obviousscreen

5AnalogApplicationsJournalCalibrationintouch-screensystemsIntroductionToday,moreandmoredifferentfieldsareadoptingtouchscreensortouchpanelsforapplicationswithhuman/machineryorhuman/computerinter-faces.
Figure1isablockdiagramofatouch-screensystemwherethetouchscreensensorliesontopofthesystem'sdisplay,inthiscaseanLCDpanel.
Thetouch-screencontrollerinFigure1doesnotneedanycalibrationbyitself.
However,productsorinstrumentationequippedwithatouchscreennormallyrequireacalibrationroutineuponpowerupbecauseitisdifficulttoperfectlyalignatouchscreen'scoordinateswiththoseofthedisplayunderneathit.
Calibrationisnecessarywhenthecoordinatesoftheareatouchedonthescreenarenotsuf-ficientlyclosetothecoordinatesonthedisplay.
Withoutpropercalibration,softwaremaynotrespondcorrectlywhenasoftbuttonoriconispressed.
Thisarticlepresentsconceptsandmethodsforthecali-brationoftouch-screensystems.
Software-programmingalgorithmsandtheirimplementationarealsodiscussed.
Touch-coordinateerrorsWhenpressureisappliedtothetouchscreen,thetouch-screencontrollersensesitandtakesameasurementoftheXandYcoordinates.
Severalsourcesoferrorcanaffecttheaccuracyandreliabilityofthismeasurement.
Themajorityoftheseerrorscanbeattributedtoelectricalnoise,scalingfactors,andmechanicalmisalignments.
Electricalnoisecomesfromthedisplayandbacklight,thehumaninterface,thepanelsurface'svibration,andtheelectrostaticdischargeandelectromagneticpulsescausedbyusersandtheirenvironments.
Thisarticledoesnotaddressnoiseissues.
Formoreinformationonhandlingnoise,pleaseseeReference1.
Scalingfactorsandmechanicalmisalignmentsoriginateinthepartsandassemblyofthetouchscreenandthedisplay.
Typically,thetouch-screencontrolleranddisplayinasystemdonothavethesameresolution,soscalingfactorsareneededtomatchtheircoordinatestoeachother.
Forexample,consideratouch-screensystemthatusesanLCDwitharesolutionof1024(Xcoordinate)*768(Ycoordi-nate)andtheTexasInstrumentsTSC2005touch-screencontrollerwith12-bit(4096*4096)resolution.
ThescalingfactorstomatchthemarekX=SX/S′X=1024/4096=0.
25fortheX-axiscoordinateandkY=SY/S′Y=768/4096=0.
1875fortheY-axiscoordinate,whereSXistheLCD'sX-axisresolution,S′Xisthetouch-screencontroller'sX-axisresolution,SYistheLCD'sY-axisresolution,andS′Yisthetouch-screencontroller'sY-axisresolution.
Thus,atouch-screencontroller'sXcoordinate,X′,shouldbeunderstoodbytheLCD(thehost)asX=kX*X′;andatouch-screencontroller'sYcoordinate,Y′,shouldbeunderstoodbytheLCD(thehost)asY=kY*Y′.
Intheprecedingexample,kXandkYaresimplelinearscalingfactorsbasedontheresolutionspecificationsforthedisplayandtouch-screencontroller.
"Real-world"scalingfactorsmayvaryfromparttopartandmayneedtobecalibratedtoreduceoreliminateanymismatch.
AnexampleisshowninFigure2,wheretheX-axisscaleisthesameontheLCDandthetouchscreen,orkX=SX/S′X=1;buttheY-axisscaleontheLCDislargerthanthatonthetouchscreen,withthescalingfactorofkY=SY/S′Y=3.
6/4=0.
9.
Thus,apointP(X′,Y′)=(2,2.
222)onthetouchscreenshouldbescaledto(X,Y)=(2,2)fortheLCD(thehost).
TexasInstrumentsIncorporatedDataAcquisitionByWendyFang,PrecisionAnalogApplications,High-PerformanceAnalog,andTonyChang,PrecisionAnalogNyquist,High-PerformanceAnalog3Q2007www.
ti.
com/aajHigh-PerformanceAnalogProductsAnalogInterfaceDigitalInterfaceAnalogInputCircuitryHostProcessorICorSPIBus2InterruptLCDX+,X–,Y+,Y–ResistiveTouchScreenTouch-ScreenControllerFigure1.
Typicalfour-wireresistivetouch-screensystemTouch-ScreenGridSharedGridLinesTouchPointPLCDGridPk=/YSYS'Yk=/X=1SXS'Xk=0.
9YS'=4YS=3.
6YSX==4S'Y(X,Y)=(2,2)(X',Y')=(2,2.
222)Figure2.
ScalingfactorsontheYaxesofLCDandtouchscreenMechanicalmisalignmentbetweenthedisplayandthetouchscreenincludesmovingandrotationerrors,asshowninFigure3.
Figure3ashowstherelativepositionshiftsofΔXintheXdirectionandΔYintheYdirection;andFigure3bshowstherelativerotation,Δθ,betweentheLCDandthetouchscreen.
ConsiderapointP,readas(X′,Y′)onthetouchscreen.
ThedisplayshouldreadamovingerrorlikethatshowninFigure3aas(X′+ΔX,Y′+ΔY).
ForarotationerrorlikethatshowninFigure3b,thepointonthetouchscreenis(R*cosθ,R*sinθ),oronthedisplayis[R*cos(θ–Δθ),R*sin(θ–Δθ)],whereRisthedistancefromoriginC,or(0,0),tothepointP.
MathematicalexpressionCalibrationofthetouchscreentranslatesthecoordinatesreportedbythetouch-screencontrollerintocoordinatesthataccuratelyrepresentthepointandimagelocationonthedisplayorLCD.
Theresultofcalibrationisasetofscalingfactorsthatallowcorrectionofthemovingandrotationerrorsthatareduetomechanicalmisalignments.
ConsiderthepointP,representedas(X,Y)onthedisplayand(X′,Y′)onthetouchpanel.
CountinginthescalingTexasInstrumentsIncorporatedDataAcquisition6AnalogApplicationsJournalHigh-PerformanceAnalogProductswww.
ti.
com/aaj3Q2007factorinFigure2andthemovingandrotationerrorsinFigure3,thetouch-screencoordinateXcanbeexpressedaswhereX′=R*cosθ,Y′=R*sinθ,αX=kX*cos(Δθ),andβX=kX*sin(Δθ).
Similarly,thetouch-screencoordinateYcanbeexpressedaswhereαY=–kY*sin(Δθ),andβY=kY*cos(Δθ).
FromEquations1and2itisobviousthat,togetthecoefficientsαX,αY,βX,βY,ΔX,andΔY,atleastthreeinde-pendentpointsareneeded.
Thepointsareindependentiftheyarenotononelinearline(seeFigure4).
Assumingthat(X1,Y1),(X2,Y2),and(X3,Y3)arethreeindependentYkRYkRkRYYYYsin()sincos()cossin()θθθθθθΔΔΔΔΔ=kYkXYXYYYYYYcos()sin(),ΔΔΔΔθθαβ(2)XkRXkRkRXXXXcos()coscos()sinsin()θθθθθθΔΔΔΔΔ=kXkYXXYXXXXXcos()sin(),ΔΔΔΔθθαβ(1)}}ΔY(X,Y)X'Y'+X+YΔΔ(X',Y)'(X,Y)ΔXPTouch-ScreenGridLCDGridTouchPointPFigure3.
MechanicalmisalignmentsCCΔθ[R*cos(–),R*sin(–)]θΔθθΔθ(X,Y)=(X',Y')=(R*cos,R*sin)θθ(X',Y)'(X,Y)Pθ–ΔθθTouch-ScreenGridLCDGridTouchPointP(a)Movingerror(b)Rotationerror(X,Y)11(X,Y)22(X,Y)33Figure4.
Independent(notononelinearline)anddependentpoints(X,Y)11(X,Y)22(X,Y)33(a)Threeindependentpoints(b)ThreedependentpointsTexasInstrumentsIncorporatedDataAcquisition7AnalogApplicationsJournal3Q2007www.
ti.
com/aajHigh-PerformanceAnalogProductspointsselectedontheLCD,and(X′1,Y′1),(X′2,Y′2),and(X′3,Y′3)arethecorrespondingpointsonthetouchscreen,Equations1and2canbeusedtowriteEquation3:(3)Equation3canberewritteninmatrixform:(4)whereCalibrationmethodsThethreeindependentcalibrationpointsshowninEquation4shouldbesufficienttogetthescalingfactorsrequiredtocorrectthemechanicalmisalignmentbetweenthetouchscreenandthesystemdisplay.
ToresolveEquation4,bothsidescanbemultipliedbytheinverseofmatrixAtoget(5)whereA–1istheinverseofmatrixA.
Thethreepoints—(X1,Y1),(X2,Y2),and(X3,Y3)—aredesigned/selectedonthedisplaysurface;andtheelementsinmatrixAaremeasuredfromthetouchscreenduringcalibration.
Example1:Three-pointcalibrationOnadisplaywith256*768resolution,threecalibrationpointsarechosen:(64,384),(192,192),and(192,576).
RefertoFigure5a.
Duringcalibration,thethreepoints(678,2169),(2807,1327),and(2629,3367)aremeasuredfromatouchpanelwith12-bitor4096*4096resolution.
Equation4canthenbepopulatedwiththeseknownvalues.
XXXYYY12312364192192384192==557667821691280713271262933671=AαβαβXXYYXAXXXYΔΔ=*1123and==*AYYY1123,A=′′′′′′XYXYXY112233111.
XXXAXYYYAXX123123=*=αβΔand**αβYYYΔ,YXYYYXYYYXYYYYYYYY111222333αβαβαβΔΔΔXXYXXXYXXXYXXXXXXX111222333αβαβαβΔΔΔApplyingEquation5resultsinαX=0.
0623,βX=0.
0054,ΔX=9.
9951,αY=–0.
0163,βY=0.
1868,andΔY=–10.
1458.
ThustheequationforX,fromEquation1,isX=0.
0623*X′+0.
0054*Y′+9.
9951;andtheequationforY,fromEquation2,isY=–0.
0163*X′+0.
1868*Y′–10.
1458.
Inmanyapplications,usersmayusemorethanthreepointsintheircalibrationroutinestoaverageorfilterthenoisyreadingsfromthetouch-screencontroller.
Forcali-brationwithn>3,(6)whereAisann*3matrixwithn>3andrank(A)=3,orA=′′′′′′XYXYXYnn1122111MMM.
XXXAXYYYnXXn1212MM=*αβΔand=*AYYYαβΔ,(X,Y)22(X,Y)33(X,Y)11Figure5.
Examplesforselectingcalibrationpoints(X,Y)11(X,Y)22(X,Y)33(X,Y)44(X,Y)55(a)Threepoints(b)FivepointsTexasInstrumentsIncorporatedDataAcquisition8AnalogApplicationsJournalHigh-PerformanceAnalogProductswww.
ti.
com/aaj3Q2007ToresolveEquation6,bothsidescanbemultipliedbyA'spseudo-inversematrix,(AT*A)–1*AT,whereATisA'stransposematrix.
Thatis,theunknownvariablesαX,βX,ΔX,αY,βY,andΔYareresolvedfrom(7)ThesolutionofEquation7istheleast-square-errorestimation2oftheseunknownvariables.
Example2:Five-pointcalibrationThesamesystemasinExample1isused,butfivecalibra-tionpointsonthedisplayarechosen:(128,384),(64,192),(192,192),(192,576),and(64,576).
RefertoFigure5b.
Equation6canthenbepopulatedwiththefivepointsαβYYTTYAAAYYYΔ=*()**1123.
αβXXTTXAAAXXXΔ=*()**1123andmeasuredfromthetouchpanel:(1698,2258),(767,1149),(2807,1327),(2629,3367),and(588,3189).
UsingEquation7providesasolutionsimilartothatfoundinExample1:X=0.
0623*X′+0.
0054*Y′+10.
0043,andY=–0.
0163*X′+0.
1868*Y′–10.
1482.
XXXXXY1234511286419219264=YYYYYA2345384192192576576===1698767225811491128071327126295883367318911CalibrationalgorithmsToperformthesecalibrationmethodsinanembeddedsystem,thelinearalgebraequationset,Equation4orEquation6,mustberesolved.
ThesolutioncanbederivedsimplyfromCramer'srule:Forthelinearequationsetb=A*x,bisaknownrealvectorequalto(b1,b2,bn)T;Aisaknownreal,square,full-rankmatrix;andxisanunknownrealvectorequalto(x1,x2,xn)T.
Theunknownelementsinxcanbecalculatedbyx1=Δ1/Δ,x2=Δ2/Δ,xn=Δn/Δ,whereΔisthedeterminantofmatrixA,det(A);Δk=det(Ak)fork=1,2,n;andthematrixAkisthematrixAbutwithitskthcolumnreplacedbythevectorx.
Three-pointcalibrationalgorithmAssumingthatthedimensionofAis3*3,Equation8canbedeterminedfromEquation4,basedonCramer'srule:(8)VariablesinEquation8aredefinedinthesidebaronpage9.
n-pointcalibrationalgorithmAsinEquation6,itcanbeassumedthatthedimensionofAisn*3withn>3.
Togettheleast-squaresolutionsofthelinearequationset,Equation7mustfirstberewrittenasαβαβxxyand======ΔΔΔΔΔΔΔΔΔΔΔΔΔΔxxxyyyyXY123123,,,,,.
(9)whereA=AT*A,(X1,X2,X3)T=AT*(X1,X2,X3)T,and(Y1,Y2,Y3)T=AT*(Y1,Y2,Y3)T.
Then,basedonCramer'srule,Equation10canbedetermined:(10)whereXXXYY112131112=′*∑=′*∑=∑=′∑*====XXYXXXYkkknkkknkknkknk,,,,==′*∑=∑==YYYkkknkkn,.
131andYaXbYcXYdXeYkknkknkkknkknkk=′∑=′∑=′∑=′21211111n∑ΔΔ=**nabccdeaebdnbcedx222112212,XXXX**()ecebdnacdedcdxXXXXXX3221123,Δaaeabccebdcdaenxy*()=**()=**,,ΔΔ3321211XXXYbbcedecebdnacdy*()()+*YYYYYYY2213221,Δ11233321**()=**()+edcdaeabccebdyYYYY,andΔYY2***()cdae;andαβαβxxyand======ΔΔΔΔΔΔΔΔΔΔΔΔΔΔxxxyyyyXY123123,,,,,,αβαβXXYYXYΔΔ=*AXXX1123and==*AYYY1123,TexasInstrumentsIncorporatedDataAcquisition9AnalogApplicationsJournal3Q2007www.
ti.
com/aajHigh-PerformanceAnalogProductsDefinitionsforEquation8Δ==′′′′′′=′′det()AXYXYXYXXYYXX112233132323111(()YY13ΔxxAXYXYXYXXYYXX11112233132323111=()=′′′=()()*det′′′()=()=′′′=′′()*(YYAXXXXXXXXXXxx13221122331323111Δdet))′′()*()=()=′′′′′′=XXXXAXYXXYXXYXxx231333111222333ΔdetXXXYXYXXYXYXXYXY123322133131221()ΔyyAYYYYYYYYYYYY11112233132323111=()=′′′=()()*det′′′()=()=′′′=′′()*(YYAXYXYXYXXYYyy13221122331323111Δdet))′′()*()=()=′′′′′′=XXYYAXYYXYYXYYyy231333111222333ΔdetYYXYXYYXYXYYXYXY123322133131221()ReferencesFormoreinformationrelatedtothisarticle,youcandown-loadanAcrobatReaderfileatwww-s.
ti.
com/sc/techlit/litnumberandreplace"litnumber"withtheTILit.
#forthematerialslistedbelow.
DocumentTitleTILit.
#1.
WendyFang,"ReducingAnalogInputNoiseinTouchScreenSystems,"ApplicationReportsbaa1552.
FrankL.
Lewis,OptimalEstimation:WithanIntroductiontoStochasticControlTheory(JohnWiley&Sons,Inc.
,1986).
—RelatedWebsitesdataconverter.
ti.
comwww.
ti.
com/sc/device/partnumberReplacepartnumberwithADS7843,ADS7845,ADS7846,TSC2003,TSC2004,TSC2005,TSC2006,TSC2007,orTSC2046AlgorithmimplementationToimplementtheprecedingcalibrationalgorithms,oneofthefirsttasksaftersystempowerupistodevelopandrunasoftwareroutinetoperformthefollowingsteps:Selectthedisplaycalibrationpoints(Xk,Yk)fork=1,2,nandn≥3.
Callthetouch-screencontrollerfunctiontoaccesstouch-screendata.
Touchthefirstpoint(X1,Y1)onthedisplay,acquiredatafromthetouch-screencontroller,andsavethetouchcoordinates(X′1,Y′1).
Repeattheprevioussteptogetall(X′k,Y′k)fork=2,3,nandn≥3.
Callthefunctiontocalculateαx,βx,ΔX,αy,βy,andΔY—forexample,callEquation10forfive-pointcalibration.
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