Light Scattering Reviews 3: Light Scattering and Reflection

420 Pages·2008·10.33 MB·English

by  Alexander A. Kokhanovsky

Light Scattering Reviews 3
Light Scattering and Reflection
Alexander A. Kokhanovsky (Editor)
Light Scattering
Reviews 3
Light Scattering and Reflection
Published in association with
Praxis Publishing
Chichester, UK
Editor
Dr Alexander A. Kokhanovsky
Institute of Environmental Physics
University of Bremen
Bremen
Germany
SPRINGER–PRAXIS BOOKS IN ENVIRONMENTAL SCIENCES (LIGHT SCATTERING SUB-SERIES)
SUBJECT ADVISORY EDITOR: John Mason B.Sc., M.Sc., Ph.D.
EDITORIAL ADVISORY BOARD MEMBER: Dr Alexander A. Kokhanovsky, Ph.D. Institute of Environmental
Physics, University of Bremen, Bremen, Germany
ISBN 978-3-540-48305-2 Springer Berlin Heidelberg New York
Springer is part of Springer-Science + Business Media (springer.com)
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Contents
List of contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI
Notes on the contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XIII
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .XXI
Part I Single Light Scattering
1 Observational quantification of the optical properties of cirrus
cloud
Timothy J. Garrett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Measurement of the asymmetry parameter in cirrus . . . . . . . . . . . . . . . 5
1.2.1 Indirect estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 Nephelometer measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.3 Reconciling discrepancies between theory and observations . . 11
1.3 Extinction coefficient and effective radius . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.1 Indirect measurement of effective radius . . . . . . . . . . . . . . . . . . 15
1.3.2 Direct measurement of effective radius . . . . . . . . . . . . . . . . . . . . 16
1.3.3 Optical evaluation of ice crystal effective radius using halos . . 19
1.4 Summary of outstanding problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2 Statistical interpretation of light anomalous diffraction by
small particles and its applications in bio-agent detection and
monitoring
Min Xu, A. Katz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 Review of recent developments in ADT . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.1 Light anomalous diffraction using geometrical path statistics
of rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Ray distributions for various shapes . . . . . . . . . . . . . . . . . . . . . . 32
2.2.3 Gaussian ray approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.4 Performance of Gaussian ray approximation and difference
in optical efficiencies between cylinders and spheroids . . . . . . . 47
2.2.5 Implications on particle sizing with light scattering techniques 50
VI Contents
2.3 Applications of light scattering to bacteria monitoring and detection . 52
2.3.1 Angular scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.2 Bacteria size determined by transmission measurements . . . . . 58
2.3.3 In vivo monitoring of biological processes in bacteria . . . . . . . 59
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3 Light scattering by particles with boundary symmetries
Michael Kahnert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2 Symmetries in linear boundary-value problems . . . . . . . . . . . . . . . . . . . . 71
3.2.1 Green’s functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.2.2 Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.3 Boundary symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3 Symmetries in electromagnetic and acoustic scattering problems . . . . 78
3.3.1 Self-consistent Green’s function formalism . . . . . . . . . . . . . . . . . 78
3.3.2 Symmetry relations of GΓ
+, G∂Γ+, and W∂Γ+ . . . . . . . . . . . . . . 82
3.3.3 Symmetry relations in matrix form . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.4 Unitary, reducible representations of point-groups . . . . . . . . . . 88
3.3.5 Explicit symmetry relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.3.6 Irreducible representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.4 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4 Scattering by particles on or near a plane surface
Adrian Doicu, Roman Schuh and Thomas Wriedt . . . . . . . . . . . . . . . . . . . . . . 109
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.2 Single particle on or near a plane surface . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.3 Single particle on or near a plane surface coated with a film . . . . . . . . 119
4.4 System of particles on or near a plane surface . . . . . . . . . . . . . . . . . . . . 121
4.5 Numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Part II Radiative Transfer and Inverse Problems
5 Impact of single- and multi-layered cloudiness on ozone
vertical column retrievals using nadir observations of
backscattered solar radiation
V. V. Rozanov and A. A. Kokhanovsky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.3 Atmospheric and cloud models used for forward simulations . . . . . . . . 137
5.4 Forward simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.4.1 Reflection function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.4.2 Weighting function and differential absorption . . . . . . . . . . . . . 142
Contents VII
5.4.3 Impact of cloud parameters on the integral absorption . . . . . . 146
5.4.4 Linear approximation for the reflection function with
respect to the cloud parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.4.5 Scaling approximation and weighting function for ozone
vertical columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.5 Inverse problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.5.1 Retrieval of cloud parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.5.2 Total ozone column retrieval algorithm . . . . . . . . . . . . . . . . . . . 155
5.6 Results of numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.6.1 Single cloud layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5.6.2 Two-layered cloud systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.6.3 Three-layered cloud systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
A.1 Gaseous absorber number density WF . . . . . . . . . . . . . . . . . . . . 179
A.2 Cloud optical thickness WF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
A.3 Cloud geometrical parameters WFs . . . . . . . . . . . . . . . . . . . . . . 181
A.4 LER altitude (surface elevation) WF . . . . . . . . . . . . . . . . . . . . . 182
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6 Remote sensing of clouds using linearly and circularly
polarized laser beams: techniques to compute signal polarization
L. I. Chaikovskaya . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.2 Basic theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.2.1 Matrix describing the light field produced by a normally
incident beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
6.2.2 Matrices of propagation and near-backward scattering . . . . . . 199
6.2.3 Simplified transfer equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
6.3 Polarized light transmission by a cloud . . . . . . . . . . . . . . . . . . . . . . . . . . 211
6.3.1 Generalization of the multicomponent technique . . . . . . . . . . . 212
6.3.2 Transmission of an infinitely wide beam through water
cloud: computation and discussion . . . . . . . . . . . . . . . . . . . . . . . 215
6.4 Polarization of the pulsed lidar return from a cloud . . . . . . . . . . . . . . . 218
6.4.1 Semi-analytical technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
6.4.2 Backscattering of linearly and circularly polarized pulses
from a water cloud: computation and discussion . . . . . . . . . . . 220
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
7 LIDORT and VLIDORT: Linearized pseudo-spherical scalar
and vector discrete ordinate radiative transfer models for use in
remote sensing retrieval problems
Robert Spurr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
7.2 Description of VLIDORT and LIDORT . . . . . . . . . . . . . . . . . . . . . . . . . . 232
VIII Contents
7.2.1 Theoretical framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
7.2.2 Homogeneous RTE solutions and their linearization . . . . . . . . 238
7.2.3 Solar sources: particular integrals and linearization . . . . . . . . . 242
7.2.4 Thermal sources: particular integrals and linearization . . . . . . 246
7.2.5 Boundary value problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
7.2.6 Post processing: source function integration . . . . . . . . . . . . . . . 248
7.2.7 Spherical and single-scatter corrections . . . . . . . . . . . . . . . . . . . 251
7.2.8 Surface reflectance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
7.3 Performance and benchmarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
7.3.1 Performance considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
7.3.2 VLIDORT validation and benchmarking . . . . . . . . . . . . . . . . . . 266
7.4 Preparation of inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
7.4.1 Example: specification of atmospheric IOP inputs . . . . . . . . . . 267
7.4.2 Surface and other atmospheric inputs . . . . . . . . . . . . . . . . . . . . . 269
7.5 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Part III Bi-directional Reflectance of Light from Natural and
Artificial Surfaces
8 Bi-directional reflectance measurements of closely packed
natural and prepared particulate surfaces
Hao Zhang and Kenneth J. Voss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
8.2 Definitions of bi-directional reflectance and related quantities . . . . . . . 280
8.3 BRDF models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
8.3.1 Hapke’s isotropic multiple-scattering approximation (HIMSA)282
8.3.2 Hapke’s anisotropic multiple-scattering approximation
(HAMSA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
8.3.3 Lumme–Bowell’s (LB) model . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
8.3.4 Mishchenko et al.’s BRF algorithm (MBRF) . . . . . . . . . . . . . . 284
8.3.5 The DISORT model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
8.3.6 Some remarks on the models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
8.4 BRDF instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
8.4.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
8.4.2 An in situ BRDF-meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
8.4.3 A simple goniometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
8.4.4 An example of the calibration measurements . . . . . . . . . . . . . . 290
8.5 Controlled BRDF measurements on prepared packed surfaces and
comparisons with models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
8.5.1 Samples and single-scattering quantities . . . . . . . . . . . . . . . . . . 292
8.5.2 Some parameters of packed surfaces and measurement results 292
8.5.3 Some discussions on controlled BRDF measurements . . . . . . . 297
8.6 In situ BRDF measurements on benthic sediment floors . . . . . . . . . . . . 301
8.6.1 Typical features of benthic sediment BRDF . . . . . . . . . . . . . . . 301
Contents IX
8.6.2 A simple model for sediment BRDF . . . . . . . . . . . . . . . . . . . . . . 308
8.7 Effects of translucent grains and pore liquid complex refractive
index on particulate BRDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
8.7.1 Sample descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
8.7.2 Effects of translucent particle concentrations on wetting . . . . 314
8.7.3 Effects of the wetting liquid absorption coefficient . . . . . . . . . . 318
8.8 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
9 Light scattering from particulate surfaces in geometrical
optics approximation
Yevgen Grynko and Yuriy G. Shkuratov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
9.1.1 Practical tasks in optical remote sensing . . . . . . . . . . . . . . . . . . 329
9.1.2 Principle and history of the ray tracing method . . . . . . . . . . . . 333
9.1.3 Problems of analytical accounting for multiple scattering in
particulate media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
9.1.4 Range of applicability of ray tracing . . . . . . . . . . . . . . . . . . . . . . 336
9.2 Computer modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
9.2.1 Particulate medium generation and description of irregular
shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
9.2.2 Ray tracing algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
9.3 The shadow-hiding effect and multiple scattering in systems of
opaque particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
9.3.1 Ray tracing modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
9.3.2 Results of simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
9.4 Single scattering component. Transparent and semitransparent
particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
9.4.1 Faceted spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
9.4.2 Binary spheres and faceted ellipsoids . . . . . . . . . . . . . . . . . . . . . 357
9.4.3 Perfect and ‘spoiled’ cubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
9.4.4 RGF particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
9.5 Incoherent multiple scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
9.5.1 Photometric and polarimetric phase curves . . . . . . . . . . . . . . . . 363
9.5.2 Spectrophotometry of particulate surfaces . . . . . . . . . . . . . . . . . 369
9.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
10 Laboratory measurements of reflected light intensity and
polarization for selected particulate surfaces
Yuriy G. Shkuratov, Andrey A. Ovcharenko, Vladimir A. Psarev and
Sergey Y. Bondarenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
10.2 Laboratory instruments and samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
10.2.1 The wide-phase-angle photometer/polarimeter . . . . . . . . . . . . . 384
10.2.2 The small-phase-angle photometer/polarimeter . . . . . . . . . . . . 385
X Contents
10.2.3 The laser super-small-phase-angle photometer/polarimeter . . 387
10.2.4 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
10.3 Results of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
10.3.1 Albedo and particle size effects . . . . . . . . . . . . . . . . . . . . . . . . . . 392
10.3.2 The contribution of single light scattering . . . . . . . . . . . . . . . . . 393
10.3.3 Opposition spikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
10.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403