Development of a new Confocal Tracking sensor for shape measurement of optical surfaces
Abstract
[ANGLÈS] In this thesis work, a new contact sensor applied to the shape measurement of optical surfaces is presented. This contact sensor is based on confocal tracking technology. This technique consists on tracking the focus of the sample while it is moved along the horizontal axis at a constant speed. It is capable of providing nm level accuracy as required by state of the art optical designs. Existing applications of such technology use an all-optical approach, which have advantages such as being non-contact technique but also some limitations such as the maximum slope measureable. The sensor developed in this work is designed to seamlessly integrate onto existing systems extending the maximum measurable slope to more than 60 degrees. Even though the sensor requires contacting the surface to operate, its force can be easily adjusted, thus making it flexible and adaptive to different samples and applications.
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Deve l De v se n su r l opmentofa v elop m n sor f r faces newConfoc a M A D m en t f ors h a lTrackings e M aste r A lbert S D irector: Re g ofa h ape e nsorforsha p r thesi S ánche z Ferran P r g istere d ne w mea s p emeasure m sWor k z Lafore t Laguar t r esented o d at: Con f s urem e m entofoptic a k t t a o nFebru a f ocal e nt o a lsurfaces a ry26 th , 2 Trac k o fop t 2 015 k ing t ical
DevelopmentofanewConfocalTrackingsensorforshapemeasurementofopticalsurfaces AlbertSánchezLaforet SensofarTechS.L,ParcAudiovisualdeCatalunya,Crta.BV‐1274Km1.E‐08225Terrassa (Spain) E‐mail:[email protected]ABSTRACT Inthisthesiswork,anewcontactsensorappliedtotheshapemeasurementofoptical surfacesispresented. Thiscontactsensorisbasedonconfocaltrackingtechnology.Thistechniqueconsistson trackingthefocusofthesamplewhileitismovedalongthehorizontalaxisataconstant speed.Itiscapableofprovidingnmlevelaccuracyasrequiredbystateoftheartoptical designs. Existing applications of such technology use an all‐optical approach, which have advantagessuchasbeingnon‐contacttechniquebutalsosomelimitationssuchasthe maximumslopemeasureable.Thesensordevelopedinthisworkisdesignedtoseamlessly integrateontoexistingsystemsextendingthemaximummeasurableslopetomorethan 60degrees.Eventhoughthesensorrequirescontactingthesurfacetooperate,itsforce canbeeasily adjusted, thus making it flexibleandadaptivetodifferentsamplesand applications. Keywords:confocaltracking,singlepointtechnique,contactobjective,contactobjective withtunableforce,opticalsurface,shapemeasurement. 1. INTRODUCTION Beingonleadingedgeofthemetrologyfield for optical surfaces requires both high accuracyandfastmeasurementspeed.Inordertoreachthesespecifications,several companieshavedevelopedinthepastdifferentmeasurementtechnologiesbasedeither onnon‐contacttechniquessuchasconfocaltracking[1][2],focusdetectionorpattern projectionoronthewell‐knowncontacttechniquessuchasthestylusprofilometersor atomicforcemicroscopes[3]. Non‐contacttechniquessuchasconfocaltracking,developedandpatentedbySensofar TechS.L[1],consistsontrackingthefocusonthesurfacewhileitismovedalongthe horizontalaxisataconstantspeed.Sinceitisanimage‐basedtechniqueitisableto correctforthetrackingerrorspresentinsinglepointtechnologies.It’safastandvery accuratetechniqueforthemeasurementofasphericandfree‐formopticswithadditional advantageofbeinganon‐contacttechnique,avoidingpotentialscratches onthesample. However,thistechniquehaslimitationssuchasthatisitnotcapableofmeasuringlocal slopeslargerthan35degreesandtherelativelyshortworkingdistancebetweenthe microscopeobjectiveandthesample. Contacttechniquessuchasthestylusprofilometers[4],whichdragastylusalongthe sampleandmonitoritspositiontoobtaininformationonthesurfaceprofileareableto measurelargerlocalslopesbuthavethedrawbackthattheycaneasilyscratchthesample. Moreover, sample alignment and navigation is quite difficult. AFM based stylus profilometersminimize surfacescratching asthey applylessforcebut are extremely expensive. Giventhedrawbacksoftheexisting technologies, in this thesis work we focused on developinganewsensor,capableofovercomingtheexistingproblemsbutkeepingit simpleintermsofdesignandusingthesamepatentedtechnologybySensofarcalled “confocaltracking”.
DevelopmentofanewConfocalTrackingsensorforshapemeasurementofopticalsurfaces 1.1 NEWDEVELOPEDCONTACTSENSOR Themaingoalofthisproject hasbeendevelopinganewsensor,calledcontactobjective, which combines the advantages of both contact and non‐contact technologies, while improvingtheirlimitations.Butalsofulfillingthekeyspecificationsforbeingcompetitive in the optical surfaces metrology field: high accuracy, high speed and non‐sample scratching.ThecontactobjectivehasbeendesignedfromscratchusingCADsoftware1to beseamlesslyintegratedontotheinstrumentcalledPluApex,whichusesthepatented technology from Sensofar called “confocal tracking”. This guarantees to achieve high accuracyandhighspeed.UsingthiscontactobjectivemakesitpossibleforthePluApex systemtomeasurelocalslopeslargerthan60°withoutscratchingthesamplethanksto thesmallandcontrolledamountofforceappliedonthesurface. 2. WHATISALREADYINTHEMARKETANDWHATMAKEUSUNIQUE SincemanyyearscontactsystemsfromPanasonicorTaylorHobsonhavebeentheusedin thededicatedmetrologyof3Dformsoflensesandmolds[3]. The“TalysurfPGI”systemfromTaylorHobson[5]hasbeenareferencesystemforthe measurementofforms,texturesanddimensionssincemid80’s.Itwasdevelopedin1984, specificallyfortheprecisionbearingindustryanduntiltoday,itisstillwidelyused.Its workingprincipleconsistsondraggingastylusalongthesurface and to monitor its positionasittravelsacrosspeaksandvalleysfromthesurfaceusinganinductivegauge2. Thestylusislocatedattheendofaleverarmwhichmayintroducemeasurementerrors. Thissystemusesaminimummeasurementforceof20mNanditiscapableofmeasuring localslopesupto80°.Duetothefactofusinganinductivegauge,itsnoiseisaround4nm underbestcircumstances.Furthermore,itisabigandheavysystemandcanbequite expensiveinsomeofitsconfigurations. Panasonichasalsoawidelyusedcontactsysteminthemarketcalled“UA3P”[6].The workingprincipleofthisinstrumentisbasedonatomicforcemicroscopy(AFM).Inorder tomeasurethissystemapproachesanAtomicForceProve(AFP)tothesampleuntil atomicforcesgeneraterepulsionagainstthemeasurementsurface andthenaclosed‐loop systemkeepsthisatomicforceconstantwhiletheproveisdraggedalongthesurface.This systemworkswithmeasurementforcesof0.15‐0.3mN,muchlowerthanthoseinthe TaylorHobsonsystemthankstoitsAFPmethod.Becauseofthefactthatitdoesn’tusea leverarmandthatituseslaserfeedbackencoders,itsaccuracyisextremelygoodandthe measurementnoiseissmallerthanthatofthe“TalysurfPGI”.However,thissystemcan onlyperformmeasurements on sample with local slopes up to 60°.Moreover,this productisnotablyheavyandbulkyandwaymoreexpensive. The contact objective that is proposed in this work, improves the performance and overcomes the limitations of the existing products in the market. It is based on the “confocaltracking”techniquepatentedbySensofarTechS.L.Itstunablemeasurement forceanditsprecisedeterminationofsampleposition,makethistechniqueuniquein termsofadvancedmeasurementmethodsinthemarket.Ithaslownoisethankstoits simpledesign,havingnoleverarm.Moreover,whereasthetwosystemspresentedusea 1CreoParametricPTCsoftwarehasbeenusedfortheOpto‐mechanicaldesignandsimulation. 2Electro‐mechanicaldevicethatmeasuresintwodirections.Aprocessunitrecordstheamplitudeand frequencyofondulationsandconvertsthedataintoinformationabouttheroundness,shapeorform.
Deve l cons bet w this p syst e bee n beco The f SLW D perf o 50μ verti ball o ofth e The s eith e the b surf a Fina l light was t Ino r shou obje c the m The o posi t 768 x Maxi 3Itis seen thes u l opmentofa tant meas u w een4mNt o p rototype m e mandit’s n designed a mingaco m f iguresabo v D microsco o rmance(1 0 μ m(104,10 5 calmovem e o f1mmdia m e stylussha f s tylusshaf t e rmoveup b estinfocus a ce. l ly,itiswo r andcheap t obuildap r r dertocalc u ld be kno w c tiveused) a m aximumal l o ptimumsl t ionsensor x 576pixels. mumdispl a possibletotu n thatthiscaus e u rfacecontin u newConfoc a u rement fo r o 30mN3a n m easuresw i capableof a salightw e m petitivealt e 3. Figure1C v eshowth e peobjecti v 0 1).Akey p 5 ).These m e ntofthec o m eter.Final f tforsafety t withthec o ordowntr a pointdete c r thtocom m intermso f r oto t ypein o u latetheth i w n. This w i a ndthetilt i l oweddefo r opeofthe i whichis3 0 Assumingt h a cement(W h n ethemeasur e serrorswhe n u ously.Thisef f a lTrackings e r ce, our d e n d,hence,a d i thhighacc u measuring e ightandb a e rnativein t DESIGN O A Ddesignperf o e designof t v e(100)w h p artofour d m embranes h o ntacttip( 1 ly,therear e reasons(1 0 o ntacttipa t a ckingthe s c tedbythe o m entthatth f manufact u o rdertoch e 3.1 DESIG N cknessoft h i ll depend o i ngofthei n r mationoft h i nternalmi r 0 nm/pixela n h attheCCD h oleFOV): e mentforced o n trackingthe s f ectismoreap p 1 10 1 10 0 e nsorforsha p e sign allow d justittoe a uracyand a localslope s a lancedqua l t henearfut u O FTHECO N o rmedwithCAT I t hecontact o h ichimage s d esignaret w h oldthest y 1 07)upan d e twomech a 0 2,106). titsbotto m s amplesur f o bjecti v e, w iscontact o u ring.Howe v e ckthefeas i N OFTHEI N h emembra n o n the FO V n ternalmir r h emembra n r rorcanbe ndfromth e cameraha s 30 o wnto0.1mN . s ur f acebecau s preciablewhe 1 02 103 1 0 106 p emeasure m s us to tu a chsample c a fastspeed s upto75 ° l it y ‐costde v u re. N TACTOBJ E I AV5andCREO o bjective, w s anintern a w othinme y lusshaft( d down.Th i a nicalcont a m andthei n f ace.This w w hichwillal l o bjectiveha s v er,itisn e i bilityofthe N TERNAL M n es,theall o V size(whi r or.Thema x n es. calculated e resolution s 1000pixel 1000 . However,aft e s ethecontact t nreachinghi g 5 1 1 m entofoptic a n e the me a c haracterist i asitisinst a .Finally,t h v ice.Ithas t E CTIVE Parametric. w hichisco m a lmirrort i m branesw i 103)anda l i scontactti ctstolimit t n ternalmir r illtranslat e owtherec o s beendesi g cessaryto s technolog y M IRRO R wedvertic a c h in turn x imumdis p f romthere oftheCCD s: 30 e rtesting,ith a t ipisnotable t g hlocalslopes. 05 04 a lsurfaces asurement ics.Further t alledinPlu h isprototy p thepossibi l m posedbya i ltedforo p i thathickn llowtheo p i pisasmal l t hedisplac e r oratitsto p e ontochan g o nstruction g nedtobe s s aythatou r y . a ldisplace m depends o p lacement w e solutionof cameraw h E a sbeen t ofollow force m ore, Apex p ehas l ityof 100X p timal e ssof p timal l Rubi e ment p will g esof ofthe s mall, r goal m en t n the w illbe theZ h ichis E q.1
DevelopmentofanewConfocalTrackingsensorforshapemeasurementofopticalsurfaces Therefore,thealloweddisplacementofbothmembraneswouldbe 15. Thetiltangle()oftheinternalmirrorcanbecalculatedfromthemaximumvertical alloweddisplacementandthehorizontalsizeoftheFOV.Usinga100XSLWDmicroscope objectivefromNikon,theFOVhorizontalsizeis128.Therefore,theangleofthe internalmirroris: tan →atan ~13,5° Eq.2 Eventhoughthemaximumverticaldisplacementcalculatedforthemembranes could be15,asecurityfactorof1.5istakeninordertoprotectthemembranesfrom damage.Takingthissecurityfactor,thealloweddisplacementis 10. 3.2 DESIGNOFTHEMEMBRANES Inourcontactsensordevice,theinternalmembranesareakeypartandneedtobe designedinordertoachieveadesiredperformance.Giventhediameterofthemembranes, materialcharacteristicsandthemaximumverticaldeformation,thethicknessofthose membranescanbecalculatedanalytically. Inourcase,wehavestudiedtwodifferentmaterials;stainlesssteelandaluminum.After consideration,“stainlesssteel”hasbeenchosenforourdesignandfollowingprototype. Stainless steel (“Steel structural”ASTM‐A36)hasaYoung’smodule of E 200 210GPaandaPoissoncoefficientofν 0.300.31. Knowingthatthedensityofthematerial(stainlesssteel)isρ 7,85g/cm andthe geometryofthestylusshaft,itispossibletocalculatethetotalmassbycalculatingits volume.Wehaveapproximatedtherealgeometrytoasimplifiedmodelofacylinder, simplifyingthecalculusandgivingasafervalue.Thethicknesscalculatedwilltakeinto accountahighermassthantherealone,ensuringthatthemembranes will not be damaged. Acylinderapproximationhasbeenusedtocalculatethetotalmass: Mass: m densityvolume 7,85 π 51mm 2.83g Eq.3 Finally,takingintoaccountthattheradiusofthemembraneisequalto10mm,wehaveall informationneeded(mass,membraneradius,Poissoncoefficient,Young’smodule,δ)for calculatingthethicknessofthemembranes[8]: → → ~50 Eq.4 Wherein: Fistheforceaapliedonthemembrane,kisthestiffnessofthemembrane,Eis theYoung’smodule,υisthePoissoncoefficient,ristheradiusofthemembrane,gisthe gravityandhisthethicknessofthemembrane. 4. MEASUREMENTMETHOD The measurement method of the new contact objective is based ontheprincipleof ConfocalTrackingTechnique[1]whichwaspreviouslydevelopedfromtheconceptofslit confocalmicroscopy.Inaconfocaltrackingprofiler[7]apatternofparallelslitsisimaged
DevelopmentofanewConfocalTrackingsensorforshapemeasurementofopticalsurfaces byahighnumericallensonthesurfacetobemeasured.Instead,inthecontactobjective, suchslitpatternisimagedonthesurfaceoftheinternaltiltedmirror,whichislocatedon thetopofthestylussupportedonthemembranes. TheslitsareprojectedparalleltotheXaxis.Onlythecentralslitwillbeusedforthe measurementandthemidpointwithinthefieldofviewalongthiscentralslitwillbe consideredasthereferencepixel(seefig3and4).Sideslitswillbeveryusefulforaligning theinternaltiltedmirrorintheXdirection.Suchalignmentisattainedwhenthebest focusedpixelsoftheslitsappearwellalignedalongtheYaxis. Inafirststep,thesensorheadholdingthecontactobjectiveismoveddownuntilthetip contactsthesurfacetobemeasured.Aftercontact,theheadcontinues to move downwardsuntilthebestinfocuspixelofthecentralslitispositionedascloseaspossible tothereferencepixel,whichcorrespondstoadeformationofboth membranes that doesn’thavetobenecessarily0,butdependsontheinitialnon‐contactsettingposition (explainedlateronindetail). Onceweareatthisinitialposition,thesampleismovedalongthehorizontalXaxisat constantspeedwhilethesensorheadholdingthecontactobjectiveiscontinuouslymoved alongtheverticalZaxis.Thiscoordinatedmoveiscarriedoutinawaythatthebestin focuspixelofthecentralslitismaintainedascloseaspossibletothereferencepixel.This focussetpointcanbeattainedbyusingaPIDclosedloopautofocusalgorithm.Inthisway, thecontactobjectiveistrackingthesurfacetobemeasuredwhilemaintainingalmost constanttheforcebetweenthetipandthesurfaceallalongthemeasuredlength. Whileperformingthetrackingofthesurface,aCCDcameraacquiresaseriesofframesof thecorrespondingfieldsofviewataconstantframerate(50Hz).TheCCDistriggeringthe readingofXandZpositionsensors,sothatapoint(x,z)isobtainedforeachframe.Itis worthnotingthatthissetof(x,z)pointswouldbetheoutputofameasuredsurface shapegivenbyaprofilerbasedonasingle‐pointtechnique. However,itiswellknowthateventhebestandfastestclosedloop autofocus has a residualtrackingerror,whichcanbeacceptableifthegoalwouldbetokeepthebestin focuspixelnearthereferencepixel.Nonetheless,thistrackingerrormaybetoohighwhen IMAGE PROCESS FOCUS (ce n t r o i d) PID CORRECTION 50Hz Figure2Simplifiedsequencemeasurement Figure3CentralslitprojectedalongXaxis.Best‐in‐focus pixelisfoundatthepositionofthemaximumoftheaxial response Referencepixel Figure4Correctionofresidualtracking error;distancebetweenthebestinfocus pointandreferencepoint Bestinfocus pixel Heighttracking error∆
DevelopmentofanewConfocalTrackingsensorforshapemeasurementofopticalsurfaces surfaceshapemeasurementsatthenm‐levelarebeingpursued.Theconfocaltracking methodmakesitpossibletoovercomethislimitbycorrectingtheheighttrackingerrors. Theprincipleunderlyingtheconfocaltrackingmethodistocorrecttheheightzofeach measuredpointx.Thecorrespondingtrackingerrors∆zareobtainedforeachframeas thedistancealongthecentralslitbetweenthebestinfocuspixelandthereferencepixel (inpixelunits)multipliedbythecalibratedslopeofthetiltedmirror(innm/pixelunits), asitcanbeseeninFig.6. Therefore,theshapeoftheopticalsurfacebeingmeasuredisobtainedbybuildinga2D curvecomposedbythefollowingpoints: ,∆,,∆…,∆Eq.5 Wherein: ,,..RefertothemeasuredpointsofthesurfaceintheXaxis;,,..referto readingoftheHeidenhaincloseloopinthezaxiscorrespondingtoeachpositionand ∆,∆,..∆refertothe“heighttrackingerrors”inzforeachdifferentposition.These correctiondifferentialscanbeconvertedfrompixelunitsontheCCDimagesintoheight unitsontheopticalsurfaceofthesamplebeingmeasured,takingintoaccountthereal magnificationoftheobjectivebeingused;∆Referstothecorrectedheightforeach position. Itisobviousthattheshapesobtainedwiththeconfocaltrackingtechniquewillbemuch more accurate than those obtained with single‐point based techniques, because the representation of the surface is composed entirely of points with corrected tracking errors. 5. TUNINGOFTHECONTACTFORCE Thecontactforcebetweenthetipand thesurfaceduringthemeasurementcan betunedveryeasily.Whenthereisno contactbetweenthetipandthesurface, the membranes are supporting the completeweightofthestylusand thereforetheirdeformationwillbethe maximum (approximately 15 μm with the current design). Under these noncontact conditions we can adjust the distancebetweenthetiltedmirrorand theobjective.Ifthe probe holdingthe stylusismoveddowninrelationtothe objective (see Fig. 1), then the slit patternwillfocusonanupperheightof themirrorandthebestinfocuspixel willbeshiftedtotherightpartofthe fieldofview.Werefertosuchposition as"non‐contactsettingposition". InFigure5wecanseetwodifferentexamplesoftuningconditions.Inoneofthemthe probe was moved down until the "non‐contact setting position" wasshiftedtothe rightmostpartofthefieldofview(pixel#333).Withthissetting,whenthesensorheadis -300 -200 -100 0100 200 300 FOV internal mirror -300 -200 -100 0100 200 300 0 20 40 60 Tuning of contact forces Force [mN] pixel #333: force 32mN pixel #167: force 17mN -300 -200 -100 0100 200 300 -15 -6.5 0 6.5 15 Deformation of the membrane x position [#pixel] Membrane deformation [ N] pixel #333: MAX 15 m pixel #167: MAX 6.5 m Figure5Behaviorofmembranesandforceswhentuningthe contactforce
Deve l mov e focu s corr e the d Inth ispi x initi a the d Thu s posi t defo r smal "non Whe n one b and t intr o mea s The l thes expr e Int h are p mea s Figu r erro r Whe n curv e whe n sho w Figur e l opmentofa e ddownwa s pixelis p e spondingt d eformation eseconde x x el#167.I n a lmeasure m d eformation s , the close t ion(refere n r mationof t lestcontac t ‐contactse t n measurin g b utitisalw a t hesurface d o ducesane r s ured.This h l ocalslope i pecificloca l e ssion: h issection, d p resented. s urements o r e7shows r incompar i n theheigh t e showss m n themeas u w nwitha0. 0 e 6Detailofthe newConfoc a rdsuntilre p ositioned opixel#0) , oftheme m x ample,the p n thiscase, w m entpositio oftheme m r is the " n n cepixel),t h t hemembra t forcethat t tingposi t io g theprofil e a yslarger; t d ependson r rorwhich d h asbeenm o i scalculate d l slope.Th e d ifferentm e Inordert o o nacalibra t themeasu r i sonwitht h t trackinge r m ootherpe a u remen t sp e 0 8umroug h measuredradiu a lTrackings e achingthe i as close a s , theresulti m braneswill p robewas p w henthes e n,theresul t m braneswill n on‐contact h esmaller w neduringt h canstill w n"isplaced 6. BA L e ofasurfa c t hisisduet o thelocalsl o d ependson t o delledand d every10 p e zcorrecti o ∆ e asurement o measure t edspheric a r ementofa ebestfitra d r rorcorrec t a ksincom p e edislarge r h nessfilter a swithrespectt o e nsorforsha p initialmea s s possible ngcontact f bealmost z p ositioneds e nsorheadi t ingcontac t beapproxi m setting po w illbethe c h emeasure m w orkproper d aroundpix L LSHAPEC O c e,themea s o thefactth o peasseen t heradius o compensat e p ixelsinor d o n∆ factor ∝ 7. RESU L t sperforme d the accur a a lballwere p ballstand a diuserrorc t ionisappli e p arisonto t r .Inthelas t a ppliedino r o therealone.T i p emeasure m s urementp o tothere f f orcewillb z ero(blueli n othatthe" n smovedd o t forcewill b m ately6.5 μ s ition" to t c ontactforc m ent.Expe lyis4mN, el#80. O RRECTIO N s uredradiu s a t thecont a infigure8. o ftheballit s e dbyasoft w d ertofind w iscalculat e 1 L TS d usingthe a cy of this p erformed. a rdandthe orrectingt h e dthenois e t herawda t t subplott h r dertoextr a i ptrackingerro r m entofoptic a o sition(in w e rence me a e approxim n esinFig.7 n on‐contact o wnwards u b eapproxi m μ m(redline t he referen c e andtheg r r imentsha v whichisa t N s doesn’tm a ctpointbe t Theballtra s elfandthe w arealgori t w hichisth e e daccordin g contactob j contact o b bestfitra d h eheighttr a e obtainedi s a .Thiseffe h esameres i a c t themea s ∝ ∆ ∝ r dependsonth e a lsurfaces w hichtheb a surement m ately32m N 7 ). t settingpo s u ntilreachi n m ately17m N e sinFig.7). ce measur e r eaterwill b v eshownth t tainedwh e atchtheno t weentheb a ckingthes u localslope t hm. e zcorrecti o g tothefoll o E q j ectivetech b jective, a s d iusrawre s a ckingerro r s smallera n e ctiseven l i dualprofil e s urementn o e localslope. estin point N and ition" n gthe N and e ment b ethe atthe e nthe minal alltip u rface being o nfor o wing q .6 nique s et of s idual r . n dthe l arger e sare o ise.
DevelopmentofanewConfocalTrackingsensorforshapemeasurementofopticalsurfaces Figure8showsacomparisonbetweenameasurementapplyingaradiuscorrectionofthe ballwithrespecttorawdatameasurement.TheeffectoftheRubiballtrackingthesample is clearly seen. The measurement has been performed on a calibration ball standard performingasymmetrical20mmrangemeasurementthroughtheapexofthesamplewith aspeedof0.1mm/s. Figure9showsastudyofthemembranelateraldeformation(orstylusshaftdeformation) whendifferentforcesareappliedonthesample.Ithasbeeninterestingtomeasurea rangefromtheapextoaslopeangleof61degrees,wherethemaximumdeformationwill takeplace.Ascanbeseeninthefigure,themembranesbehavealmost identically regardlessoftheforceapplied(between4.5and30mN).Athirdplotshowsthelocalslope ofthesurface. 246810 12 14 16 18 -11.5 -11 -10.5 -10 -9.5 -9 Measured Profile Z position [mm] 246810 12 14 16 18 0 0.5 1 Residuals Profile at 0.5mm/s Error [ m] 246810 12 14 16 18 -0.1 -0.05 0 0.05 0.1 X position [mm] Error [ m] Residuals Profile at 0.5mm/s - Roughness 0.08um filter Raw data Centroid correction 0 2 4 6 8 10 12 14 16 18 -20 -15 -10 Measured Profile Z position [mm] 0 2 4 6 8 10 12 14 16 18 20 0 20 40 60 80 Residuals Profile X position [mm] Error [ m] 0 5 10 15 20 26 32 38 45 53 62 0 20 40 60 80 Ball Angle Angle [deg] Error [ m] pixel 100: 23.5mN pixel 208: 13.5mN pixel 306: 4.5mN Figure7Measurementofacalibratedballstandard. Measured Profile and the best fit residuals. Measurementspeed:0.5mm/s.Forcesapplied:4.5mN. Green curve (centroid correction) VS red curve (no centroid correction). Rms (centroid correction) =6, Rms(rawdata)=7nm 2 4 6 8 10 12 14 16 18 -11.5 -11 -10.5 -10 -9.5 -9 Measured Profile Z position [mm] 2 4 6 8 10 12 14 16 18 0 10 20 30 40 Residuals Profile X position [mm] Error [ m] raw data radius correction Figure8Measurementofacalibratedballstandard. Measured Profile and nominal radius fit residuals. Measurement speed: 0.1mm/s. Force applied: 30mN (non‐contact setting position pixel #308). Nominal radius 22.5035mm. Best‐fit radius with radius correction:22.5334mm.Best‐fitradiususingrawdata: Figure9Measurementofacalibratedballstandard. Measured Profile and nominal radius fit residuals. Measurementspeed:0.3mm/s.Forcesapplied:23.5mN, 13.5mNand4.5mN.Nominalradiusof22.5035mm. 2 4 6 8 10 12 14 16 18 -11.5 -11 -10.5 -10 -9.5 -9 Measured Profile Z position [mm] 2 4 6 8 10 12 14 16 18 -1 -0.5 0 0.5 1 Residuals Profile at 0.5mm/s Error [ m] X position [mm] Contact sensor Apex (optical) Figure12Comparison of a measurement of a calibrated ball standard taken with APEX (optical system)andcontactsensor.MeasuredProfileandbest fit residuals. Measurement speed: 0.5mm/s. Green curve (Contact Sensor) VS red curve (APEX). Rms (APEX)=125nm,Rms(Contactsensor)=95nmnm