Light Scattering Reviews 5 (eBook)

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