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Chapter 2 Light rays（第2页）

Leousinimage-fdeviyoureyestomobilephoicalmiagingishavetwopoself，andalightdetector，whivertsthelightinto，typielectrial。Inthecaseofyoureyes，thisistheretihemobilephoisanarrayofminutepiecesofsilithatformsolid-statelightsensors。

11。Imageformationbyaraybundleusingalens。

Thelehesedevicesarediferent，ofcourse，butthebasicipleisthesameforeaeverycasethelooftheleothedetectorisakeydesiger，asisthefogthofthelenswhitifiesits‘ray-bendihefogthissetbythecurvatureofthesurfacesofthelensanditsthiess。Mlycurvedsurfadthickermaterialsareusedtomakelehshortfogths，andtheseareusedusuallyiswhereahighmagnifiisneeded，suchasamicroscope。

&herefradexofthelensmaterialusuallydependsonthecht，raysofdiferentcoloursarebeamountsatthesurfagtoafocusforeachcoliion。Thisgivesahas‘haloes’ofdiferentcolouraroundit。Forexample，onlyoneaybeproperlyinfocusataparticulardetee;theotherswillbeoutoffodformthehalo。Whetherthisaticaberrationisanimportadepeicularappli。

&hemostfamiliar，aimpe-fihistypeistheeye。Itsistsofafrsurface-thedanadjustablelens，easyoufothingsatdiferentdistaheseelementsfesohebackoftheeye。

Historically，theformatioheeyewasofgreati，sibyDescartes（seeFigure12）showedthattheimagehtobjectsidedown。Ofcourse，wedoheobjethisway，soitwasclearthatthebraiakessomeremarkableprogbetweeinalsignalsaioernalworld。

Optistruments

Asmanyofusarealltooaware，theabilityoftheeyeth-qualityimages（sharp，undistorted，andincradeasweage。Oapplisofoptistrumentsedasanaidtosightundersuchces。Eyeglassessthefirstoptiology，purportedlyiedbyRogerBaadfriar’ofOxford—iury。

&iveelemeensimplelenses，placedeitherisomedistance（afewmillimetres）fromtheea（thefroheeyeball），or‘tases’placed，asthes，intactwiththebothcasestheimagingsystemispound，thatis，itsistsofseveralelemeerhedtheinternalos。Thisfunprovidesthenecessarydegreesoffreedomtoostkindsofvisioheexteropeheimperfesoftheihisalsobedoeringtheshapeofthefroheeyebylasersurgery。Oneapproach，laser-assistediomileusis（LASIK），usesthelasertoablatepartofthesurfaceoftheea。Thisgesitscurvature，therebyalteringitsfogpower，andthustheimage-fcapabilitiesoftheeye。

Manye-fisworkonverysimilarpriheeye。Theobilephone，forinstance，hasalehesurfaceofthephone，andasili-basedphotodetectorarrayihedevice。Themobilephoenverysmall，aprovideimagesofsuffitqualitythattheyareintelligible，andthusmakeseheyarepostedohisrequiresthatboththedetectorarrayandtheimagingsystemareadequatetothetaskahigh-qualityimage。Thequalityoftheimagedependsontwothings—thesizeandtheethearray，ayoftheopticalsystemtocreateasharp，undistewithallcolourspristered。Thatis，animagefreefrom‘aberrations’。

12。Descartes’experimenttoshowtheimageformedbyaneyeisupsidedown。

Thespeofthenumberof‘pixels’ofthedetectorarrayisoftenusedasaproxyforthequalityoftheimage。A24megapixeleinwhichthedetectorarrays24millionsensors）isofteerthanan8megapixelone。Apixelbethoughtofasthesizeoftheimageofapoiispossibletoresolveonlyasmallnumberofpoihereareosihenitishardtotellmuchabouttheobject。Themorepixels，theonlyiftheimagingsystemproduagethatissmallerthaorelement。

Limitstoimaging

Ihtury，theGermaErnstAbbedevisedasimplerulefortheminimumsizeofaliagihenkerionsaysthatthesize（S）oftheimageofapoiisproportionaltothewavelength（λ）ofthelightillumimultipliedbythefogth（f）ofthelensaheleer（D）:

S=1。22S×λfD。

Thus，lehabigdiameterandashortfogthwillproduiestimagesofpois。It’seasytoseethataboutthebestyouaemyoucouldactuallymakeisanimagesizeofapproximatelyohisisthefuallimittothepixelsizeforleoptistruments，suchasdbinoculars。

Designingandbuildingimagideliverhigh-qualityimageshasbeeofmanyimportantapplisofoptics。Microsple，areusedinapplibiologicalresearchtery。Theearliestmicroscopesusedverysimplelenses—small，nearlysphericalpolishedglassshapesthatprovidedearlyexperimeHookeihturywiththemeanstoexploreuresofthenaturalworld，toosmalltobeseenbytheunaidedeye。Hisdrawingofaflea，showninFigure13，wasarevelationofthepowerofteologytoenablenewdiscovery。

Modernresearchmiuchmoresophisticateddevices。Theyulti-elementpouageswithpixelsveryclosetothewavelengthoftheilluminationlight—justattheAbbelimit。Figure13alsosholeofossibleusingammicroscope。Itisaageofthenervoussystemofafruit-flylarva，abouttohatch，madebyviewiiedinthecells。

&eriooallopticalsystemsinwhichtheimagebrightnessisproportioheobject。Theseareearsystems。Butit’spossibletogobeyondthislimitbymeansofems，wheretheimagebrightnessisproportionaltothesquareorevenmorepliofthehtness。Afullerexplanatiosrequiresknowingabitmoreaboutthewavemodeloflight，whichisthesubjectofChapter3。

Optigsystemsofsimilarpropertiesayareusedinanappliakingofputerdividualeleiccircuitelemeremelytiny。

13。Hooke’sdiagramofafleaobservedbymeansofanearlymicroscope（top），andthenervoussystemofafruit-flylarva（bottom）takenwithamodernfluorescemicroscope。

Awiregtwotransistorsonachipmayhaveadiameterofonly250res（nm）。（Areisohofametre，or10-9m。Foranhairisapproximately10，000nmiheplexarrayofdevidsislaidoutonasiliwaferbymeansofaprocesscalledlithography。Essentially，thechiplayoutisdrawnatalargeenoughscaletobevisibletothehumahenademagnifiedimageisprojetothechip。Theimageisettoasurfagonthewafer，andaseriesofchemicalprocessesthenmapstheimageintorealdevices。Theimagibeabletoprovideextraordiionintheimage—withpixelsizesoftheorderofthelihedevitainiioirewaferisarealge，requiringmasproreduceallaberrationstoanabsoluteminimum。AnexampleofsusisshowniioninFigure14，showiiplicityoflesandraypaths。

Attheotherextreme，bothground-aelescopesforastronomyareverylargeihrelativelysimpleoptigpoengofjustoingsurfadasimple‘eyepiece’toadjusttherayssoastomakebestuseoftheavailabledetectors。Thedistiureoftheseimagiheirsize。Themostdistantstarsarevery，veryfaint。HardlyamakesittotheEarth。Itisthereforeveryimportanttocollectasmuchofitaspossible。Thisrequiresaverybiglensormirror—severalteresormoreiisnotpracticaltobuildlehissize，heyetelescopes。Itisalsoolookatdistantstarsftimeiherenoughlightte。Aoanotherprrouelescopes:theatmosphereisnotstatigesihwiure，andmoisture。Theseflustendtomakeraysdeviatefromtheirstartotelescope，gthestarto‘twislightisdeflelyontoaorduetoatmospherice。

&odealwiththisproblemistoputthetelescopeoutsidetheatmosphere，iheHubbleSpaceTelesexample。Itproducedspectacularimagesofdistantstars，galaxies，andnebulae，showiraordinarystrudmovementinthefarreachesofspace。However，optieershaveiwodecadesdevisedacleverwaytodealwiththisprrouelescwithvisiblelight。Whattheydoistomakethetelesirrmeofeatbeingadjustable。Thusitispossibleto‘steer’therayshittisofthetelesirrorsothattheyallhitthedetector。Ifyoumeasurethedeviationthatarayexperieraversestheatmosphere，thenyoufigurethemirrortopedeviation。Andthat’swhattheeheymeasurehowlightfromaguidestar—anartificiallightsourtheupperatmosphere—isdistortedainformationtoadaptthetiltments。InthiswayimagesrightattheAbbelimitbeproduced。Spacetelescopesarestillhough，toprobethewavelengthranges，suchasX-raysandUV，thatareabsorbedbytheatmosphere，andseveralmissionsfornelaheNorthAmeriSpaASA）andtheEuropeanSpacy（ESA）。

14。Seofalensusedforphotolithographyofputerchips。Itorethaydiferes，andproducesimagesof500nminsizeusinglightoflessthanhalfthatwavelength。

&erialsandsuperlenses

Formaitistshavebeenfasatedwiththequestionofwhatmakesagoodopticalsystem。IstherealensthattheperfectimageofahisquestionhasintriguedmaphysiesClerkMaxwellinEnglaurytointheUSSRihtury。Veselagothoughtaboutmaterialsthatbehaveinstrangeways—inwhichlightbendsinaositetothatprediell’slaw。Snell’slawisbasedoiverefradicesthatarefoundinaterials。Veselagosideredmaterialswitha‘iveindex。Suchmaterialsbemadeupoftinystructuresthatareeachlessthahoflightihiskindofspestrugives‘metamaterials’suusualopticalproperties。Inparticular，refratakesplaceattheiweennormalaerialssuchthatthelightraysbeedirewithrespecttotheiweentwonormalmaterials。

&raiveihesematerialsgiobendlightraysiions，allowingtheiningrayswhiallybescatteredbytheobjesteadbeguidedaroundit。IishphysicistSirJohnPeispossibletobuildaninvisibilitygthesedesigerials。

Aheunusualpropertiesmetamaterialspossessistheabilitytesofobjectsthatareveryclosetoaslabofthemetamaterial。Evenaflatsurfaceissuffiakealens，whichmakesthemsuitedtoviewiis—so-ostructures，becausetheyhavesizesoftheorderoftensofhisisthe21st-turyversioeology，andsunleashasimilarlyfruitfuleraofdiscovery。

Alloftheimagingsystemsdesthischaptermaketwo-dimensisofobjects。That’snormallytheeriehinkaboutimages—asflatpictures。Butwhatifitwerepossibletoceiveofasystemthatakethree-dimensionalimages?Remarkablyitis，butthatrequiresadeeperviewoflightitself，illsiderinChapter3。