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Now，justasacurvedreflegsurfaageofa，soacurvedtrasurface.HoensisshowninFigure11.Abundleofraysfromapoiarebroughttofocusattheimage.hatdoesthis-ithasthesamecrossseasalentil.Thisistheinoftheword‘lens’.
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，or10-9Foranhairisapproximately10，000nmiheplexarrayofdevidsislaidoutonasiliwaferbymeansofaprocesscalledlithography.Essentially，thechiplayoutisdrawnatalargeenoughscaletobevisibletothehumahenademagnifiedimageisprojetothechip.Theimageisettoasurfagonthewafer，andaseriesofchemicalprocessesthenmapstheimageintorealdevices.Theimagibeabletoprovideextraordiionintheimage—withpixelsizesoftheorderofthelihedevitainiioirewaferisarealge，requiringmasproreduceallaberrationstoanabsoluteminimuAnexampleofsusisshowniioninFigure14，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
FormaitistshavebeenfasatedwiththequestionofwhatmakesagoodopticalsysteIstherealensthattheperfectimageofahisquestionhasintriguedmaphysiesClerkMaxwellinEnglaurytointheUSSRihtury.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.
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