DesignandPerformanceofaLow-costRefractionInstrumentforLow-ResourceSettings

PadenTroxella,*,CharlesKima,BobLipskibaBucknellUniversity,DepartmentofMechanicalEngineering,701MooreAve,Lewisburg,PA17837,UnitedStatesbLipskiEyeCenter,2212OldTurnpikeRd,Lewisburg,PA17837,UnitedStates*CorrespondingAuthor,Email:paden.troxell@bucknell.edu

Abstract

Accesstoeyecareinlow-resourcesettings,commonlyknownasthedevelopingworld,islimitedduetoavailabilityofoptometricinstrumentationandexpertise.Anaffordable,easy-to-userefractioninstrumentwouldprovidehealthclinicsinlow-resourcesettingstheabilitytoprovidebasiceyecareservices.Thegoalsofthecurrentworkaretodesignaninstrumentcapableofdiagnosingrefractiveerrorwithin+/-0.50DforlessthanUS$20.TheSlidingOptometerwasdevelopedforUS$10andwasdesignedsuchthatuserscouldself-determinetheirrefractiveerror.Clinicaltestingwasperformedtomeasuretheaccuracyandprecisionoftheinstrument.Threerefractiveerrormeasurementswerecollectedfromeacheyeof25subjectsusingtheSlidingOptometer.Measurementswerealsocollectedbyapracticingoptometristusingacombinationofsubjectiveandobjectiverefractionmethods.Meanvalueswerecalculatedfromeachthree-measurementsampleandcomparedwiththesphericalequivalentvalueobtainedbytheoptometrist.Theabsolutemeasurementerrorwas1.15D,whichfellshortofthequalitygoal.Errorbiasedinthemyopicdirectionbyapproximately1.00Dformyopiccasesandbiasedapproximately1.00Dinthehyperopicdirectionforhyperopiccases.Weconcludedthattheerrorwaslikelyduetolensmisalignmentandaccommodationratherthanimpropercalibration.Wesuggestimprovingthemanufacturingprocessanddesigntoensureproperlensalignment.Alternativemethodsoffoggingwillalsobeexploredtopreventaccommodation.Theaveragemeasurementaccuracyimproved29%fromthefirstmeasurementtothethird.Weconcludedthatalargerdatasampleshouldberecordedpereyeinordertoobtainvalidprecisionstatistics.Afuturestudyincorporatingtheabovesuggestionsandagreatersubjectsamplesizewouldprovidefurtherinsightintoerrortrends,leadingtoaccuracyimprovementwithfurtherdesigniterations.Overall,weconcludethatfurtherstudyoftheSlidingOptometershouldbeconductedasitshowspromiseasaviableoptionforlow-cost,easy-to-userefraction. 1.Introduction

TheWorldHealthOrganizationestimates703millioncasesofvisualimpairmentduetouncorrectedrefractiveerrorexistworldwide[1].About90%ofthevisuallyimpairedliveinlow-resourcesettings,commonlyreferredtoasthedevelopingworld[2].Uncorrectedrefractiveerrorsaretheleadingcauseofvisualimpairment,whichmayresultinproductivitylossifsevere[3].In2009,theWorldHealthOrganizationestimatedthattheglobaleconomicproductivitylossduetouncorrectedrefractiveerrorsrangedfromUS$121billiontoUS$424billion[4].Eyeglassesareacommontreatmentoptionforrefractiveerror.Ifaccessibleinlow-resourcesettings,availabilityofeyeglassescouldresultinlocalandglobaleconomicgrowthaswellassocialempowermentamongthepopulation.

Refractiveerroristypicallydiagnosedusingacombinationofobjectiveandsubjectivemethods.Objectiverefractionisusedasabaselinemeasurementforrefinementbysubjectivemethods.Objectiverefractionmethodsofretinoscopyandautorefractionrelyonoptometricexpertiseandautomatedequipment,respectively.Subjectiverefractioniscommonlyperformedusingaphoropterortriallensset.Bothobjectiveandsubjectrefractionarewidelyunavailableinlow-resourcesettingsduetothehighcostofinstrumentsandexpertise.

Theavailabilityofalow-cost,easy-to-userefractioninstrumentwouldprovidegeneralhealthclinicstheabilitytoaddrefractiveerrorscreeningtotheirlistofcurrentservices.Ifarefractiveerrorisidentified,thecliniccouldreferpatientstothenearesteyeglassesdispensary.Asadisruptiveinnovation,alow-costrefractioninstrumentprovideshealthclinicstheabilitytoofferapreviouslynonexistenteyecareservice.

Effortshavebeenestablishedtodeveloplow-cost,easy-to-usesubjectiverefractioninstruments.Subjectiverefractioninstrumentshavebeenpreferredoverobjectiveinstrumentsastheyarehistoricallylesscomplexsystemsandcanberedesignedaffordability.OnesuchdeviceistheGood-Lite®I-test™VisionScreener,ahand-heldphoropterusedtomeasurerefractiveerrorwitharangeof-4.00diopter(D)to+4.00Dinincrementsof0.50D[5].TheVisionFinderisaphoropter-basedvision-screeningprototypedevelopedatUCDavisforanestimatedUS$80,makingittheleastexpensiveinstrumentindevelopment[6].TheFOCOMETERisanoptometer-basedinstrument,whichisnotlimitedtodiscretemeasurementstepsandutilizesfewlensestofunction[7].Eachofthesesolutionsextendspossibilitiesforeyecareaccessinlow-resourcesettings.Atanorderofmagnitudelessthanahandheldautorefractor,theVisionFinderisthemostaffordableoption[8].However,thusfarthesesolutionshaveyettoobtainscaleanddistribution.Couldaneasy-to-usesubjectiverefractioninstrumentbedevelopedforanorderofmagnitudelessthancurrentsolutions?

ThispaperdescribesthedesignandperformanceoftheSlidingOptometer,asubjectiverefractiveprototypedevelopedforglobaleyecareaccessinlow-resourcesettings.Designoutlinesthedesignrequirements,designapproach,operationalprinciple,anddesignembodimentoftheSlidingOptometer.Thedesignwasrootedin

historicalresearchtoestablishafunctional,inexpensiveprototype.Twosignificantdesigniterationswerecompletedtoimproveusabilityandreduceusererror.Aftertheinstrumentwasrefined,emphasiswasplacedoninteractiondesigntocreateaconcise,accuratediagnosisprocess.Methodologydescribesa25subject,50-eyetrialperformedtoevaluatetheaccuracyandperformanceoftheinstrumentcomparedtoobjectivemethods.ThestatisticalmethodsusedtoanalyzetherefractiveerrormeasurementsarepresentedinDataAnalysis.AsummaryoftherefractiveerrormeasurementsandthestatisticalresultsarepresentedinResults.Adiscussionofresults,generaldeductions,andplansforfutureworkareincludedinConclusions.

2.Design 2.1DesignRequirements KochandCaradonnaidentifythreedesignprinciplesascommonamongsuccessfuldevelopmentprojects:affordability,deskilling,andquality[9].Affordabilitypermitsaproductorservicetobeaccessibletopopulationsinlow-resourcesettingswhereeconomicbuyingpowerislow.Deskillingrendersaproductorserviceusabletotheintendedpopulationwithoutthenecessityofspecializedknowledgeorskill,whichmaybeunavailableamongthepopulation.Qualityensuresthattheproductorservicedeliversvaluetotheend-userdespitetheaffordablecost[9]. TheprimaryfunctionalgoalwastodesignasubjectiverefractioninstrumentforlessthanUS$20thatwouldallowuserstoself-determinesphericalrefractiveerrorwithin+/-0.50Dafterminimalinstruction.ThetargetpricefortheprototypewassettoUS$20,whichisanorderofmagnitudelessexpensivethanthecomparableFOCOMETER[10].Suchalowtargetpriceforproductdevelopmentforcedamindsettodesignforextreme-affordabilityinsystemcomplexityandmaterialselection.Productdesignersoftenhidecomplexitybydesigningitintotheproductinordertoincreaseusability.Inthecaseofthisproject,complexitywastobehiddentothepointuserscouldself-determinetheirrefractiveerrorwithouttheneedofcostlyexpertise.Muchconcernwasplacedontheusererrorinvolvedinaself-determinedsubjectiverefractionmeasurement.Thegoalwastominimizetheusererrorthroughcarefulinteractiondesign.TheWorldHealthOrganizationsuggeststhatrefractiveprecisioncanbesacrificedforwidescaleimplementationbyutilizingsphericallensesinstepsof0.50Dor1.00Dforvisioncorrection[11].Fromthisrecommendation,wededucethataninstrumentof+/-0.50Disacceptableforprovidingeyecareaccessatscaleinlow-resourcesettings.2.2DesignApproach

Wesoughtanexistinginstrumentdesignorlateraltechnologyasafoundationforthedesignasaleanalternativetofront-enddevelopment.Theredesignofanexisting,provensolutionforlow-resourcesettingsprimarilyrequireddesignforaffordability.Onceaworkingsolutionwasdevelopedatanaccessiblecost,itwasadaptedforusabilityandquality.Thisleandesignmethodologywasconsideredfromthefirstminimumviableprototypethroughthecurrentdesign.

Pastandpresentrefractioninstrumentswerereviewedfortheirbenefitstowardsachievingthedesignrequirements.Overtime,subjectiverefractioninstrumentdesignhasincreasedincomplexity.Older,subjectivetechnologiessuchasthephoropterandoptometerwerepreferableastheywerepurelymechanicalsystems.Mechanicalsystemsareoptimalforaffordableredesignassystemcomplexityandmaterialselectioncanbeleveragedforcostreduction.Theoptometerwasselectedasastartingpointforthedesign,inplaceofthephoropter,asitiscapableofalargediagnosticrangeusingonlytwolenses,comparedtothelargenumberoflensesrequiredbythephoropter.

2.3OperationalPrinciple

TheoperationalprincipleoftheoptometerwasleveragedforthedesignoftheSlidingOptometer.Theoptometerisatwo-lensopticalsystem,whichcontainsaconverginganddiverginglens.Theequivalentpowerofthetwo-lenssystemisvariedbyadjustingthedistancebetweenthelenses.Thisequivalentpoweriscalibratedtoarefractiveerrorscalelocatedontheoptometer.

Lensesmanipulatelightthroughthephysicalmodeofrefraction.Converginglensesfocuseslighttotheback-sidefocalpointofthelens.Diverginglenseshavetheoppositeeffect,refractinglightawayfromthefront-sidefocal

pointofthelens.Refractioncanbegraphicallydepictedusingraytracediagrams.TheraytracediagramsforconverginganddiverginglensesareshowninFigure1.

Figure1.Raytracediagramforconverginglens(top)anddiverginglens(bottom).

Araytraceprovidesausefulillustrationoftheobject-imagerelationship,butdoesnotyieldquantitativeresults.Forthinlenses,therelationshipbetweenfocallength(f),objectdistance(s),andimagedistance(s’)isdefinedbyEquation1.Thislensequationappliestomultiplelenssystems.Foracombinationoftwolenses,thelensequationisappliedtothefirstlenstoobtainanimage,whichisusedastheobjectforthesecondlens.Equation2definestherelationshipbetweenfocallengthofthefirstlens(f1),objectdistanceofthefirstlens(s1),andimagedistanceofthefirstlens(s’1).Theimagedistanceoffirstlensistheobjectdistanceofthesecondlens(s2).Therelationshipmustaccountfortheseparationofthelenses(d),whichisdefinedinEquation3.Equation4definestherelationshipbetweenthefocallengthofthesecondlens(f2),objectdistanceofthesecondlens(s2),andtheimagedistanceofthesecondlens(s’2).Thefocallengthofthesecondlensisexpressedasafunctionofthelensseparation,focallengthofthefirstlens,objectdistanceofthefirstlens,andimagedistanceinthesecondlensinEquation5.Araytraceforaconverging-diverginglenscombinationisshowninFigure2.

(Eq.1)1 𝑓 = 1 𝑠 + 1 𝑠′(Eq.2)1 𝑓! = 1 𝑠! + 1 𝑠!! (Eq.3)𝑠! = 𝑑 − 𝑠!! (Eq.4)1 𝑓! = 1 𝑠! + 1 𝑠!!

(Eq.5)1 𝑓! = 𝑑 − !!!!! !!!

!!

+ 1 𝑠!!

Figure2.Raytracediagramofconverging-diverginglenscombination.

Visioncorrectionisanapplicationofthetwo-lenssystem.Thetworefractiveerrorconditionscorrectablewithsingle-visionsphericallensesaremyopiaandhyperopia.Forpropervision,knownasemmetropia,thelensoftheeyemustfocusimagesontheretina.Myopia,commonlyknowasnearsightedness,isaconditioninwhichthelensoftheeyefocusesimagesofdistantobjectsinfrontoftheretina.Amyopiceyehasafarpoint,whichisthefurthestdistancethatanimagecanbefocused.Myopiaiscorrectedbyplacingadiverginglensinfrontoftheeye,whichcreatesamultiplelenssystemtoplacetheobjectonthefarpointandimageontheretina.Hyperopia,commonlyknownasfarsightedness,istheoppositecaseinwhichimagesarefocusedbehindtheretina.Ahyperopiceyehasnearpoint,whichisthenearestdistancethatanimagecanbefocused.Hyperopiaiscorrectedwithaconverginglens,whichplacestheobjectonthenearpoint.Theinformaltermfarsightednesshasledtoamisconceptionthatfarsightedpeoplehaveexcellentdistancevision,wheniffactsignificanthyperopiamayalsocausedistancevisionloss[12].TheraytracediagramsofmyopiaandhyperopiaareshowninFigure3.

Figure3.Raytracediagramofanemmetropiceye(top),hyperopiceye(middle),andmyopiceye(bottom).

Theoptometerisusedtodeterminetherequiredrefractiveerrorcorrection.Theequivalentfocallengthoftheoptometerisdisplacedwithrespecttotheeyeuntiltheimagebecomesalignedwiththefarornearpointoftheeye.Adjustingthedistancebetweentheconverginganddiverginglenseschangestheequivalentfocallengthofthesystem.Thisisasubjectiverefractionprocess,asthepatientmustidentifythepointofclarity.Toquantifyapatient’srefractiveerrorcorrection,thelensequationisappliedtothetwo-lenssystemoftheoptometershowninFigure4.Intheoptometer,theconverginglensisplacednearesttotheobjectandisdesignatedtheobjectivelens.Thediverginglensisplacednearesttotheeyeandisdesignatedtheocularlens.Invisioncorrection,lensesarecommonlycharacterizedbypower(P)ratherthanfocallength.PowerisdefinedinEquation6andrepresentedbyunitsofdiopters,theinverseoffocallengthinmeters.ByapplyingEquation5intermsofocularlenspower(Poc),objectivelenspower(Pobj),lensseparation(d),andrefractiveerrorcorrectionpower(Pre)weobtainEquation7.Thisexpressionisrewrittenasafunctionofocularpower,objectivepower,andrefractivecorrectionpowerinEquation8.(Eq.6)𝑃 = 1 𝑓

(Eq.7)𝑃!" = 𝑃!" − 𝑑 − !!!"#

!!

(Eq.8)𝑑 = 1 𝑃!"# + (𝑃!" − 𝑃!")!!

2.4DesignEmbodiment2.4.1DesignIteration1

Theoptimalconverging-diverginglenscombinationforuseintheSlidingOptometerdesignwasdeterminedthroughparametricanalysis.Apreliminarysetofconverging-diverginglenscombinationsweredeterminedthroughparametricanalysisandconstraintcriteria.LensseparationwascalculatedusingEquation8forocularlensesrangingfrom-1.00Dto-16.00Dandobjectivelensesrangingfrom1.00Dto16.00Dforthecaseofarefractivecorrectionpowerof0.00D.Lenscombinationsthatresultedinalensseparationbetween0.10meter(m)and0.20mwereacceptedforfurtherinspection.Theupperlimitof0.20mwasestablishedbasedonergonomics,consideringusersshouldnothavetoextendtheirarmbeyondthatdistance.Thelowerlimitof0.10mwasbasedoffofaconsiderationforresolutionofthemeasurement. Aparametricanalysisofrefractiveerrormeasurementresolutionwasconductedtodeterminetheoptimallenscombinationwithinthepreliminaryset.AmeasurementscalewasgeneratedforeachlenscombinationusingEquation8.Lenscombinationsthatextendlessthan0.20mat-8.00Dwereacceptedforfurtherinspection.Thelimitof0.20Dfollowsasanergonomicsrequirementfromabove,whilethemyopicrangerequirementof-8.00Dwasaddedtoensurethedevicecouldscreenawiderangeofcasesfrom-8.00Dto+8.00D.Theoptimallenspairwasselectedbycomparingtheresultsoftheparametricanalyses.Aconverginglensof4.00Danddiverginglensof-12.00Dwerechosenastheoptimalpair.Thiscombinationmaximizesthesizeofthemeasurementscaledivisionswithintheconstraintsdescribedabove.ThescalegeneratedfromthislenscombinationisshownbelowinFigure4[13].

Figure4.SlidingOptometermeasurementscale.

TheSlidingOptometerisaredesignofthe19thcenturyoptometeroptimizedforaffordability,deskilling,andquality.Materialselectionandsystemcomplexitywereleveragedforcostsavings.Theoriginaloptometerdesignincludedmetalcomponents,glasslenses,andprecisionmechanisms[14].Replacingmetalandglasswithplasticswherepossiblereducedcost.Polycarbonatelenseswereselectedinplaceoftheoriginalglasslensesandpolyvinyl

chloride(PVC)pipereplacedtheoriginalmetalhousing.Lenseswereinstalledinsidethepipewithhigh-strengthadhesive.The19thcenturydesignutilizedarackandpinionforprecisioncontroloverthelensseparationdistance.Thismechanismwasreplacedbyalinearbushingconstructedfromlayeredstripsofvinyltape.Themeasurementscalewasprintedonpaperandadheredtotheexterioroftheinnertubeusingcleartape.AlabeleddiagramoftheSlidingOptometerfirstiterationprototypeisshowninFigure5.

Figure5.DiagramoftheSlidingOptometerfirstiterationprototype.

Thefirstiterationprototypeperformancewasevaluatedinthelaboratoryandfield.Thegeneralsetupincludedinbothsituationsincludedtheoptometerattachedtoatripod,placed6mfromaSnellenchart.Userswereinstructedtoviewthechartthoughthedeviceandadjusttheinnertubeuntilthechartbecamemostclear.Wefoundthatsubjectsexperienceddifficultywithinterpretinginstructionsforlocatingtheclearpoint.Wealsofoundthatyoungsubjectswouldoftenover-diagnosethemselves,passingtheinitialpointofclaritybytheresponseofaccommodation,whichiseye’sabilitytoremainfocusedonanobjectasitischangingdistance.Wedesiredtoimprovetheusabilityandreducetheusererrorwithfurtherdesignimprovements.Specifically,wesoughttoemphasizethepointofclarityfortheuserthroughdesign,therebyreducingthepossibilityforusererror.2.4.2DesignIteration2

SimilartothebeginningofSlidingOptometerdesignprocess,weperformedsignificantresearchintoexistingsolutionsandlateraltechnologies.Theautorefractorwasfavorableforinspectionduetoitsobjectivityandautomatedprocesses.TheautorefractorfundamentallyoperatesusingtheScheinerprinciple[15].ThisprinciplewasderivedfromtheScheinerdiskapparatus,whichsplitslightintotworaysbeforeenteringthepupil.Similartotheraytracesshownabove,thetworaysfocusinfrontorbehindtheretinaifarefractiveerrorexists.Theserayscanbefocusedontheretinabyalteringthefocalpointwithaconvergingordiverginglens.Theautorefractorautomatesthisprocessbyusinguniquelightfrequencies,amotorizedlensarray,andadetectortodeterminethepointatwhichthelightisfocusedontheretina[16].

TheScheinerprinciplewasleveragedtoemphasizethepointofclarityforsubjectsusingtheSlidingOptometer.InoneformofaScheinerdisk,pinholesseparatetheimageintotwodistinctimageswhenthecorrectivepowerisgreaterthanorlessthantherequiredcorrectivepower.Thetwoimagesconvergetooneimage,indicatingthattheraysarefocusedontheretina,onlywhentherequiredcorrectivepowerisobtained.Adiskcontainingtwosmallpinholeswasaddedneartheocularlens.Thepinholesizeandspacingwasbasedonthedesignofpinholeoccluderglasses,whichwere1.5millimeter(mm)indiameterwith3.5mmcenter-to-centerspacing.Severalvariationsofspacingandholesizewereanalyzedtofindwhichmaximizedtheeffect.Thechosenpinholeswereof1.0mmdiameterwith1.5mmcenter-to-centerspacing.WelaterfoundthattheScheinerprinciplehadbeenappliedinexistingoptometerdesigns,butnotinthemannerstatedabove[17].AlabeledpictureoftheSlidingOptometerseconditerationprototypeisshowninFigure6.PhotosofthefrontandendviewoftheseconditerationprototypeareshowninFigure7.

Figure6.DiagramoftheSlidingOptometerseconditerationprototype.

Figure7.Frontview(left)andendview(right)oftheSlidingOptometerseconditerationprototypemountedtoatripod.

Severalsmallinteractiondesignfeatureswereaddedtoimproveease-of-useandreduceusererror.Anendcapwasaddedtocenterthesubject’seyeonthedoublepinholeandprovideaconsistentcontactpointfortheface.Variousgraphicsweretestedtodetermineanoptimaltargetforthedouble-pinholeconfiguration.AcollectionofthesegraphicsisshowninFigure8,withthefinaltargetshowninthebottomleftcorner.Thesmiley-faceisanapproachablegraphicwithbold,multi-directionalfeaturesthatenhancetheeffectoftheScheinerprinciple.Forcingoneeyeshutmaycauseeyestrainandmeasurementerror,soinexpensiveocculderglasseswereaddedtothescreeningprocess.Theinstructionsetwasalteredtopreventtheeffectsofaccommodationnotedfromtesting.Subjectsweretobeginwiththeinnertubefullyextendedandretracttheinnertubeinwardslowly,stoppingatthelocationinwhichthedoubledorblurredimagesconverge.Thischangeofinstructionwastopreventsubjectsfromaccommodatinginthemyopicdirection.

Figure8.Collectionoftargetprototypes.Selectedtargetislocatedinlowerleftcorneroftheimage.

3.Methodology

TheaccuracyandprecisionoftheSlidingOptometerwasdeterminedthroughclinicalandstatisticalmethods.TheBucknellUniversityInstitutionalReviewBoardapprovedthecourseofresearchandethicalpracticeinvolvedintheclinicalstudy.PotentialsubjectswereinformedofthestudyandrecruitedatLipskiEyeCenterinLewisburg,PA.Informedconsentwasobtainedfor25subjects.Therefractiveerrorofeachsubject’sleftandrighteyewasself-determinedusingtheSlidingOptometer.Apracticingoptometristcollectedrefractiveerrormeasurementsusingacombinationofobjectiveandsubjectivemethods.

3.1ClinicalTesting

ThemeasurementsobtainedbytheoptometristwereconsideredthecontrolmeasurementsforwhichtheSlidingOptometermeasurementswouldbecompared.Theoptometristobtainedabase-linemeasurementusingautorefractionandretinoscopyandverifiedtheresultsusingaphoropterand/ortriallenses.Theoptometristreportedasphericalpowerofcorrection,cylindricalpowerofcorrection,andaxisofastigmatismforeacheye.

AseparateexaminerfacilitatedrefractiveerrortestingusingtheSlidingOptometer.Theexaminerprovidedinstructiontosubjectswhomthenself-determinedtheirrefractiveerrorusingtheinstrument.TheSlidingOptometerwasplacedonatripodforstabilityandvariableheightadjustment.Thetargetwasplacedonawell-litwallateyelevelatahorizontaldistanceof6metersfromtheinstrument.Subjectswereinstructedhowtooperatetheinstrumentandprovidedanddescribedtheappearanceofanout-of-focusandin-focusimage.Theexamineralsodemonstratedtheprocessforeachsubject.Subjectswereprovidedoccluderglassestocovertheoppositeeyeduringtesting.Theoptometerwasadjustedtotheeyelevelofeachsubject.Subjectswereaskedmakecontactwiththeendcapwhenlookingthroughthedevice.Eachsubjectwasprovidedapproximately1minutetofamiliarizehimorherselfwiththeprocess.Whenthesubjectindicatedtheywerecomfortablewiththeprocess,theexaminerfullyextendedtheoculartubeinthehyperopicdirectionofthescale.Subjectswereaskedtoretracttheoculartubeuntilthedistorted,doubleimagefirstbecameaclear,singleimage.Thisprocesswasrepeatedthreetimesforeacheye,whichyieldedsixsphericalequivalentmeasurementsforeachpatient.Thefulldiagnosticprocedurerequiredlessthan5minutespersubject.3.2DataAnalysis 3.2.1InstrumentPrecision Thestandarddeviationofthethree-measurementsampleobtainedusingtheSlidingOptometerwascalculatedfortheleftandrighteyeofeachsubject.Theinstrumentprecisionwasobtainedbycalculatedthemeanofthe50standarddeviationvalues.3.2.2InstrumentAccuracy InstrumentaccuracywasobtainedbycomparingSlidingOptometermeasurementswithcontrolmeasurements.Themeanofthethree-measurementsamplewascalculatedfortheleftandrighteyeofeachsubject.Thesphericalequivalent(SE)ofeachcontrolmeasurementwascalculatedasafunctionofeachsphericalpowerofcorrection(S)andcylindricalpowerofcorrection(C)usingEquation9.Theerror,accountingforthesignofthemeasurement,oftheoptometermeanmeasurementcomparedtothecontrolsphericalequivalentwascomputedforeacheye.Theabsoluteerror,neglectingthesignofthemeasurement,oftheoptometermeanmeasurementcomparedtothecontrolsphericalequivalentwasalsocomputedforeacheye.Theinstrumentaccuracywasobtainedbycalculatingthemeanoftheabsoluteerrorresults.(Eq.9)𝑆𝐸 = 𝑆 + 0.5𝐶3.2.3Decreaseinerrorwithuse Asthepotentialusererrorishighintheself-determinedsubjectivemeasurement,thisanalysiswasperformedtodetermineifusererrordecreaseswithincreaseduse.Specifically,apercentchangeinaccuracywascalculatedbycomparingtheabsoluteerrorofthefirstandthirdsamples.4.Results

Therefractiveerrorcontrolmeasurementsrangedbetween-8.50Dand+4.00Dinthesphericalpowerandupto-1.50Dinthecylindricalpower.Insubjectswithastigmatism,thecylindricalpowerwaslessthanone-fourthofthesphericalpower.Thesphericalequivalentcontrolvaluesrangedbetween-8.25Dand+3.25D.Thesphericalequivalentwaslessthan+/-1.00Dinbotheyesforthreesubjects.Outoftheremaining22subjects,16weremyopicand5werehyperopicinbotheyes.Onesubjecthadhyperopiainoneeyeandmyopiaintheother.

Themeanoftheself-determinedrefractiveerrormeasurementsrangedbetween-7.25Dand+3.00D.Thestandarddeviationofthethree-measurementsamplesrangedfrom0.00Dto1.76D.Themeanstandarddeviationofthethree-measurementsampleswas0.50D.

Figure9.MeanSlidingOptometermeasurementsplottedasafunctionofsphericalequivalentcontrolmeasurements.

Themeanerrorbetweentheself-determinedmeasurementmeanandthecontrolsphericalequivalentmeasurementwas0.32D,withahyperopicmeanerrorof1.31Dandamyopicmeanerrorof–0.94D.Themeanabsoluteerrorwas1.15D.Themeanabsoluteerrorfromthefirstofthethreemeasurementwas1.38D.Themeanabsoluteerrorfromthelastofthethreemeasurementswas1.07D.Themeanabsoluteerrorwasreducedby29%fromthefirsttothethirdmeasurement.Thethirdmeasurementwasalso7%moreaccuratethanthree-measurementmeanonaverage.5.Discussion

Adiscrepancyexistsbetweenthemeanerrorandtheabsoluteerrorinthemeasurements.Measurementsofhyperopiceyesexhibitameanerrorof1.31Dwhilemyopiceyemeasurementsexhibitanerrorof-0.94D.Sincetheresultsarenotbiastoonedirection,wecannotconcludethattheerrorissimplyduetoimpropercalibration.Otherfactorsthatmayhavecontributedtotheerrorincludelensmisalignmentandaccommodation[15].Manufacturingmethodsanddesignmaybeimprovedinfutureiterationstoensurethatthelensesareproperlyalignedduringinstallation.Additionally,furtherstudymaybeconductedintopreventionofaccommodationusingfogging.

Bycalculatingthestandarddeviationbetweenconsecutivemeasurements,theprecisionoftheSlidingOptometerwasdeterminedtobe+/-0.50D.Theresultsshowedthattheinstrumentaccuracyimprovedby29%onaveragefromthefirsttothethirdmeasurement.Theseresultssuggestthattheaccuracymayimprovefurtherbyobtainingmorethanthreemeasurementspereye.Themeasurementprecisionof+/-0.50Dislikelyaninvalidcharacterizationastheresultsindicatethatthatabsoluteerrordecreaseswithconsecutivemeasurements.Avalidprecisionvaluecouldlikelybeobtainedusingasampleoftenormoremeasurementspereye.

6.Conclusions

Thegoalwastodesignanaffordabledevicetoallowsubjectstoself-determinerefractiveerrorwithin+/-0.50D.Theresultsindicatethatthequalitygoalof+/-0.50Dwasnotachievedwiththecurrentprototype.ThedevicewasbuiltforatotalrawmaterialcostofUS$10,whichislessthanhalfoftheoriginalgoalofUS$20.All25subjectsself-determinedtheirrefractiveerrorusingtheSlidingOptometer.Althoughthequalitygoalwasnotachieved,the

SlidingOptometershowspromiseforfurtherdevelopmentasanextremelyaffordablesubjectiverefractioninstrument.Uponfurtherrefinement,applicationoftheSlidingOptometerseemspracticalinlow-resourcesettingswheretheneedforeyecareisgreatbutaccesstomedicalexpertiseandfundingislow.

TheSlidingOptometermaybeappliedinvarioussettingssuchasschools,hospitals,healthclinics,andprivatebusinesses.Theinstrumentmayserveasaneffectivescreeningtoolforschoolsandclinicsaroundtheglobe.Ascreeningtoolwouldprovideschoolstheabilitytoself-assesstherefractivehealthofthestudentpopulation,withouttheneedofoutsideequipmentandclinicians.Healthcliniciansmayfindtheportableinstrumentmosteffectiveforremotescreening,marketing,andreferrals.Ifcoupledwithaffordablelenses,frames,andedgingequipment,theSlidingOptometermayalsoserveasadiagnosticinstrumentinanall-inclusiverefractivecarekit.Suchakitcouldbeprovidedwithtrainingtocommunityentrepreneursorclinicianswhowishtooffereyecareservices.Weplantotestthefeasiblyofsucharefractivecarekitinthenearfuture.Inamulti-monthpilotstudy,aNicaraguanclinicwillbeequippedwiththekitandtrainingnecessarytoproviderefractivecaretotheircurrentservices.Thequalityofcareandeconomicfeasibilitywillbeevaluatedtodeterminehowthekitmightbestbeusedinthefutureasasustainablebusiness.

TheprocessusedtodesigntheSlidingOptometermayofferdesignersandeducatorsanewperspectiveondesignforlow-resourceenvironments.TodesigntheSlidingOptometer,wesearchedexistingdesignsandexpiredpatentsinsearchforafunctionaldesignthatfitourrequirements.Theeaseofusewasimprovedbyincorporatingthesuccessfulattributesoflateraltechnologies.Theendproductwasdeliveredatalowcostbyutilizinginexpensivematerialsandlimitingproductcomplexity.Inthefutureweplantodefineasetofprinciplestocharacterizethisprocessinamannersuchthatitcanberepeatedlypracticedandtaught.

Thesignificanceofthisprojecttothefieldofdevelopmentengineeringisbothintheproductandthedesignprocess.Thedeviceandtheprocessmayopendoorstoprovideaccesstopreviouslyunobtainableproductsandservicesinthedevelopingworld.Additionally,theymayserveasafoundationforfurtherresearchintothedesignofquality,low-cost,andeasy-to-userefractivecareinstruments,healthcareinstruments,andproductsforlow-resourceenvironments.

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