Optical Correlation Techniques and Applications

286 Pages·2007·18.68 MB·English

by  Oleg V. Angelsky

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: [phone]
Fax: [phone]
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