
7.1.3;8.3 Approach;353
7.1.4;8.4 Sea ice microstructure;355
7.1.4.1;8.4.1 Overview;355
7.1.4.2;8.4.2 Laboratory observations;358
7.1.4.3;8.4.3 Microstructure at -15.C;360
7.1.4.4;8.4.4 Temperature-dependent changes;368
7.1.4.5;8.4.5 Summary of microstructure observations;375
7.1.5;8.5 Apparent optical property observations;377
7.1.6;8.6 Radiative transfer in a cylindrical domain withrefractive boundaries;381
7.1.6.1;8.6.1 Model overview;382
7.1.6.2;8.6.2 Implementation;385
7.1.6.3;8.6.3 Similarity;389
7.1.6.4;8.6.4 Simulation of laboratory observations;389
7.1.7;8.7 Structural-optical model;391
7.1.7.1;8.7.1 Structural-optical relationships;391
7.1.7.2;8.7.2 Phase functions;395
7.1.7.3;8.7.3 Model development and testing;397
7.1.7.4;8.7.4 Discussion;402
7.1.8;8.8 Conclusions;408
7.1.9;References;409
7.2;9 Reflectance of various snow types:measurements, modeling, and potentialfor snow melt monitoring;413
7.2.1;9.1 Introduction;413
7.2.2;9.2 Snow;415
7.2.3;9.3 BRF, definitions;416
7.2.4;9.4 Instrumentation;418
7.2.4.1;9.4.1 Model 2, 1996: a simple one-angle manual field goniometer;419
7.2.4.2;9.4.2 Goniometer model 3, 1999–2005;419
7.2.4.3;9.4.3 FIGIFIGO, 2005–;421
7.2.4.4;9.4.4 Light sources;423
7.2.4.5;9.4.5 Data processing;424
7.2.5;9.5 Main research efforts;426
7.2.6;9.6 Modeling;431
7.2.7;9.7 Results;433
7.2.7.1;9.7.1 Forward scattering signatures;442
7.2.7.2;9.7.3 Spectral effects;453
7.2.7.3;9.7.4 Polarization signals;454
7.2.7.4;9.7.5 Albedos;454
7.2.8;9.8 Discussion;459
7.2.8.1;9.8.1 Melting signatures – a summary;459
7.2.8.2;9.8.2 Development of BRF measurement techniques;460
7.2.8.3;9.8.3 Supporting snow measurements;461
7.2.8.4;9.8.4 Modeling;462
7.2.9;9.9 Conclusions;462
7.2.10;References;463
7.3;10 Simulation and modeling of light scattering inpaper and print applications;470
7.3.1;10.1 Introduction;470
7.3.2;10.2 Current industrial use of light scattering models;470
7.3.2.1;10.2.1 Standardized use of Kubelka–Munk;470
7.3.2.2;10.2.2 Deficiencies of Kubelka–Munk;473
7.3.2.3;10.2.3 Suggested extensions to Kubelka–Munk;478
7.3.2.4;10.2.4 New and higher demands drive the need for new models;480
7.3.3;10.3 Benefits of newer models;481
7.3.3.1;10.3.1 Radiative transfer modeling;481
7.3.3.2;10.3.2 Monte Carlo modeling;486
7.3.4;10.4 Discussion;490
7.3.5;10.5 Conclusions;492
7.3.6;References;492
7.4;11 Coherent backscattering in planetary regoliths;495
7.4.1;11.1 Introduction;495
7.4.2;11.2 Single-particle light scattering;498
7.4.2.1;11.2.1 Scattering matrix, cross-section, and asymmetry parameters;498
7.4.2.2;11.2.2 Scattering by Gaussian-random-sphere andagglomerated-debris particles;499
7.4.2.3;11.2.3 Internal vs. scattered fields;500
7.4.2.4;11.2.4 Interference in single scattering;505
7.4.3;11.3 Coherent backscattering;512
7.4.3.1;11.3.1 Coherent-backscattering mechanism;513
7.4.3.2;11.3.2 Theoretical framework for multiple scattering;515
7.4.3.3;11.3.3 Scalar approximation;517
7.4.3.4;11.3.4 Vector approach;522
7.4.4;11.4 Physical modeling;527
7.4.4.1;11.4.1 Polarization fits;527
7.4.4.2;11.4.2 Coherent-backscattering simulations;530
7.4.5;11.5 Conclusion;530
7.4.6;Acknowledgments;532
7.4.7;References;532
7.5;Color Section;537
7.5.1;Chapter 3;537
7.5.2;Chapter 6;539
7.5.3;Chapter 8;540
7.5.4;Chapter 9;542
8;Index;563