Sources of error in clinical measurement of the amplitude of accommodation

City, University of London Institutional Repository

Citation

:

Burns, D. H., Allen, P. M., Edgar, D. F. ORCID: 0000-0001-9004-264X and

Evans, B. J. W. (2019). Sources of error in clinical measurement of the amplitude of

accommodation. Journal of Optometry, doi: 10.1016/j.optom.2019.05.002

This is the published version of the paper.

This version of the publication may differ from the final published

version.

Permanent repository link:

http://openaccess.city.ac.uk/id/eprint/23065/

Link to published version

:

http://dx.doi.org/10.1016/j.optom.2019.05.002

Copyright and reuse:

City Research Online aims to make research

outputs of City, University of London available to a wider audience.

Copyright and Moral Rights remain with the author(s) and/or copyright

holders. URLs from City Research Online may be freely distributed and

linked to.

www.journalofoptometry.org

REVIEW

Sources

of

error

in

clinical

measurement

of

the

amplitude

of

accommodation

David

H.

Burns

_,

_Peter

_M.

_Allen

_,

_David

_F.

_Edgar

_,

_Bruce

_J.W.

_Evans

a_{119HighRoad,LondonN28AG,UK}

b_{InstituteofOptometry,56-62NewingtonCauseway,LondonSE16DS,UK}

c_{SchoolofHealthandSocialCare,LondonSouthBankUniversity,103BoroughRoad,LondonSE10AA,UK}

d_{DepartmentofVisionandHearingSciences&VisionandEyeResearchUnit,AngliaRuskinUniversity,EastRoad,CambridgeCB1}

1PT,UK

e_{DivisionofOptometryandVisualScience,SchoolofHealthSciences,City,UniversityofLondon,NorthamptonSquare,London}

EC1V0HB,UK

KEYWORDS Amplitudeof accommodation; Accommodative amplitude;

Measurementerror; Clinical;

Push-up

Abstract Measurementoftheamplitudeofaccommodationisestablishedasaprocedureina

routineoptometriceyeexamination.However,clinicalmethodsofmeasurementofthisbasic optical function haveseveralsourcesoferror.Theyarenumerous anddiverse,andinclude depthoffocus,reactiontime,instrumentdesign,specificationofthemeasurementend-point, specificationofthereferencepointofmeasurement,measurementconditions,consideration ofrefractiveerror,andpsychologicalfactors.Severalofthesesourcesofinaccuracyare com-posedofmultiplesub-sources,andmanyofthesub-sourcesinfluencethecommonmethodsof measurementofamplitudeofaccommodation.Considerationofthesesourcesofmeasurement errorcastsdoubtonthereliabilityoftheresultsofmeasurement,onthevalidityofestablished normativevaluesthathavebeenproducedusingthesemethods,andonthevalueofreportsof theresultsofsurgerydesignedtorestoreaccommodation.Clinicianscanreducetheeffectsof someofthesourcesoferrorbymodifyingtechniquesofmeasurementwithexistingmethods, butanewmethodmayfurtherimproveaccuracy.

©2019SpanishGeneralCouncilofOptometry.PublishedbyElsevierEspa˜na,S.L.U.Thisisan openaccessarticleundertheCCBY-NC-NDlicense( http://creativecommons.org/licenses/by-nc-nd/4.0/).

PALABRASCLAVE Amplitudde acomodación; Amplitud acomodativa;

Fuentesdeerrorenlamediciónclínicadelaamplituddeacomodación

Resumen Lamedicióndela amplituddeacomodaciónsehaestablecido comoun

proced-imientodelexamenoptométricoocularrutinario.Sinembargo,losmétodosclínicosdemedición deestafunciónópticabásicatienendiversasfuentesdeerror.Estassonnumerosasydiversas, eincluyenprofundidaddefoco,tiempodereacción,dise˜nodelinstrumento,especificacióndel puntofinaldelamedición,especificacióndelpuntodereferenciadelamedición,condiciones

∗_{Correspondingauthorat:119HighRoad,LondonN28AG,UK.}

E-mailaddress:[email protected](D.H.Burns).

https://doi.org/10.1016/j.optom.2019.05.002

2 D.H.Burnsetal.

Errordemedición; Clínico;

Push-up

delamedición, consideracióndelerrorrefractivo,y factorespsicológicos. Algunasdeestas fuentesdeimprecisiónsecomponendemúltiplessub-fuentes,muchasdelascualesinfluyenen losmétodoscomunesdemedicióndelaamplituddeacomodación.Laconsideracióndeestas fuentesdeerrorenlamediciónplanteadudassobrela fiabilidaddelosresultadosdedicha medición, lavalidezdelosvalores normativosestablecidosquesehanproducidoutilizando estosmétodos,yelvalordelosinformessobreresultadosdelacirugíadise˜nadapararestablecer la acomodación.Los clínicospueden reducirlosefectos dealgunasde lasfuentesde error, modificandolastécnicasdemediciónconayudadelosmétodosexistentes,aunqueeldesarrollo deunnuevométodopodríamejorarlaprecisión.

©2019SpanishGeneralCouncilofOptometry.PublicadoporElsevierEspa˜na,S.L.U.Esteesun art´ıculoOpenAccessbajolalicenciaCCBY-NC-ND( http://creativecommons.org/licenses/by-nc-nd/4.0/).

Background

Amplitude of accommodation (AoA) is an eye’s maximum rangeoffocussingpowerataparticulartime.Itisexpressed indioptres.

In the United Kingdom (UK), AoA is the parameter of accommodationthatismost commonlyassessedclinically. Competencein the measurementof AoA, andin noother aspectof accommodation, is statutorilyrequiredof every aspiringUKoptometrist1_{andmeasurementofAoAisa}

rec-ommendedcomponentofaroutineeyeexaminationwhen

‘‘clinicallyappropriate’’.2

‘‘Accommodationrule’’isincludedinthelistoftwenty

principalitems of clinical equipmentrequired for routine

eye examinations in the UK.3 _{In North America}

measure-mentofAoAisoneoftheitemsintheSkeffington21-point

routine.4 _{AoAisincludedinthesyllabi oftheWorld}

Coun-cilofOptometry5 _{andEuropeanCouncilof Optometryand}

Optics.6

AreviewoftheclinicalmeasurementofAoAbriefly

men-tionedsourcesoferror.7_{Thepresentreviewdescribesthese}

sourcesof error in moredetail, facilitating better

under-standingoftheaccuracyofcurrentmethods.

TheRAFRuleistheonlydevicemarketedintheUKfor

theclinical measurementof AoA.Itwasfirstdescribed in

1956.8_{ShowninFig.1,itisagraduatedrailjustover0.5m}

inlengthwithahandleatoneend,abifurcationattheother

endtobeheldagainstthepatient’scheekbones,andbearing

avisualtest-object.Thetest-objectdisplayshigh-contrast

black-on-whiteprintinarangeofsizesandcanbeslidalong

therail.

Methods

of

measurement

FourmethodsofmeasuringAoAareencounteredinclinical

practiceanddescribedintheliterature.Theyarepush-up,

push-down,minuslens,andretinoscopy,andaredescribed

below.

Push-up

Many authors assert that push-up is the most prevalent

method.9---11 _{Inthepush-upmethodtheexaminerinstructs}

thepatienttoreportwhenatest-object becomesblurred

asitisbroughtgraduallynearertotheeye.Deviceswhich

arearulerwithaslidingtest-objectareoftenusedforthis

measurement.TheRAFruleisanexampleofsuchadevice.

Itisusedasfollows.Whenthefirstslightbutsustainedblur

ofthevisualtest-objectisreportedtheexaminernotesthe

positionoftheprintonascalemarkedontherail.Thisscale

shows thedistanceof theprintfromtheeyeandalsothe

AoAasthereciprocal,inmetres,ofthatdistance.Textbooks

ofbasicoptometrygenerallyprovidefullerdescriptions12---15

oftheuseoftheRAFRule,differingmoderatelyfromeach

otherinsomedetailsoftechnique.

Push-down

Thepush-downmethodcanalsousetheRAFRuleandsimilar

devices.The objectismovedawayfromthepatient,from

being toonear for thepatient toresolve, until it can be

seen.

Thismethodparticularlylacksstandardisationof

nomen-clature and of technique. For example, different authors

specify differing end-points. In the earliest description16

of the push-down method the test object is moved away

fromtheeyeuntilthepatientreportswhenitfirstbecomes

‘‘quite clear’’ but in subsequent reports differing

end-pointcriteriawereusedsuchas‘‘sharpandclear’’17 _‘‘just

becomesclear’’18_{‘‘absolutelyclear’’}14_{and‘‘just}

recognis-able’’.15

Namingthemethod,anditsendpointcriterion,presents

someconfusion.Whenthe‘‘justrecognisable’’criterionwas

firstdescribed19 _{thepush-downapproachwasdescribedas}

the ‘‘modifiedpush-up method’’which hasbeen used20,21

inresearchwhereithasbeentermedthe‘‘modified

push-downmethod’’22_{whichresembledthe‘‘modifiedpull-away}

method’’inanotherreport.15_{However,the‘‘modified}

push-downmethod’’inonereport17 _{differedsignificantlytothe}

‘‘modified push-down method’’ in another22 _{and to the}

‘‘modifiedpush-upmethod’’inanother23 _{allofwhichused}

auxiliary fixed-power diverging trial lenses to extend the

Figure1 TheRAFRule.

Minuslens

Intheminuslensmethod24,25_{negativesphericallenspower}

is added to the distance refractive correction until the

patientcannotmaintaintheinitialacuityatapre-set

view-ingdistancewellbeyondtheexpectednearpoint.TheAoA

is given by the maximum power added while the patient

can maintain focus, corrected for the viewing distance’s

vergence.

This method should only be used for monocular

mea-surement and only under monocular conditions. These

limitationsarisebecauseaccommodationandconvergence

worktogetheralthoughthelinkbetweentheiroperationis

notrigid.26,27_{Therefore,theminuslensmethodmayinduce}

more convergence than would be required for the

view-ing distance, causing one eye toover-converge, resulting

indiplopia;or,ifbinocularviewingismaintained,the

pre-settingofconvergencemaylimitaccommodation.However,

unlikethepush-upmethodandsomevariantsofthe

push-downmethod,itonlyrequirestheresolutionofanobject,

andsomaybeeasiertoperform,fortheexaminerandfor

thepatient,thanreportingontheclarityofthetarget.

Retinoscopy

AoA can also be measured using a retinoscope. Although

retinoscopy relies on the clinician’s interpretation of the

retinoscopyreflex,itrequiresnojudgementbythepatient.

ItcanbeusedformeasurementofAoAbystimulating

accom-modationmaximallywhilethepractitionerdeterminesthe

end-point. Several investigators28---31 _{have described the}

techniqueindetail.

This method requirespractitioner skill,judgement and

experience.28,30,32 _{That may explain why its use has}

been reported less often than other methods. The need

to minimise glare from the retinoscope beam in AoA

measurement28,30_{isanotherdifficultywiththismethod.}

Sources

of

measurement

error

Thereareseveraldistinctsourcesoferrorthataffect

cur-rentclinicalmethodsofmeasuringAoA.Theyarelistedin

Table 1 which also shows the methods affected by each

source of error, andare described inmore detail laterin

thispaper.Theiroveralleffectwouldreducethereliability

ofmeasurement.

Depth

of

focus

Thissourceoferrorwasdefined33_{astherangeofanobject’s}

vergence at the eye without any blur being detected. It

is the result of a wide range of factors, some of which,

suchasdiffraction,cannotbeeliminated,andsome,such

aspupildiameter,thatvary.Therefore,thecontributionof

depthoffocustomeasurementofAoAbyanymethodthat

requirestherecognitionofblurcannotbeaccurately

esti-mated.However,areview34_{foundthatitwouldbelikelyto}

exceedanyothersourceoferror.

During measurement of AoA, by most methods that

requiretherecognitionofblur,thesizeoftheretinalimage

ofthevisualtargetcontinuallychanges.Thesizeisinversely

proportionaltothevisualworking-distance,anddecreases

slightlyduringmeasurementbytheminuslensmethod.This

size-change affects the accuracy of the measurement of

AoA,sincetheeye’sdepthoffocusvarieswithretinalimage

size.47

Ithasbeenproposedthatdepthoffocus,unliketheother

sourcesoferror listedin Table1, isboth an inherentand

abeneficial component of accommodation, ratherthan a

sourceof error. An explorationintothe depthof focusof

theaccommodatedeye35_{concludedthat‘‘themainpurpose}

ofaccommodationisnottomaximiseretinalimagequality

buttoformone thatisgoodenough.’’ Itshould

nonethe-lessbeexcludedwhenmeasuringAoAasdepthoffocusand

accommodationareseparatefunctions.

Reaction

time

Reactiontimeisasourceoferrorthatinfluencesmethodsin

whichmeasurementismadewhilethevergenceofthetest

objectchanges.This errorcanbelimited byreducingthe

rateof change,althoughslower ratesofchange makethe

end-pointlessobvioussoitmaybehardertodiscern.

Reaction timeis the sumof four separate components

thatoccurinthefollowingorderwhentestobjectvergence

changes past the point where noticeable blur (or, in the

push-downmethod,eitherclarityorlegibility)firstoccurs.

Thesecomponentsare:

1. thetimetakentodecidethatthevisualobjectappears

blurredorclear

2. then,thetimetakentovocalisethatdecision

3. followingthat,thetimetakentoregisterthatmessage

4. andfinally,thetimetakentostopthemovementofthe

4 D.H.Burnsetal.

Table1 SourcesoferroraffectingtheclinicalmeasurementofAoA.

Sourceoferror Methodofmeasurement

Push-upandpush-down MinusLens Retinoscopy

Depthoffocus Yi Yi N

Reactiontime Ye N N

Displacement (push-downonly)yi N N

Definitionofthereferencepoint ye N N

Definitionoftheend-point Yi y Yi

Monocularorbinocular ye N N

Correctionofrefractiveerror Ye Ye ye

Instrumenterror Yi N e

Examinerbias YI Yi Yi

Anomalousdistancecues N Yi N

Feedbackfromachievement yi N Yi

YmajoreffectyminoreffectNnegligibleeffectiinherenteffecteeffectcanbeeradicated.

Components1and2listedabovedependonthepatient. Components3and4listedabovedependontheexaminer.

Component1,unliketheotherthree,isinfluencedbythe measurementtechnique.Itincreaseslinearlywiththerate ofchange oftest-objectvergencewhenmeasuring accom-modationwiththeminus-lensmethod,andnon-linearlywith therateofchange oftest-object distancewhen measure-mentisonascaleofdistance11_{becausedioptricdemandis}

inverselyproportionaltoviewingdistance.Attypical

max-imumaccommodation levels, moving the test-object one

centimetrerepresentslessthan 0.1D for aforty-year-old

butabout1Dforaten-year-old.

To reduce this error caused by the target being near

tothe eye at the end-point, extra minus lens power can

beaddedinthetrialframewhenmeasuringhigh levelsof

AoA.13,15,17_{Althoughitcanbeexpectedtoreducethe}

reac-tiontimeerror,albeitunsystematically,itwouldintroduce

error due to anomalous distance cues (another source of

error,describedbelow).Furthermore,whenviewingthrough

extra minus spectacle lenses, AoA may be influenced by

refractiveerror.36

Therefore,itwouldbepreferabletomovethetestobject

ataconstantandslowrateofdioptres,ratherthan

centime-tres,persecond.Constantrateofdioptricchange(0.5D/s)

forpush-upmeasurementofAoAhasbeenreported.37 _This

strategywouldspreadreaction-timeerror evenlyoverthe

rangeofresultvaluesbutmaybedifficulttoreliablyachieve

without automation.Researchershave adopted quite

var-ied rates including 0.4cm/s,9 _1cm/s,38 _2cm/s,39 _4cm/s

with participants controlling push-down movement17 _and

5cm/s20,40,41 _{which is so fast that the effect of reaction}

timeonthetestresultcouldexceedone-thirdofthe

high-est reportedvalues. Forexample, if thenear point were

at7.5cm(13.3D)movementcouldstopat5cm(20D).This

may be one reason why researchers from the earliest42

to present times38,39,43 _{obtained particularly high values,}

exceeding20D,withthepush-upmethod.

Thesecondcomponentofreaction-timelistedabovemay

increaseifthepatientfeelsapprehensiveaboutthe

proce-dureandhencereluctanttodeclarethatthetestobjectis

blurred.Itmayalsoincreaseifthepatientisaccustomedto

blur.44

It would appearlikely that components2 and 3 listed

above,ofreaction-time,couldbeeliminatedifthepatient,

insteadoftheexaminer,weretomovethetarget.This

pos-sibilitywasaddressedinonestudy45 _{andnotsupported,as}

thestudyfoundslightlyhigherresultswhentheparticipant

heldthetarget,moresowhenusingpush-upthanwhenusing

push-down.However,thedatawerenotpresentedtoenable

anestimateofthestatisticalsignificanceofthisresult.

Fur-thermore,an advantageof theexaminer,notthepatient,

movingthetargetwouldbetoretainsomestandardisation

ofthespeedofmovement.

Some early investigators41,45,46 _{found lower results for}

AoA with the push-down method than with the push-up

method. Later researchers17,18 _{found similar results with}

the twomethods and speculated that the earlier findings

were dueto thedifferencein reaction timebetween the

push-upandpush-downmethods.Anotherstudy40_found

sim-ilarresultswiththetwomethods,for25participantsaged

10---40years,citingotherstudiesthatfoundthesameeffect,

buttheirpush-downmethodusedtheend-pointcriterionof

just recognisingthe test-object, giving large errordue to

depthoffocusasshownbyearlierresearch.47_Theerrordue

todepthoffocusin push-downtorecognitionwouldhave

tendedtocounterbalancetheerrorduetoreactiontimein

push-up.

Someresearch11,48,49_{adoptedthestrategyofmovingthe}

push-uptestobjectinstepchanges.Thiswouldhave

elimi-natedreaction-timeerrorbecausethetargetwasstationary

duringmeasurement.However,theincreasedtestingtimeof

thisstrategymayhavereduceditsutilityanditsaccuracy.

Displacement

This error is causedby displacement of themoving visual

objectbeyondthe end-point,asfollows.The end-point is

registered when, in the push-downmethod, the observer

detectsthatthetestobject’ssharpnessstopschanging.This

judgementrequirescomparisonofsharpnessatpointsafter

passing the near point, whereas in push-up the observer

seeksforthesharpnesstostartchanging,bycomparingthe

Therefore,theend-pointisdisplacedfurtherfromthenear

pointinpush-downbecausethetest-objectmusttravel

fur-therfromtheend-pointtoestablishthatthereisnofurther

improvementinclarity.

Displacement affectsonlythepush-downmethodusing

theend-point criterionofclarity,causing underestimation

ofAoA.Thedisplacementerrorwouldbeexpectedtooccur

in the minus lens method if the end point was a change

fromblurtoclarity,althoughnotinthemoreusual

proce-durewhenthepatientisaskedtodetectadropinacuity13

Displacementwouldincreasewithalargerreactiontimeof

the patient. Displacement does not appear to have been

addressedintheliterature.

Measurement

conditions

Resultswithanymethodofmeasurementcanbeaffectedby

theconditionsofmeasurement.Therefore,theseconditions

shouldbe specified, andstandardisedif possible.In

mea-suringAoA,thereareseveralaspectsofthe measurement

conditionsthatcaninfluencetheoutcomeandtheseare

dis-cussedbelowusingexamplesfromAoAstudies.There has

beennostandardisationoftheseorothertestconditions.

Definitionofthereferencepoint

Astraightlineistheshortestdistancebetweentwopoints,

and the points must be specified when giving the length

oftheline.When measuringAoA,alengthmeasuredfrom

thepatientistheprevalentmeasurementbutthereference

point,wherethelinemeetsthepatient,hasnotbeen

stan-dardised.

Someresearch50,51_{didnotgiveanyreferencepoint.}

Oth-ersreportedmeasuringfromthetargettodifferentpoints

suchas7mmbehindtheanteriorcornealpole,42_13or14mm

infrontoftheeye,52_theeye,53---55_{thespectacleplane,}16,17,25

thetrialframe,28_{‘‘thecornealplane’’,}11_{theanteriorpole}

of thecornea,56,57 _theforehead39 _{andthe chin.}58 _Noneof

thesereports gave a reasonfor their choice of reference

point.Thesepositions,someofwhich(suchas‘‘theeye’’)

areimprecise,coveralargeenoughrangetoinfluencethe

resultsignificantlyat moderatelevelsofAoAand

substan-tiallymoreathigherlevels.

Definitionoftheend-point

Definition of the end-point is inherently imprecise in the

retinoscopy,push-upandpush-downmethodsofmeasuring

AoA.

The distance of the retinoscope sighthole from the

patient’seye,typicallythedistancetothespectacleplane,

is known as the Retinoscopy Working Distance (RWD).

Measurement of accommodation by retinoscopy has

gen-erally involved a shorter (often much shorter) RWD than

is usual for determination of distance refractive error

by retinoscopy. In reports of measurement of AoA by

retinoscopy13,17,28---31,51,58---60 _{the RWD is the outcome}

mea-sure.Thiswouldleadtoimprecision,forreasonsincluding

thefollowing:

- the participantis likely to move, altering the distance

fromparticipanttoretinoscope.

- theexaminerislikelytomove,independentlyofthe

par-ticipant.

- theexaminer ispositionedneartotheparticipant,

per-hapsasnearas10cmorless,thereforeanyerror,suchas

due tomovement or parallax,would bea large

propor-tionofthemeasurement.Inonestudy28 _{negativelenses}

wereaddedtothepatient’sspectacleplanetoincrease

theRWD,perhapstoreducethaterrorbuttheresultsdid

notshowmoreprecisionthanthoseofotherinvestigations

usingretinoscopy.

- theaccuracyofretinoscopydecreasesunpredictablywhen

measuring away from the visual axis32 _{and this error}

increaseswithnearnessof afixed-size targetdisplacing

theretinoscopebeam.

- themeasurementis takensometimeafterreachingthe

end-point.

- themeasurementmayincludeerrorsduetoparallaxsince

therulermayhavetobeheldawayfrompointstowhich

itmeasured.Thiswaswellillustratedphotographicallyin

theresearchreportsthatshowedthisdetail.51,58

- the precision of retinoscopy is proportional to the

RWD.61,62

- the measurement end-point may involve the subjective

judgement ofretinoscopic reflexes thatareparticularly

unusualduetochangesinocularaberrationwith

accom-modationdescribed inother research.63 _Thiscouldbea

reason why research51 _{found substantial inter-examiner}

variation, over 20%, in measuring AoA by retinoscopy.

However, excellent reproducibility was found for this

technique in a later and larger study17 _{in which ten}

examiners measured fourteen participants’ AoA using

additionaltrial lensestokeep theRWDbetween14and

67cm.They found that 95% of the measurementswere

within7%ofeachother.

Methodsof measuringAoAthat requirethe participant

tostatewhenatargetisclearor blurredhavealsolacked

apreciseend-point.Someauthors18,28,54,64,65_havereported

onyoungparticipantswithwhomthatsubjectiveend-point

wouldbeevenlessreliable, includingone65 _whoreported

measuringAoAsubjectivelyinchildrenundertwoyearsof

age.

In the minus-lens method, the end-point depends on

howfinethefocusmustbetodiscernthetarget.Different

researchersusingtheminus-lensmethodhaveuseddifferent

targetsizes,corresponding,forexample,to:

6/624,66

6/6−41

6/925,31

6/9−57

6/12+21

and6/15.17

Someofthesewouldbelikelytointroduceimprecisionof

morethan1Dduetodepthoffocusalone,giventhelarge

reduction(andtheconsequentincreaseindepthof focus)

shown26_{inpupildiameterathighaccommodationlevels.}

Thereisalwayssomeerrorinpinpointingtheend-point

6 D.H.Burnsetal.

measuringlengthislargelyindependentofthelengthbeing

measured, such as in measuring AoA by measuringa

dis-tance.Therefore,end-pointerrorisahigherproportionof

the measurement when higherlevels of AoA (i.e. shorter

distances)aremeasured.

Fortunately, in clinical measurement of AoA, accuracy

at lower levels of AoA tends to be more important than

accuracyathigherlevels.Itcanbeargued thatanAoAof

about4D (morefor hypermetropesreluctanttowear

dis-tancerefractivecorrection)wouldcoveralmosteveryone’s

practicalneeds.

On the other hand, accuracy in higher values may be

useful in identifying change that may be of

pathologi-calsignificance, suchasinteroculardifferenceor outliers

attributabletoapathologicalprocess.Researchhasnotyet

identifiedalevelofaccuracythatmightachievethesegoals.

Monocularorbinocular

Whennotaddressing interoculardifference,measurement

of AoA would generally be binocular, since in everyday

lifeaccommodationisnormallystimulatedunderbinocular

conditions.However,binocularmeasurementisnotalways

possible because of restrictions due to the measurement

methodasshown,forexample,withtheminuslensmethod,

asdescribedpreviously.Thisraisesthepossibilityoferror.

Measurements of one eye or of both together, under

monocularorbinocularstimulation,maydifferbyunknown

amounts,because:

- binocular visualacuityishigherthan monocular67 _which

mayaffect thespeed andprecisionof detectionofblur

(or itsabsence)particularlyinmethodsofmeasurement

ofAoAthatareaffectedbyreactiontime.

- convergence induces accommodation and vice versa.

Binocularity requires a fixed degree of convergence for

the object distance. Therefore, the amount of

accom-modation may be influencedby whether the viewing is

monocularorbinocular.

- changesinpupilsize,duetoconvergence,influencedepth

offocus.52

- morenaturalbinocularviewingconditionsmayallow

opti-malexpressionofaccommodation,asfoundinonestudy.68

Thismaybebecausemonocularviewingcangive

anoma-lousdistancecueswhichmaycausetheparticipanttofeel

somewhat disconnected from the task, and would

pre-vent any stereoscopic sense of nearness of the target.

This sense of nearness influences accommodation.83---85

One study52 _{found that binocular viewing gave higher}

results than monocular viewing. However, that

investi-gationtook placea centuryago andthe resultwasnot

supported by any work published sincethen. Moreover,

anotherinvestigation45 _{didnotshowhigherresultswhen}

AoAwasmeasuredbinocularlythanwhenitwasmeasured

monocularly.

- if the AoA of one eye differs from itsfellow, binocular

measurementismostlikelytogivethehigherofthetwo

eyes’amplitudes.

Researchers’ approach to binocularity has varied.

Some54,69 _{stimulated and measured binocularly, or took}

both monocular andbinocular measurements16 _{or did not}

state whether the measurementsweremade monocularly

orbinocularly.70_{Thosewhousedtheminus-lensmethod}24,51

(which,asexplainedabove,cannotgivebinocularresults)

measured monocularly only. In at least one study50 _one

eye was covered. Others measured monocularly as they

refractedbyobjectivemeans12,51_{perhapsastherewerefew}

reports ofan objectivemethod thatgaveresults forboth

eyessimultaneously.

Correctionofrefractiveerror

Correction of refractive error before measuring AoA is

importantbecausethemeansphericalrefractivecorrection

mustbeaddedtothemeasurement(andreferencedtothe

samepointasit).Furthermore,latenthypermetropiacould

causesubstantialandvaryingerrors,Moreover,ifspectacles

areworn,theaccommodativestimulusisinfluencedbythe

typeandpoweroftheprescription.71

ThetypeofrefractiveerrormayalsoinfluenceAoAbut

investigationshavenotshowntheinfluence tobelargeor

predictable.Astudy72_{setouttoreporttheextenttowhich}

AoA and refractiveerror were correlated.This study’s 80

participantswereaged18---22yearsandameanofpush-up

andpush-downmeasurementswastaken.The results

indi-catedthatthesignandamountofrefractiveerrorandthe

mannerofonsetofmyopiainfluencedAoA.Theassociation

wasweak but supported by measurements ofpupil

diam-eter since hyperopic participants tended to have smaller

pupils,and hence greater depthof focus,yet lower AoA.

AsimilareffectofrefractiveerroronAoAwasfound48_with

thepush-upmethodmodifiedtoreduceerrorsasin

previ-ousworkdescribedabove11 _{forasimilarparticipantgroup.}

Theseresultssuggestthatrefractiveerrorisavariablethat

shouldbecontrolledinAoAresearch.However,normative

studies of AoA have generally not recorded participants’

refractiveerror.

The approachto correctingrefractiveerror hasvaried

between studies and sometimes within individual studies

of AoA.In onestudy,cycloplegiceyedrops wereused52 _to

attempttoeliminateaccommodationforthemeasurement

ofrefractiveerror,includinglatenthypermetropia,except

forsomeparticipantsoverage46years,whereasinanother

study16 _{cycloplegic eyedrops were instilled only for some}

participantsyoungerthan20.Neitherstudyexplainedwhy

theyadministeredadrugorgaveanybasisforitsselective

allocation. Itsuse could be supported by anotherstudy72

thatimplicitlyrelatedlatenthypermetropiatoAoA.

IntheearlieststudiesofAoA42,53_{correctionofrefractive}

error was not clearly described. It wasnot mentioned in

somelaterresearch50,54,70_{anditsmethodofcorrectionwas}

moreapproximate thannormal methodsin amore recent

study.73

Taskluminance

Methodsof measuringAoA that requirethe patient’s

per-ceptionofavisualtargetdonotstipulatethatthelighting

of the visual task should be set to a particular level.

However, target perception is influenced by the

Figure2 TwoRAFRules,showingpositionofscalediffers.

described.74 _{The influenceof taskluminanceonAoA}

mea-surementresults,independentoftheeye’sdepthoffocus,

hasbeendemonstrated75_{andithasalsobeenshown}76,77_that

taskluminanceinfluencesdepthoffocuswhich,asdiscussed

previously,alsoinfluencesAoAmeasurementresults.

Instrument

error

TheRAFRuleistheprevalentinstrumentusedformeasuring

AoAintheUK.Althoughitisasimpledevice,thereappear

tobefifteensourcesoferror,listedbelow,initsdesignand

production.

Other accommodation rules that have been produced

forclinical usearecurrentlyrarely usedintheUK,tothe

authors’ knowledge, andmay beexpected toshare some

oftheRAFRule’ssourcesoferror.Theyusethesame

gen-eral principle of measurement by locating the near-point

andmeasuringhowfaritisfromtheeye.Practitionersmay

improviseanaccommodationrulebyusingarulerand

hand-heldvisualobject.

EachofthesefifteensourcesoferrorintheRAFRulehas

thepotentialtocauseclinicallysignificanterror.The

resul-ting errors can allbe additive. Theiroverall effect could

beaddressed by revising the design although thishas not

enjoyed a clinically-guided change during its

production-span of over sixtyyears. The fifteen sources of error are

asfollows:

1. ambiguity about which part ofthe sliding component

indicatesthereading;

2. ambiguityregardingwhichscale-graduation(orneither)

thescale’snumbersdescribe,becauseeachnumberis

equidistantbetweentwograduationsandindicates

nei-ther;

3. uncertaintyaboutthelocationofthescale’szeropoint,

asRAFRulesappeartovaryinthedistanceofany

par-ticularscalegraduationfromthecheekrest,asshown

inFig.2whichdepictsthefirsttwoRAFRulessourced

randomlybyoneoftheauthors;

4. the slider’s opaqueness, obscuring interpolation

betweengraduations;

5. theeffectonthelocationofthescalearisingfrom

inter-individual differencesin facial anatomy,at anygiven

distance,d,ofthecheekrestbelowthecornealvertex;

6. the effectof notspecifyingd, mentionedin point(5)

above, asfacial anatomy is not perpendicular tothe

RAFRule;

7. theeffectofnotspecifyingd,asfacialanatomyvaries

betweenpeople;

8. theeffectofnotspecifyingthedistancedonpoint(14)

below;

9. the variabilityofluminance contrastofthe text.The

contrastcouldbestandardisedbybacklightingthetext;

10. the limitsof thescale. ValuesofAoA higherthanthe

measurementrangeoftheunmodifiedinstrumenthave

oftenbeenreported22,37,38,42,78_;

11. thevariablelocationoffixationwithinonelineoftarget

print,sincedifferentlettersintheline,whichis27mm

long, areat differentdistances fromeither eye,

pro-ducingdifferingaccommodativedemandofupto0.25

Dwhenmeasuringapproximately6Dofaccommodation

withtheRAFRule.Highererrorsoccuratshortertarget

distances;

12. the effect of target detail size, through depth of

focus34_;

13. theeffectofscale intervallinearity,throughreaction

timeaspreviouslydiscussed;

14. thevariabilityofraildeclination.ThisisshowninFig.3,

twopicturestakenoftheinstrumentinroutineclinical

use,showinghowtherulemaybeheldaboveorbelow

theprimarypositionofgaze.

The declinationinfluences theresult,for thefollowing

reason.Thereisaquadrilateralformedbythecornealvertex

orotherreferencepointofmeasurement,thetestobject,

the measurement index on the slider, and the midpoint

between the cheek rests. This quadrilateral is generally

irregular and its shapevaries with the measurement and

theRule’sposition.Theeffectofdeclinationcanbe

8 D.H.Burnsetal.

Figure3 RAFRulesinnormaluse,showingvariationofdeclination.

theRuleshownintheupperphotographinFig.3wouldgive

ameasurementofAoAapproximately1Dlowerthanifthe

Ruleweretiltedasinthelowerphotograph.

There is no consensus onhow the RAF Rule shouldbe

held.Guidancevariesbetweenauthorities12,13,15_sometimes

picturingtheinstrumenttiltedsubstantiallydowninuse.

Furthermore,therearereportsthatdeclinationofgaze

influences AoA.79,80 _{Moreover, if the rail is tilted too far}

down,the normal narrowing of the palpebral aperture in

downgazemayreducepupilarea,increasingdepthoffocus.

Wherea phoropteris usedinAoAmeasurement,itsrailis

horizontal.

15. The other source of error inherent in the design of

this instrument applies to monocular measurements.

The error is that the rule is placed on the midline

betweenthetwoeyes,ratherthanonthevisualaxisof

theeyebeingmeasured.45_{Thiswouldinflateresultsby}

an amountthatcanbetrigonometricallyestimatedas

about5%atthehighestlevelsofAoAandapproximately

proportionatelylessatlowerlevels,soitisnotaslarge

assome other errorslisted above.Correctionfor this

source of error has been precise,45,72 _approximate16

or missing42,78 _{withthelatterstudiesreportinghigher}

uppermeasurementsofAoAthanotherstudies.

Intheabovelistofsourcesoferrorarisingfromapparent

weaknessesin thedesignandproduction oftheRAFRule,

publishedinformationwasnotfoundforitems1---13.

Measurement withthe minus-lens method minifies the

target because it is viewed through negatively-powered

lenses.Thenegativepower,andhencetheminification, is

greater athigherlevelsofmeasurement. Theminification

hasbeencited14,41_{asapossiblesourceoferror.No}

theoret-icalorempiricalreportswerefoundofthesizeofthiserror

beingclinicallysignificant.

Whenviewingthroughspectaclelenses,AoAmaybe

influ-encedbyrefractiveerror,thedegreeofinfluencedepending

onthepowerofthelens.36_{Thismaybeanadditionalsource}

oferrorwiththeminus-lensmethod.66

Examiner

bias

This is a source of error in any measurement that is not

fully automatic. The practitioner examining the patient

will often, and perhaps always, have an expectation of

approximatelywherethemeasurementend-pointshouldbe.

Thatexpectation,and inevitable differencesin technique

betweenpractitioners,mayinfluencehowthemeasurement

istaken(e.g.,thevisualobject’sspeed),whichmayinturn

influencetheresult.Itmayaffectnaivepatientsmore.

Research of accommodative response81 _{and fixation}

disparity82 _{has shown that the exact wording of}

instruc-tionscaninfluencetheresultsofmeasurement.Significant

differences between five different examiners’ results for

push-up measurement of AoA were found and attributed

to possible differencesbetween examiners’ measurement

techniques.38

Examinerbiasmay besuspected particularlywhen the

generallevelofmethodologicalrigourappearslowandthe

resultsarenotcorroboratedelsewhere.Anormativestudy

discussedtheconclusionthatAoAwasinfluencedbyrace70

and another found a 5 D difference between amplitudes

ofaccommodationofurbanandruralchildrenagedfiveto

eight,usingamethoddescribedonlybrieflyandinunspecific

terms.54

Anomalous

distance

cues

Awareness of a visual object’s distance influences

accommodation.83---85 _{In comparing methods of}

measur-ing AoA, the test object is further away in the minus

lens method and measurement conditions aremonocular,

reducingawarenessofproximity.Othermethodsgivehigher

results, todifferingextents.28,41,46,59 _{The lowest valuesof}

all investigations of AoA were obtained using the

minus-lens method with objective measurement (simultaneous

autorefraction).56

Results for AoA with the minus-lens method were

sig-nificantly higherwhen using a shorter viewingdistance.66

Measurement was monocular so the difference was not

attributable to the induction of extra accommodation by

extra convergence. The authors attributed the effect to

proximalaccommodation.

With particularly careful methodology it was found

thataccommodation measured witheitherthepush-up or

the push-down methods washigher when the participant

grasped and guided the target than when the target was

heldandguidedbytheexaminer.45_{Noreasonforthis}

find-inghasbeen demonstratedbut itcouldhave been dueto

variouspsychologicalfactorsincludingincreasedawareness

ofproximitywhentheparticipantconnectedwith,and

con-trolled, thetarget. Accommodationrules suchasthe RAF

Rule maytherefore givehigher measurementsbecauseof

reasonsincludingtheirphysicalcontactwiththepatient.

Feedback

from

achievement

Methods of measurement that reward patients striving to

improvetheirperformancebyfeedingbackhowwellthey

areachievingdiscernment ofdetail,encouragingeffortto

achieve the best visual performance, tend togive higher

results for AoA and other aspects of accommodation.86,87

Encouragementofeffortisadvisedforeventhemostbasic

subjectiveassessmentofvisualperformance.88

The reward for effort differs in different methods.

Obtainingnearness,thegoalforthepatientusingthe

push-up method, probably offers little motivation to produce

higherresults,althoughthismaydependontheinstructions

given.Maximumaccommodativeeffortwouldbemorelikely

tomeetthechallengeofdiscoveringdetailencounteredin

methods suchaspush-downwiththe ‘‘justrecognisable’’

end-point,theminuslens method,andretinoscopywitha

suitable visual object such as a Snellenchart reduced to

about5%ofitsusualsize.

Conclusions

Manysourcesoferrorhavebeendescribedinexisting

meth-odsofmeasuringAoA.Itisnoteworthythatsomanysources

ofinaccuracycanbeidentifiedinasingle-parameter,

long-established,basicandubiquitousclinicalmeasurement.

The sourcesof errordifferconsiderablyintheir nature

andin themagnitudeof their effect.Some arerelatively

systematicwhile othersareofunpredictablesizeor

direc-tionorboth,someaffectlowerreadingsmorethanhigher

readingsandviceversa,someaffectonlycertainmethods

ofmeasurement,someaffectdifferentmethodsdifferently,

someareduetohumanfactorsofthepatientorofthe

prac-titioner,someareduetofactorsoftheequipment,orofthe

method,usedformeasurement.Theiroveralleffectgreatly

reducesthevalidityofclinicalresultswithcurrentmethods.

Themeasurementerrorscausedby thesemanysources

oferrorcanallbereduced(andafewofthemcanbe

erad-icated)bybetterattentiontomeasurementtechniqueand

bythestandardisationofequipmentandmethods.However,

such improvements to existing methods would generally

increasethecomplexity,durationanddifficultyofthe

mea-surement.

Presbyopia is normal for older people and cures for

it would find widespread application. Surgical cures for

presbyopia have long been sought. Compared to optical

management of presbyopia they are risky and can be

costly, but on review89---91 _{they showed limited success.}

Theirvalidationwouldrequireaccurateandreliable

clini-calmeasurementofAoA.Inthefuture,itseemslikelythat

improvements in the measurement of the AoA may have

applicationsinolderpatientsaswellaspeople

convention-allydescribedaspre-presbyopes.

Guidance

for

clinicians

Theindividualpractitionercantakecertainstepstoreduce

AoA measurement-error in current clinical practice,

rel-atively effectively and easily. For example, visual object

detailshouldbeclosetothelimitofresolutionatthenear

point, andthe method usedshould be recorded withthe

measurement.

Whenmeasuringwithdevicesusingarulerwithasliding

visualobject,suchastheRAFRule:

- movementoftheslidershouldbeslow,perhaps

approxi-matelyonedioptrepersecond;

- during measurementthepatientshouldreceive positive

feedbackforeffort;

- theruleshouldbeheldintheprimarypositionofgaze;

- in push-down, the end-point criterion of sharp focus

shouldbeadopted;

- measurementshouldbetoaclear,precisereferencepoint

suchasthecornealvertex;

- anycorrection forrefractiveerrorshouldbereferenced

tothesamepoint;

- thepractitionershouldchecktheindividualrule’s

accu-racybymeasuringthenear-pointdistancewithaseparate

rule;

- the practitioner shouldconsider taking a first

measure-mentusingthepush-upmethodandthenmovingtheslider

away fromthepatient toobtain apush-down

measure-ment. TherecordedAoA wouldbetheaverage ofthese

10 D.H.Burnsetal.

When using the minus-lens method, the visual object

shouldbeasclosetotheeyebeingmeasuredasfeasible,and

minus-lenspowershouldbechangedslowly.Forretinoscopy,

thepractitionermayconsiderreducingerrorbyusinga

nor-malworkingdistancesuchas67cm,addingminuslensesin

thetrialframefortherefractedeye.Thispossiblemethod

doesnotappeartohavereceivedresearchattention.

Notwithstandingthesepossibleimprovementstoexisting

methods,anewAoA-measurementmethodhasbeensought

bythecurrent authors.It isintended tobeacceptable in

clinicalpracticeandtoprovidemorereliablemeasurement.

Theauthorshopetopublishadescriptionofthisnewmethod

andtoreportinitialresultsobtainedwithit.

References

1.General Optical Council (UK). Optometry Core Com-petencies (Stage 1); 2011. https://www.optical.org/ en/Education/core-competencies–core-curricula/index.cfm

[accessed16.01.19].

2.College of Optometrists (UK). The Routine Eye Exami-nation; 2016. http://guidance.college-optometrists.org/ guidance-contents/advanced-search/?searchterm=a42

[accessed16.01.19].

3.College of Optometrists (UK). Equipment List for the Routine Eye Examination; 2016.

http://guidance.college-optometrists.org/guidance-contents/ annexes/annex-1-equipment-list-for-the-routine-eye-examination/[accessed16.01.19].

4.Optometric Extension Program Foundation (USA). 21 Point ExaminationTranslation Guide,https://www.oepf.org/sites/ default/files/21PointExaminationQuickRefe.pdf [accessed 16.01.19].

5.World Council of Optometry. Curricular Support Elements for an Optometry Programme; 2017.

https://worldcouncilofoptometry.info/wp-content/uploads/ 2017/03/curricularsupportelementfinalweb2.pdf[accessed 16.01.19].

6.The European Council of Optometry and Optics. The European Diploma in Optometry Syllabus, Learning Outcomes and Clinical/Practical Competencies; 2017.

https://www.ecoo.info/wp-content/uploads/2016/10/2017 1020Syllabus-andAccreditationself-assessment.pdf

[accessed16.01.19].

7.BurnsD,EvansB,AllenP.Clinicalmeasurementofamplitude ofaccommodation:areview.OptomPract.2014;15:75---86.

8.Neely J. The RAF near-point rule. Br J Ophthalmol. 1956;40:636---637.

9.Somers W, FordC.Effect of relative distancemagnification onthemonocularamplitudeofaccommodation.AmJOptom PhysiolOpt.1983;60:920---924.

10.GossD.Clinicalaccommodationtesting.CurrOpin Ophthal-mol.1992;3:78---82.

11.Atchison D, Capper E, McCabe K. Critical subjective mea-surement of amplitude of accommodation. Optom Vis Sci. 1994;71:699---706.

12.Keirl A. Accommodation presbyopia. In: Keirl A, Christie C, eds. Clinical Optics and Refraction. London: Elsevier; 2007:132---152.

13.RabbettsR.Bennett&Rabbetts’ClinicalVisualOptics.4thed. OxfordUK:Butterworth-Heinmann;2007:128---131.

14.Rosenfield M. Clinical assessment of accommodation. In: Rosenfield M,LoganN,eds. Optometry:Science,Techniques and Clinical Management. 2nd ed. Edinburgh,UK: Elsevier; 2009:230---232.

15.Barrett B. Assessment of binocular vision and accommoda-tion. In: Elliott D, ed. Clinical Procedures in Primary Eye Care. 4thed.Oxford,UK: Butterworth-HeinemannElsevier; 2013:178---181.

16.TurnerM.Observationsonthenormalsubjectiveamplitudeof accommodation.BrJPhysiolOpt.1958;15:70---100.

17.LeonA, Estrada J,Rosenfield M.Ageand theamplitude of accommodation measured using dynamic retinoscopy. Oph-thalmicPhysiolOpt.2016;36:5---12.

18.BenzoniJ,RosenfieldM.Clinicalamplitudeofaccommodation inchildrenbetween5and10yearsofage.JOptomVisDev. 2012;43:109---114.

19.ScheimanM,WickB.ClinicalManagementofBinocularVision. 1sted.Philadelphia:Lippincott;1994:20.

20.Koslowe K, Glassman T, Tzanani-Levi C, Shneor E. Accom-modativeamplitudedetermination:pull-awayversuspush-up method.JOptomVisDev.2010;41:28---32.

21.Taub M, Shallo-Hoffman J. A comparison of three clinical testsof accommodative amplitudeto Hofstetter’s norms to guide diagnosis and treatment. JOptom Vis Dev. 2012;43: 180---190.

22.ChenA,O’LearyD.Validityandrepeatabilityofthemodified push-upmethodformeasuringtheamplitudeof accommoda-tion.ClinExpOptom.1998;81:63---70.

23.Momeni-MoghaddamH,McAlindenC,AzimiA,SobhaniM, Ski-adaresiE.Comparing accommodative function between the dominantandthenon-dominanteye.Graefe’sArchClinExp Ophthalmol.2014;252:509---514.

24.Sheard C. The determination of the near-point and of the amplitudeofaccommodation.In:OcularAccommodation. Mis-souri:AmericanOptometricAssociation;1920:22---43.

25.WoodruffM.Ocularaccommodationinchildrenaged3to11 years.CanJOptom.1987;49:141---145.

26.MargE,MorganM.Thepupillarynearreflex;therelationof pupillary diameterto accommodationand the various com-ponentsofconvergence.AmJOptomArchAmAcadOptom. 1949;26:183---198.

27.EvansB.Binocularvisionassessment.In:RosenfieldM,LoganN, eds.Optometry:Science,Techniques&ClinicalManagement. 2nded.Edinburgh:Butterworth-Heinemann;2009.

28.WoldR.Thespectacleamplitudeofaccommodationof chil-dren aged six to ten. Am J Optom Arch Am Acad Optom. 1967;44:642---664.

29.Woodhouse M, Meades J, Leat S. Reduced accommodation inchildrenwithDown syndrome.InvestOphthalmolVisSci. 1993;34:2382---2387.

30.Roche O, Roumes C, Parsa C. Techniques de mesure du pouvoir accommodatif chez le sujet phake et le sujet pseudo-phake,distinctionentreinsuffisancesaccommodatives mécaniques et neurologiques. J Fr d’Ophtalmol. 2007;30: 953---960.

31.LeonA,MedranoS, Rosenfield M.Acomparison ofthe reli-abilityofdynamicretinoscopyand subjectivemeasurements oftheamplitudeofaccommodation.OphthalmicPhysiolOpt. 2012;32:133---141.

32.TayE,MengherL,LinX,FergusonV.Theimpactofoffthevisual axisretinoscopyonobjectivecentralrefractivemeasurement inadultclinicalpractice:aprospective,randomizedclinical study.Eye.2011;25:888---892.

33.CharmanW.Forminganopticalimage:theopticalelementsof theeye.In:RosenfieldM,LoganN,EdwardsK,eds.Optometry: Science,TechniquesandClinicalManagement.2nded.Oxford, UK:Elsevier;2009:11.

34.BurnsD,EvansB,AllenP.Areviewofdepthoffocusin measure-mentoftheamplitudeofaccommodation.Vision.2018;2:37.

36.GwiazdaJ, ThornF,BauerJ, HeldR. Myopicchildrenshow insufficient response to blur. Invest Ophthalmol Vis Sci. 1993;34:690---694.

37.EvansB,DrasdoN,RichardsI.Investigationofbinocularand accommodativefunctionindyslexia.OphthalmicPhysiolOpt. 1994;14:5---19.

38.Adler P, Scally A, Barrett B. Test---retest reproducibility of accommodation measurements gathered in an unselected sample of UK primary school children. Br J Ophthal. 2013;97:592---597.

39.CastagnoV,VilelaM,MeucciR,etal.Amplitudeof accommo-dationinschoolchildren.CurrEyeRes.2016;18:1---7.

40.Woehrle M, Peters R, Frantz K. Accommodative amplitude determination:canwesubstitutethepull-awayforthepush-up method?JOptomVisDev.2017;28:246---249.

41.AntonaB,BarraF,BarrioA,GonzalesE,SanchezI.Repeatability intraexaminer and agreement in amplitude of accommo-dation measurements. Graefe’s Arch Clin Exp Ophthalmol. 2009;247:121---127.

42.Donders F. On the Anomalies of the Accommodation and RefractionoftheEye.(W.MooreTrans.).UK:TheNew Syden-hamSociety;1864:207---209.

43.Ovenseri-OgbomoG,OduntanO.Comparisonofmeasuredwith calculatedamplitudeofaccommodationinNigerianchildren agedsixto16years.ClinExpOptom.2017;101:571---577.

44.CufflinM,MankowskaA,MallenE.Effectofbluradaptationon blursensitivityanddiscriminationinemmetropesandmyopes.

InvestOphthalmolVisSci.2007;48:2932---2939.

45.Fitch R. Procedural effects on the manifest human ampli-tudeofaccommodation.AmJOptomArchAmAcadOptom. 1971;48:918---926.

46.RosenfieldM,CohenA.Repeatabilityofclinicalmeasurements oftheamplitudeofaccommodation.OphthalmicPhysiolOpt. 1996;16:247---249.

47.RosenfieldM,CohenA.Push-upamplitudeofaccommodation andtargetsize.OphthalmicPhysiolOpt.1995;15:231---232.

48.AllenP,O’LearyD.Accommodationfunctions:co-dependency andrelationtorefractiveerror.VisRes.2006;46:491---505.

49.Sergienko N, Nikonenko D. Measurement of amplitude of accommodation in young persons. Clin Exp Optom. 2015;98:359---361.

50.AyrshireStudyCircle.Aninvestigationintoaccommodation.Br JPhysiolOpt.1964;21:31---35.

51.Rutstein R, Fuhr P, Swiatocha J. Comparing the amplitude ofaccommodation determinedobjectively and subjectively.

OptomVisSci.1993;70:496---500.

52.DuaneA.Studiesinmonocularandbinocularaccommodation with their clinical applications. Trans Am Ophthalmol Soc. 1922;20:132---157.

53.Kaufmann J. Die absolut und relativ accommodationsbre-iteindenverscheidenenlebensaltern.(Inauguraldissertation, GeorgAugustUniversitat,Göttingen);1894.

54.EamesT. Accommodationin schoolchildren, aged five,six, seven,andeightyears.AmJOphthalmol.1961;51:1255---1257.

55.MossS, KleinR,KleinB.Accommodative abilityin younger-onsetdiabetes.ArchOphthalmol.1987;105:508---512.

56.Anderson H, Hentz G, Glasser A, Steubing K, Manny R. Minus-lens---stimulatedaccommodativeamplitudedecreases sigmoidallywithage:astudyofobjectivelymeasured accom-modativeamplitudesfrom age3.InvestOphthalmolVisSci. 2008;49:2919---2926.

57.AndersonH,StuebingK. Subjectiveversusobjective accom-modativeamplitude:preschooltopresbyopia.OptomVisSci. 2014;91:1290---1301.

58.McLelland J, Saunders K. The repeatability and validity of dynamicretinoscopyinassessingtheaccommodativeresponse.

OphthalmicPhysiolOpt.2003;23:243---250.

59.HokodaS,CiuffredaK.Measurementofaccommodative ampli-tudeinamblyopia.OphthalmicPhysiolOpt.1982;2:205---212.

60.JimenezR,GonzalezM,PerezM,GarciaJ.Evolutionof accom-modativefunctionanddevelopmentofocularmovementsin children.OphthalmicPhysiolOpt.2003;23:97---107.

61.CorboyJ,NorathJ,ReffnerR,StoneR.TheRetinoscopyBook: AnIntroductory Manualfor EyeCareProfessionals. 5thed. Thorofare,NJ,USA:Slack;2003:31.

62.Atchison D.Objectiverefraction.In:Rosenfield M,LoganN, EdwardsK,eds.Optometry:Science,TechniquesandClinical Management.2nded.Oxford,UK:Elsevier;2009:190.

63.AldabaM,VilasecaM,ArjonaM,PujolJ.Age-relatedchanges inaccommodationmeasuredwithadouble-passsystem. Oph-thalmicPhysiolOpt.2013;33:1---8.

64.SternerB,GellerstedtM,AndersS.Theamplitudeof accom-modationin6---10-year-oldchildren---notasgoodasexpected!

OphthalmicPhysiolOpt.2004;24:246---251.

65.ChenA,O’LearyD,HowellE.Nearvisualfinctioninyoung chil-dren.PartII:Amplitudeofaccommodation.OphthalmicPhysiol Opt.2000;20:188---190.

66.Momeni-Moghaddam H, Wolffsohn J, Azimi A, Babaei-Malekkolaei E. Effect of targetdistance on accommodative amplitudemeasuredusingtheminus-lenstechnique.ClinExp Optom.2013;97:62---65.

67.Pointer J. Influence of selected variables on monocular, interocular, and binocular visual acuity. Optom Vis Sci. 2008;85:135---142.

68.Otake Y, Miyao M, IshiharaS, et al. Anexperimental study ontheobjectivemeasurementofaccommodativeamplitude underbinocularandnaturalviewingconditions.TohokuJExp Med.1993;170:93---102.

69.Kragha I. Amplitude of accommodation: population and methodological differences. Ophthalmic Physiol Opt. 1986;6:75---80.

70.CoatesW.AmplitudesofaccommodationinSouthAfrica.BrJ PhysiolOpt.1955;12:76---81.

71.Rosenfield M.Accommodation.In: ZadnikK, ed.TheOcular Examination: Measurements and Findings. 1st ed. Philadel-phia,USA:WBSaunders;1997:97.

72.McBrien N, Millodot M. Amplitude of accommodation and refractiveerror.InvestOphthalmolVisSci.1986;7:1187---1190.

73.Ovenseri-OgbomoG,KudjawuE,KioF,AbuE.Investigationof amplitudeofaccommodationamongGhanaianschoolchildren.

ClinExpOptom.2012;95:187---191.

74.Westheimer G. Visual acuity. Annu Rev Psychol. 1965;16:359---380.

75.Johnson C. Effects of luminance and stimulus distance on accommodation and visual resolution. J Optic Soc Am. 1976;66:138---142.

76.CampbellF.Thedepthoffocusofthehumaneye.JPhysiol. 1966;125:29---30.

77.TuckerJ,CharmanW.Thedepthoffocusofthehumaneyefor Snellenletters.AmJOptomPhysiolOptics.1975;52:3---21.

78.SternerB,GellerstedtM,SjöströmA.Accommodationandthe relationshiptosubjectivesymptomswithnearworkforyoung schoolchildren.OphthalmicPhysiolOpt.2006;26:148---155.

79.RippleP.Variationofaccommodationinverticaldirectionsof gaze.AmJOphthalmol.1952;35:4---1630.

80.AtchisonD,ClaydonC,IrwinS.Amplitudeofaccommodation for different head positions and different directions ofeye gaze.OptomVisSci.1994;71:339---346.

81.StarkL,AtchisonD.Subjectinstructionsandmethodsoftarget presentationinaccommodationresearch.InvestOphthalmol VisSci.1994;35:528---537.

82.Karania R, Evans B. The Mallett Fixation Disparity Test: influenceof testinstructions& relationship withsymptoms.

12 D.H.Burnsetal.

83.Heath G. The influence of visual acuity on accommodative responses of the eye. Am J Optom Arch Am Acad Optom. 1956;33:513---524.

84.Rosenfield M, Gilmartin B. Effect of target proximity on the open-loop accommodative response. Optom Vis Sci. 1990;67:74---79.

85.HungG, Ciuffreda J,Rosenfield M.Proximal contributionto alinearstaticmodelofaccommodationand vergence. Oph-thalmicPhysiolOpt.1996;16:31---41.

86.Winn B, GilmartinB,Mortimer L, EdwardsN. Theeffectof mentaleffortonopen-andclosed-loopaccommodation. Oph-thalmicPhysiolOpt.1991;11:335---339.

87.Gray L, Winn B, Gilmartin B, Eadie A. Objective concur-rent measures of open-loop accommodation and vergence

under photopic conditions. Invest Ophthalmol Vis Sci. 1993;34:2996---3003.

88.ElliottD,FlanaganJ.Assessmentofvisualfunction.In:Elliott D,ed.ClinicalProceduresinPrimaryEyeCare.4thed.Oxford, UK:Butterworth-HeinemannElsevier;2013:35.

89.Bowling B. Kanski’s Clinical Ophthalmology. 8th ed. Cam-bridge,UK:Elsevier;2016:246.

90.Pallikaris I, Kontadikis G, Portaliou D. Real and pseudoac-commodationinaccommodativelenses.JOphthalmol.2011,

http://dx.doi.org/10.1155/2011/284961.