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Chapter 3 Waves（第2页）

Limitstoimaging，redux

Theictureoflightalsoexplaiseeinfinitesimallysmallobjegamicroscope，justasAbberealized。Verytinythings—downtoabouthalfofonemiillionthofametre，orabouthalfawavelengthofvisiblelight）beseenusinganhtmiuchmoresophisticatedmethodsarerequiredtoseeevehihatthewaveputsalowerlimitonthesizeofaspotoflight。

Ihatwhentwolightbeamsmeet，theyiioude—darkfriahesefriuallydetermiwhisiheangleisverylarge，thefringespagissmall;iftheangleissmall，thefringespagislarger。Thesmallestpossibleseparationesisoh，oraboutonemiforvisiblelight。

Now，ifthisfriernisrecordedasahologram，theisilluminatedagainwiththereferewobeamswillemergeiiobeamsthatwereusedtorecordtheieroseesugepatternwithamicroscopethelensmustcapturebothofthesebeamstees。Ifthisdidn’thappehelensly，thentherewouldbenointerfereheimage。

ThisisthephysicalbasisofAbbe’sthatIintroduChapter2:themaximumaturedbythelensofanimagihemihatberesolved。It’sstraightforwardtoseetheaemdoistoseeobjectsizesofaboutthewavelengthoftheillumination。Thusallightmicrosseeverytis，aboutfiftytimessmallerthanahumanhair，butnotmuchsmallerthanthis。Theybeusedtolookatbiologicalcells，butnottheuclei，forinstance。

&ionimaging

Optitistsandengineershavefoundanumberofverycleverwaystogetarousizelimitsposedbyicroscopes，sothattheysidecells，orviewobjectsthataremorethanoimessmallerthahoflight。Theseismakeuseoferialsandprocesses，suchastheabilitytoattaetre-scaleparticlestotheobjectsyouwishtosee，ortoihatemitlightiheseemitlight（theyfluoresce）atalohwhentheyareilluminatedbyabeamoflightatshths。Siheyaremuchsmallerthaionofthemicross，theresultingimageisaspotthesizeofwhitirelylimitedbythemicroscopeoptics，agtoAbbe’sformula。Buttheexatreofthisimagebelocatedverypreciselybyusiakealonglookatthefluoresceoftheattaopartiddetermiionofthemaximumiyofthespot。Thisapproachiscalledphoto-activatedloicros，andwasiedbyEricBetzigihasrevolutionizedlivecellimaging，allowingfasteraahresolutionoverawidefieldofview。

Ahodfsmallstrulargerfluorestobjectsistoshineaseularbeamocausestheobjectsillumihisbeamtohavetheirfluoresguished，sothattheremainingfluoresbelocatedpreciselybythesameapproachasdescribedpreviously。Thismethodiscalledstimulatedemissioionmicroscopy，orSTED，andwasiefanHellinGermany。Iwilldescribetheproulatedemissioailihesenovelwaysofmakiioeracellularstruagedhavehadenormousimpabiologyandmedideedthesighisimpactwasreizedwhenthe2014NobelPrizeirywasawardedtoBetzigandHell。

TheprotifiedbyAbbeworksioo。liedtotheilluminationofasamplebymeansofamicross，itsaysthatalightbeamotbefouchsmallerihah。Agaihefodseofahelensproduthesidethatfacestowardstheobject:thebreofraydires，thetighterthefocusofthelight。

&ioherangeofaerferihesizeestructuresturnsouttobeaveryfualpropertyofwaves。ThisideawasquantifiedbyJosephFourier，aFreoftheearly19thtury，whoprovidedadetailedmathematialysisoflightagatioheoremsaysihatthesmalleryoufocuslight，thebreofwavediresyouoachievethisspot。

Diffra

Thisexplaiureoflightbeams—theygraduallydivergeastheypropagate。Thisisbecauseabeamoflight，whichbydefinitionhasalimitedspatialextent，mustbemadeupofagateihaheideabetestedusier。Thebeamemittedbythelaseritselfisabout10μm（tenmillionthsofametre）orsoier。Whehes，itisabout1mm（athousandthofametre）ier。Andifitweresentfurtheraway，saytotheMoon（approximately400，000km），thenitwouldbeabout24kmihisphenomenoniscalleddiffra。

Diffraeiingapplideterminingtheshapeaructures。Forinstanyoushineabeamoflightohsmallholesinit，ofdiameterparabletothewavelengthofthelight，thelightdiffractsthroughtheapertures，spreadingiiontothesizeoftheaperture。Thesediffractedbeamsinterferesomedistanceawayfromthesdtheresultinginterfereheso-calleddiffrapatterhingaboutthesizeaivelooftheapertures。Foriheyareinaregulararray，theionpatternwillalsularities。Theadvantageofusingsustomeasurethistypeofobjectisthatyoudoohaveveryexpensiveorplissystemsordetectorsclosetotheobjeplylookatthepatterhasnaturallyexpaodiffra。

Now，imagihesisreplacedbyatrasolidmaterial，sayacrystallizedproteinstructure。The‘holes’arereplacedbytheatomsieinmolecule，whichareverysmallindeedaedtooherbybondsiareaboutohofabillionthofametre（0。1h。Iflightwithawavelengthofaboutthissizeilluminatessuchastructure，thewillbediffracted。Theactualstruoleculeitselfbedetermihediffrapattern。ThisisthebasisofX-raydiffra。AsnotediwasfamouslyusediofiureofDNAandisnowaveryontooliry，usedregularlyfoutthestruoleculesthatmightbeusefulindevelsforexample。ItrequiresabrightX-raylightsource，aswellasameaalsoutofthemolecules。Figure20showsadiffrapatternfromacrystalofbovierovirus。

20。AnX-raydifrapatternofaproteincrystaltakenusingamodernsynX-raysource。

It’sclearthatifyouwanttotransmitlightdistahendiffracouldbeaproblem。Itwillcausetheehelightbeamtospreadout，sothatyouwouldneedabiggeraicalsystemaocaptureallofit。Thisisimportantforteleunis，sinearlyalloftheinformationtransmitted-distanunislinksiseolightbeams。

Guided>

&omaionsothatlong-distanuniispossibleistousewaveguides，suchasopticalfibres。Awaveguideisastructurethathasacarefullydesignedprofilefortherefradex。Forexample，theiionaopticalfibreisarrathe‘core’，withadiameterofafewmillionthsofametre，hasahigherihesurrounding‘g’。Thelightisedtothishigherindexovesalongthefibrewith，remainingthesamesizedistances—acrosstheAtlantiviaunderseaple。Thismeanslightisthebasisofatiationinfrastruunistosensors。

Polarization

Thefinalimportahewavemodelisthecharacteristicofpolarizatiointraheundulationsoadireatrightahedireationoftheortawosuchdiresfortheseundulations。

siderwaves，forinstanoveoneendofaropeupanddoidly，youseetheundulatioherope。Asimilarthinghappensifyoumovetheeandrightequallyrapidly。Bothvertidhorizontalossareatrightahemotionofthewavedowhewavesaresaidtobe‘transverse’。

Lightwavesbehavesimilarly。Forexample，horizontallyphthasaricfieldthatoscillatesinahorizoiveto，say，anoptich）。Similarly，thefieldofaverticallyphtbeamoscillatesiie。（Therearemoreplisofpolarizationtoo，butthesewillsuffiow。）Thephenomenenbeexplaiingthatacrystalisastrusinveryspedhighlyrepeatableucells’，gofafewatoms，maythemselvesbeasymmetridihelightispolarizedalongthelongaxisortheshortaxisoftheuwillexperienceadiffereiveihuswillbedeviatedbydifferentamountsasitpropagatesthroughabloaterial。

&heaysinwhichpolarizationoflightisexploitedisinsunglasses。Someoftheseuseleicmaterial（forexample，asheetofPolaroidplastic）thatactsasapolarizer—thatis，awhismitslightofaparticularpolarizatioidabsorbsthatonalpolarization（horizontal）。Polaroidismadefrby-ballshapedmoleculesthatarealignedaheplastier。Thesemoleculespreferentiallyabshtthatispolarizedalongtheaxisofalighemoleerallysunlightscatteredfromobjectshasarandompolarizatihly50pertofeachpolarizatiohelightofonepolarizatioivelyreducesthebrighthesebyhalf。Further，plassesreduceglare:thatis，lightrefleshinyflatsurfaces，suchasthehoodandwindsofcars。Thesesurfadtoreflectahigherproportionoflightpolarizediiohesurfaeffectdisthe19thturybySirDavidBrewsterandnownamedforhim）。Suchreflesareblockedbyspectaclesthatarestruthemaedhere，makingforclearervisionoftheroad。

Trabirefrierialsalsogethepolarizationoflightwiththelight。Thisisbecausethespeedoflightdepeionofpolarizatioothe‘orientatioerial。Somematerials，suchaslass，havenospetation:yourotatethematerialwithheeffealightbeam。Asnotedabove，atentmaterialsarearrangedinsuchawaythatthereisapreferehesymmetryaxis—alongoolight。Thatis，lightpolarizedaloryaxiswillgoslower（say）thanlightpolarizedperpendiculartotheaxis。Now，imagihelightispolarizedat45degreestothesymmetryaxis。Wesiderthathalfofthislightisthehesymmetrydiredhalfpolarizedatrightahisdire。Ifthelatterissloweddownbyasuffitamouhelightemergiherfaaterialbepolarizedat-45degrees。Thusthedireofpolarizatioed’by90degrees。

Sentmaterialsbeusedtotrolthestateofpolarization，byactivelyadjustiionofthealigaxisofthemolecules，say，usingaageaaterialitself。Ahisisaaterialscalledliquidcrystals（LCs），whisistofelongatedmolecules。TheorientationofthemoleanLbetrolledbyapplyingavoltagea。Othermaterialsbeebirefriwheressesareapplied，becausetheforcecausesthemoleculestorotateortheatomstogealighisphehestruofforthestateofpolarizationoflightattheoutputoftheoptisor。

Plagapieceewopolarizersalsoallowstrolofthelightiybymearie。Applyingavoltagereorientsthemolecules，thusgtherefradexseenbyaphtbeam。IfapolarizerisplacedaftertheLdependingontheappliedvoltageagreaterorlesseramountoflightwillbetrahroughthefinalpolarizer。Anarrayofsuch‘cells’，eabyaseparateelectrial，beusedtoformadisplaywhereeachcellisasihisisthebasisofaliquidcrystaldisplay（Ldisoftenusedforputerdisplaysdtelevisios。

Infact，suchdisplaysbeusedtoshow3Dmovies。Theillusiohesemoviesderivesfromthestereographyofhumanvision。Eachofoureyesseesasaslightlydifferentlo，siheyareafewtimetresapartinourskulls。Thetwoimagesarebinediniveusaperofdepth。

Thisillusionisreprodug3Dglassesbymeansofpolarization。Trojetothedisplayors。Eachoftheseisgeedusinglightofaspecificpolarization，andeaaslightlydifferehe3Dglassesarepolarizerssetatdiffereionsthatallowtransmissioothelefteyeaheright，eapletelyblogthealterhasthe‘wrong’polarization。Thuswehaveaseheseisaswewouldperceiveitiuralworld—thatis，theillusionofathree-dimensiemesandpeople。

Thesuccessesofthewavemodeloflighthavebeenstunning，allowingustouaantcharacteristicsoflightahisuandingtobuildeologies。AndthesuccessesoftheraypictureoflighthavebeenequallyamaziislypuzzlingthattarentlyverydifferentviewsofwhatlightisshouldbeistothisthatInowturn。