36Time-reversal waves and super resolution

Time-reversalwavesandsuperresolutionThisarticlehasbeendownloadedfromIOPscience.Pleasescrolldowntoseethefulltextarticle.2008J.Phys.:Conf.Ser.124012004()Downloaddetails:IPAddress:166.111.44.199Thearticlewasdownloadedon26/03/2010at02:56Pleasenotethattermsandconditionsapply.TheTableofContentsandmorerelatedcontentisavailableHomeSearchCollectionsJournalsAboutContactusMyIOPscienceTime-reversalwavesandsuperresolutionMathiasFinkLaboratoireOndesetAcoustique,EcoleSuprieuredePhysiqueetdeChimieIndustrielledelaVilledeParis,UniversitDenisDiderot,UMRCNRS7587,10RueVauquelin,75005Paris,FranceE-mail:[e-mail]-reversalmirrors(TRMs)refocusanincidentacousticfieldtothepositionoftheoriginalsourceregardlessofthecomplexityofthepropagationmedium.TRM’shavenowbeenimplementedinavarietyofphysicalscenariosfromMHzultrasonicswithordercentimeteraperturesizetohundreds/thousandsofHzinoceanacousticswithorderhundredmeteraperturesize.CommontothisbroadrangeofscalesisaremarkablerobustnessexemplifiedbyobservationsatallscalesthatthemorecomplexthemediumbetweentheprobesourceandtheTRM,thesharperthefocus.Therelationbetweenthemediumcomplexityandthesizeofthefocalspotisstudiedinthispaper.ItiscertainlythemostexcitingpropertyofTRMcomparedtostandardfocusingdevices.ATRMactsasanantennathatusescomplexenvironmentstoappearswiderthanitis,resultingforabroadbandpulseinarefocusingqualitythatdoesnotdependoftheTRMaperture.Inthispaper,weinvestigatethetime-reversalapproachinvariousmediaofincreasingcomplexityWewillalsodemonstratedthattime-reversalfocusingopenscompletelynewapproachestosuper-resolution.Wewillshowthatinmediummadeofrandomdistributionofsub-wavelengthscatterers,atime-reversedwavefieldinteractswiththerandommediumtoregeneratenotonlythepropagatingbutalsotheevanescentwavesrequiredtorefocusbelowthediffractionlimit.Finally,wewilldiscussthelinkexistingbetweentime-reversalapproachesandnewimagingmethodsrecentlydevelopedwhereGreen’sfunctionsofcomplexmediacanbeextractedfromdiffusivenoisebycross-correlatingtherecordingsofadiffuserandomwavefield.1.IntroductionItiswellknownthattheacousticwaveequationinanon-dissipativeheterogeneousmediumisinvariantunderatimereversaloperation.Indeed,itcontainsonlyasecond-ordertime-derivativeoperator.Therefore,foreveryburstofsoundϕ(r,t)divergingfromasource-andpossiblyreflected,refractedorscatteredbyanyheterogeneousmedia-thereexistsintheoryasetofwavesϕ(r,−t)thatpreciselyretracesallofthesecomplexpathsandconvergesinsynchrony,attheoriginalsource,asiftimeweregoingbackwards.Thisideagivesthebasisoftimereversalacoustics.Takingadvantageofthesetwopropertiestheconceptoftime-reversalmirrorhasbeendevelopedandseveraldeviceshavebeenbuiltwhichillustratedtheefficiencyofthisconcept[1,2,3].Insuchadevice,anacousticsource,locatedinsidealosslessmedium,radiatesabrieftransientpulsethatpropagatesandisdistortedbythemedium.Iftheacousticfieldcanbemeasuredoneverypointofaclosedsurfacesurroundingthemedium(acousticretina),andretransmittedthroughthemediuminatime-reversedchronology,thenthewavewilltravelbacktoitssource.Notethatitrequiresbothtimereversalinvarianceandspatialreciprocity4thAIPInternationalConferenceandthe1stCongressoftheIPIAIOPPublishingJournalofPhysics:ConferenceSeries124(2008)012004doi:10.1088/1742-6596/124/1/012004c2008IOPPublishingLtd1[4]toreconstructthetime-reversedwaveinthewholevolumebymeansofatwo-dimensionaltime-reversaloperation.FromanexperimentalpointofviewaclosedTRMconsistsofatwo-dimensionalpiezoelectrictransducerarraythatsamplesthewavefieldoveraclosedsurface.Anarraypitchoftheorderofλ/2whereλisthesmallestwavelengthofthepressurefieldisneededtoinsuretherecordingofalltheinformationonthewavefield.Eachtransducerisconnectedtoitsownelectroniccircuitrythatconsistsofareceivingamplifier,anA/Dconverter,astoragememoryandaprogrammabletransmitterabletosynthesizeatime-reversedversionofthestoredsignal.Inpractice,closedTRMsaredifficulttorealizeandtheTRoperationisusuallyperformedonalimitedangulararea,thusapparentlylimitingfocusingquality.ATRMconsiststypicallyofasmallnumberofelementsortime-reversalchannels.ThemajorinterestofTRM,comparedtoclassicalfocusingdevices(lensesandbeamforming)iscertainlytherelationbetweenthemediumcomplexityandthesizeofthefocalspot.ATRMactsasanantennathatusescomplexenvironmentstoappearwiderthanitis,resultinginarefocusingqualitythatdoesnotdependoftheTRMaperture.Itmustbenoticedthattheresearchontime-reversalacousticswasinitiallyfocusedontwomainapplications:ultrasoundtherapy(tumororkidneystonedestruction)andacousticcommunicationsintheocean.Inbothapplications,selffocusingonthesourcewithaTRMisaccomplishedwithoutanyknowledgeofthemediumbetweenthesourceandtheTRM.Activeorpassivesourcescanbeused.Thispaperfocusmainlyonthebehavioroftimereversalmirrorsincomplexmedia.Itwillbeshownthatinpresenceofmultiplereflectionsormultiplescattering,asmallsizetimereversalmirrormanagestofocusapulsebacktothesourcewithaspatialresolutionthatbeatsthediffractionlimit.Theresolutionisnomoredependentonthemirroraperturesizebutitisonlylimit