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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) Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available from the Internet at http://dnb.ddb.de Library of Congress Control Number: 2007941067 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. # Praxis Publishing Ltd, Chichester, UK, 2008 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Jim Wilkie Project copy editor: Mike Shardlow Author-generated LaTex, processed by EDV-Beratung, Germany Printed on acid-free paper 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

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