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Optical Correlation Techniques and Applications PDF

286 Pages·2007·18.68 MB·English
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Bellingham, Washington USA Library of Congress Cataloging-in-Publication Data Angelsky, Oleg V. Optical correlation techniques and applications / Oleg V. Angelsky. p. cm. Includes bibliographical references and index. ISBN 978-0-8194-6534-4 1. Optical data processing. 2. Correlation (Statistics) 3. Optical measurements. 4. Image processing. I. Title. TA1630.A6 2007 621.36'7--dc22 2007009202 Published by SPIE P.O. Box 10 Bellingham, Washington 98227-0010 USA Phone: +1 360 676 3290 Fax: +1 360 647 1445 Email: [email protected] http://spie.org Copyright © 2007 Society of Photo-Optical Instrumentation Engineers All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means without written permission of the publisher. The content of this book reflects the work and thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon. Printed in the United States of America. Contents Preface ix References x 1 Introduction to Linear Singular Optics 1 I.I.Mokhun 1.1 Introduction 1 1.2 BasicsofScalarSingularOptics 2 1.2.1 Phasevortices 2 1.2.2 Topological charge and index of singular points: elementary topologicalreactions 4 1.2.3 Experimental observation and identification of vortices in scalarfields 7 1.2.4 Generationofvorticesusingcomputer-generatedholograms 8 1.3 VorticesandthePhaseStructureofaScalarField 8 1.3.1 Signprinciple 8 1.3.2 “Breathing”ofphasespeckles 10 1.3.3 Birthofvortices 11 1.3.4 Appearanceofwavefrontdislocationsasaresultof interferenceofwaveswithsimplephasesurfaces 13 1.3.5 Topologicalindicesofthefieldofintensity:extremaand “correlation”ofphaseandintensity 18 1.3.6 Vortexnets:phaseskeletonofascalarfield 23 1.4 SingularitiesofaVectorField 31 1.4.1 Disclinations:polarizationsingularities 31 1.4.2 Vorticesofphasedifference:signprincipleforavectorfield 36 1.4.3 “Correlation”ofintensityandpolarizationofthevectorfield 49 1.4.4 InterconnectionofthecomponentvorticesandC points 51 1.4.5 Elementarypolarizationstructuresandelementarypolarization singularitiesofvectorfields 57 1.4.6 Finestructureandaveragedpolarizationcharacteristicsof inhomogeneousvectorfields 66 1.4.7 “Stokesformalism”forpolarizationsingularites:“Stokes vortices” 83 1.5 SingularitiesofthePoyntingVectorandtheStructureofOpticalFields 85 1.5.1 GeneralAssumptions:componentsofthePoyntingvector 87 1.5.2 SingularitiesofthePoyntingvectorinscalarfields 88 1.5.3 SingularitiesofthePoyntingvectoratvectorfields 94 AppendixAWavefrontApproximation 115 v vi CONTENTS AppendixBFourierImageofIsotropicVortex 121 AppendixCPoyntingVector—TheParaxialApproximation 122 References 125 2 Optical Correlation Diagnostics of Phase Singularities in Polychromatic Fields 133 P.V.Polyanskii 2.1 Introduction 133 2.2 ManifestationsofPhaseSingularitiesontheStrengthofScatteringin WhiteLight 134 2.2.1 Structuralinterferencecoloring 134 2.2.2 Interferencecoloringasapeculiareffectofsingularoptics 135 2.2.3 Experiment:thebluemoonistamed 142 2.3 Phase Singularities in Polychromatic Laguerre-Gaussian Modes (RainbowVortices)andtheYoung’sDiagnosticsofThem 144 2.4 OpticalCorrelationDiagnosticsofPhaseSingularitiesin PolychromaticSpeckleFields 151 2.4.1 Interferometric diagnostics of spectral phase singularities in polychromaticspecklefields 151 2.4.2 Chromascopicprocessingofpolychromaticspecklefields 155 References 163 3 Optical Correlation Approachesin Rough Surface Characterization 167 O.V.AngelskyandP.P.Maksimyak 3.1 Introduction 167 3.2 RandomSurfaces 170 3.2.1 Randomphasescreenmodel 170 3.2.2 Computersimulation 171 3.2.3 Experimentalstudy 177 3.2.4 Opticalcorrelationtechniqueforcharacterizingofrough surfaces 181 3.3 FractalSurfaces 189 3.3.1 Fractalapproach 189 3.3.2 Simulationofroughsurfaces 190 3.4 Interferometric Study of Phase Singularities in a Field Scattered by RoughSurfaces 194 3.4.1 Diffractionofopticalradiationoncylindricalandspherical surfaces 194 3.4.2 Interferometric study of phase singularities in a field scattered byroughsurfaces 200 3.5 Conclusions 207 References 208 CONTENTS vii 4 Statistical and Fractal Structure of Biological Tissue Mueller Matrix Images 213 O.V.Angelsky,V.P.Pishak,A.G.UshenkoandYu.A.Ushenko 4.1 TechniquesforDiagnosticsofPhase-InhomogeneousLayerStructure 213 4.2 StokesParametricDescriptionofLightPolarization 219 4.3 StatisticalAnalysisofBiologicalTissuePolarizationProperties 223 4.4 Self-SimilarityDegreeofBiologicalTissuePolarizationProperties 226 4.5 Mueller Matrix Method in Diagnostics of Pathological Changes of BiologicalTissue 232 4.6 First-ThroughFourth-OrderStatisticsofBiologicalTissueMueller MatrixImages 238 4.7 Diagnostic Possibilities of Statistic Analysis of Biological Tissue MuellerMatrixImages 247 4.8 Self-Similar (Fractal) 2D Mueller Matrix Structure of Biological Tissue 249 4.9 Reconstruction of the Orientation Structure of Biological Tissue BirefringentArchitectonicsUsingtheirMuellerMatrixImages 257 4.10 Summary 262 References 263 Index 267 Preface This monograph is devoted to the selected applications of the optical correlation approachesandtechniquesindiverseproblemsofmodernoptics.Weusetheterm correlation optics to designate a (nonquantum) wave statistical optics of partially coherent and partially (nonuniformly) polarized random light fields based on cor- relationfunctions andthehigher-order statisticalmomentsoftheparametersused for describing optical fields. The conceptual background of the optical correla- tionapproachcorrelateswiththeWolf’smethodologyofthe“opticsofobservable quantities.”1 Theessenceofthismethodology,whichisacceptedbytheauthorsof thisbook,follows: – correlationfunctionsandotherstatisticalmomentsofthefielddirectlychar- acterize the interconnection of light oscillations in two spatial-temporal points, and this interconnection can be evaluated in a quantitative manner (canbemeasured)usingobservablequantities; – statisticalmomentsofthefieldaregovernedbythewaveequationsthatelab- orate the peculiarities of their transformation under thepropagation of radi- ation, and gives reliable ground for the solution for the inverse problem of optics,includingdiagnosticsofthestatisticalparametersofrandomobjects; – the mathematical apparatus used in the theory of partial coherence is well adoptedtothetheoryofpartialpolarization,whereinterconnectionbetween the orthogonal components of the vector electromagnetic field in different spatial points and in different instants can be characterized in terms of cor- relations,i.e.,intermsofthecorrespondingstatisticalmoments. Amongobservablequantities,whichareusedthroughoutthebook,onemeetsvis- ibility and the phase of interference fringes, Stokes parameters, Poynting vector, etc. Note, that the road from the fundamental concepts and theories1,2 to the prac- tical applications is not straightforward. The interconnection of the methodology andthetechnologyisoftenmediatedbysophisticatedcomputersimulationandex- perimentaltechniques,nowundergoingimpressiveprogressinthestudyofcorrela- tionandpolarizationstructuresofthefieldintonearzone(near-fieldoptics),look- ing for the mechanisms of formation of randomly inhomogeneous speckle fields (both monochromatic and polychromatic) that follow from the presence of phase singularities, and elaborating the feasibilities for manipulating microobjects us- ing optical radiation, etc. The gap between theory and practice is partly filled in studies reported at seven International Conferences on Correlation Optics, which havebeenheldbiannuallyinChernivtsisince1993(seeSPIEProc.Volumes2108, 2647,3317,3904,4607,5477,and6254). ix

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