Nonlinear Acoustical Imaging PDF
Preview Nonlinear Acoustical Imaging
Woon Siong Gan Nonlinear Acoustical Imaging Nonlinear Acoustical Imaging Woon Siong Gan Nonlinear Acoustical Imaging WoonSiongGan AcousticalTechnologiesSingaporePteLtd. Singapore,Singapore ISBN978-981-16-7014-5 ISBN978-981-16-7015-2 (eBook) https://doi.org/10.1007/978-981-16-7015-2 ©SpringerNatureSingaporePteLtd.2021 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSingaporePteLtd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Tomyparents Foreword Nonlinearityinacousticsisusuallysomethingthatistobeavoided.Forinstance,the nonlineardistortioninamusicreproductionsystemindicatesapossibledamagein maybetheamplifierorloudspeaker.Thisdistortionappearsdisturbingtous,butit doesalsocontaininformationaboutthestructuralinhomogeneities—likecracks. Thisisoneexampleofwhenanonlinearityinacousticsyieldsinformationabout a material or medium. It also introduces the importance in that a small inhomo- geneity may result in a heavily nonlinear distortion. Nonlinear acoustic imaging doesnotfollowthesamerulesandguidelinesasnormallinearacousticimaging.For example,materialdisturbanceswhichareordersofmagnitudesmallerinsizethan theacousticwavelengthdonothaveanimpactinthelineartechniques,butcangive clearindicationsusingnonlinearacousticmethods. ThisiswhyWoonSiongGanistreatingthesubjectofnonlinearacousticimaging inthisspecificallydedicatedbook,despitethathehasgivenanextensiveoverviewof thelinearaspectsinthepreviouslypublishedbookAcousticalImaging:Techniques& Applications(2012). This book presented the equations and basics of the nonlinear acoustics, its pertinent phenomena and how these are used in imaging techniques for different applications. The subject of nonlinear acoustic imaging techniques is relatively new and has notbeenextensivelycoveredinpreviousbooks.Itisadifficultsciencetodelveinto, especiallywhilemostacousticcoursesteachonlythelinearacoustics.Thisisperhaps completelynatural,asthemoveintononlinearstudiesisnotalwaysquickandeasy sincesomeoftheacceptedconceptionsneedtobeelaborated. WoonSiongGanhas,duringthelastyears,beenprolificinsharingafractionofhis deepanddiverseknowledgethroughpublishingthefollowingbooks:NewAcoustics Based on Metamaterials (2018); Gauge Invariance Approach to Acoustic Fields (2019); Signal Processing and Image Processing for Acoustical Imaging (2020); TimeReversalAcoustics(2021). The titles and the contents of all these books show the nature of Woon Siong Ganthroughhowheconnectsthetopicalbroadspectrumallthewayfromthemost vii viii Foreword fundamentalsciencetousefulapplicationpractices—ashehasdonealsointhishis latestveryvaluablebook. ClaesHedberg Professor,BlekingeInstitute ofTechnology Karlskrona,Sweden Preface Tostudynonlinearacousticalimaging,oneneedstounderstandindepththephysics ofnonlinearacoustics.Hence,itisnecessarytostartwiththetheoreticalfoundation ofnonlinearacoustics.Themostpopularequationofnonlinearacoustics,theKZK equation only accounts for diffraction, nonlinearity and absorption in directional soundbeams.Thereareseveralotheraspectsofnonlinear acousticswhicharenot coveredbythisequation.Anexampleisthecurvilinearpathofhighintensityacoustic wavefields.Toaccountforthecurvilinearpath,thecurvilinearspacetimecoordinates have to be used. The most well-known application of curvilinear spacetime is the general theory of relativity by Albert Einstein to account for the curvilinear path ofthenonlineargravitationalfield.Thecurvilinearspacetimeapproachstartswith theintrinsicnonlinearnatureoftheprobleminsteadofextendingthelinearcaseto nonlinearitybyaddingonhigher-ordertermswhichisstillanapproximation. Twowell-knownunsolvedproblemsofnonlinearacoustics,turbulenceandsono- luminescencearephasetransitioninnature.Totreatphasetransitionproblem,statis- ticalmechanicshastobeusedtostudythecriticalpointofphasetransitionandthe singularitybehaviourofthetransportpropertiesoftheregionsurroundingthecritical point.SofarthemostacceptabletheoriesofturbulencearethatduetoKolmogorov whichisastatisticaltheoryandstatisticalmechanicshastobeused.Theothertheory is that of the description of turbulence as a critical phenomenon, a form of phase transitionandthesolvingofthesingularityproblemofthecorrelationlengthatthe criticalpointbytheuseofrenormalizationgroupmethodwhichisusedinstatistical mechanics. Gaugetheoryisusefulforsolvingseveralproblemsinnonlinearacousticssuch as multiple scattering, diffraction and electron–phonon interaction. The symmetry usedingaugetheorycansimplifyseveralcomplexitiesinnonlinearacoustics.Also theusualmethodusedforelectron–phononinteractionismanybodytheoryofDirac whichcanhandleonlyuptothesecond-orderterm.Beyondthat,divergenceoccurs, and there are infinities terms. With the use of gauge theory, the renormalization methodcancancelofftheinfinitiesterms. ix x Preface Duringthelastfortyyears,severalformatsofnonlinearacousticalimaginghave beendevelopedsuchasharmonicsimaging,fractalimaging,B/Anonlinearparam- eteracousticalimaging,non-classicalnonlinearacousticalimagingandmodulation method in nonlinear acoustical imaging. The advantages of nonlinear acoustical imaging are high sensitivity and higher image resolution. They can be applied to non-destructivetesting,medicalultrasoundandunderwateracoustics. Singapore WoonSiongGan September2021 Contents 1 IntroductiontoNonlinearAcoustics ............................ 1 1.1 Introduction ............................................. 1 1.2 ConstitutiveEquations .................................... 2 1.3 PhenomenainNonlinearAcoustics ......................... 2 References .................................................... 2 2 NonlinearAcousticWaveEquationsforSoundPropagation inFluidsandinSolids ......................................... 3 2.1 NonlinearAcousticWaveEquationsinFluids ................ 3 2.1.1 TheWesterveltEquation[1] ......................... 4 2.1.2 TheBurgers’Equation[2] ........................... 4 2.1.3 KZKEquation ..................................... 5 2.1.4 NonlinearAcousticWaveEquationsforSound PropagationinSolids ............................... 6 References .................................................... 7 3 StatisticalMechanicsApproachtoNonlinearAcoustics ........... 9 3.1 Introduction ............................................. 9 3.2 StatisticalEnergyAnalysisisTransportTheory ............... 10 3.3 StatisticalEnergyAnalysis ................................ 12 3.4 TransportTheoryApproachtoPhaseTransition .............. 14 References .................................................... 15 4 CurvilinearSpacetimeAppliedtoNonlinearAcoustics ............ 17 4.1 IntroductionandMeaningofCurvilinearSpacetime ........... 17 4.2 PrincipleofGeneralCovariance ............................ 18 4.3 ContravariantandCovariantFour-Vectors .................... 19 4.4 ContravariantTensorsandCovariantTensors ................. 20 4.5 TheCovariantFundamentalTensorgμν ...................... 21 4.6 EquationofMotionofaMaterialPointintheGravitational Field ................................................... 22 xi
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