AcuityM D Crossland, UCL Institute of Ophthalmology/Moorfields Eye Hospital, London, UK

ã 2010 Elsevier Ltd. All rights reserved.

Glossary

Cycles per degree – The number of complete

phases of a grating (e.g., the distance between the

center of a white bar and the center of the next bright

bar in a square-wave grating; or the distance

between two adjacent areas of maximum brightness

on a sine-wave grating) contained in 1� of visualangle.

Minimum angle of resolution – The size of the

angle subtended at the eye of the smallest feature

which can be reliably identified on an optotype.

Minute of arc – One-sixtieth of a degree.

Optotype – A letter, symbol, or other figure

presented at a controlled size to measure vision.

Visual angle – The angle, which a viewed object

subtends at the eye.

Detection and Resolution Acuity

Visual acuity can be defined in two broad ways. Detectionacuity is measured by determining the size of the smallestobject which can be reliably seen (is there a circle on thefirst or second screen?). Detection can be elicited reliablywith targets, which subtend an angle at the eye as small as1 s of arc (1/3600�). Even a small point of light willstimulate several photoreceptors due to the point-spreadfunction of the eye: that is, the way in which light isdiffracted through the eye’s optics (Figure 1(a)).

Tests that require the identification of a target are ameasurement of resolution acuity. These tests frequentlyinvolve identifying a letter or reporting an object’s orienta-tion (what direction is this letterC facing?). Acuity for thesetests depends on the separation of the target features: ifthey are too close, the point-spread function from eachelement will overlap and they will not be identified(Figure 1(b)). The smallest separation of the elementsrequired for identification of the target (Figure 1(c)) isknown as the minimum angle of resolution (MAR). For anadult observer with good vision, a typical MAR for acentrally presented, high-contrast target can be as good as30 s of arc (1/120�). Figure 2 shows the feature critical forthe MAR for some commonly used tests of visual acuity.

Measurement of Visual Acuity

Visual acuity tests have been used for millennia: theancient Egyptians are reported to have used discrimina-tion of the twin stars of Mizar and Alcor as a measurementof vision. The most familiar clinical test of visual acuity,the Snellen chart, was introduced in 1862, and is stillwidely used today.

Detection acuity is often measured psychophysicallyby means of a temporal two-alternative forced-choiceexperiment (did the light appear in the first or the secondinterval?). Detection acuity is rarely measured clinically.

In psychophysical experiments of the visual system,resolution acuity is commonly measured by asking obser-vers to report the orientation of a grating with variableseparation between each dark and light bar (Figure 2(b)).In clinical practice, gratings are rarely used, with theexception of forced-choice preferential looking tests inpreverbal children. These tests consist of a uniform grayfield with an isoluminant grating toward one side of thechart (Figure 3(a)). In a featureless room, the test ispresented to the child and the clinician observes whetherthe child looks toward the grating. The finest gratingtoward which the child repeatedly looks is recorded asthe visual acuity.

For cooperative patients, optotypes are more oftenused to measure clinical resolution acuity. The Landolt C(Figure 2(c)) is the standard to which letter visual acuitytests are compared. This target consists of a ring of fixedwidth with a gap, of height equal to the stroke width, atthe top, left, right, or bottom of the circle. The observer isasked to report the position of this gap. The smallest gapwhose position can be reliably reported is equivalent tothe MAR.

The National Academy of Sciences standard for visualacuity measurement advocates the presentation of 10optotypes, of equivalent difficulty to the Landolt C, ateach acuity size. The horizontal spacing between eachoptotype should be at least one character width, andvertical spacing between lines should be 1–2 times theheight of the larger optotypes. It suggests that the numberof characters on each line should be equal, and that thesize difference between consecutive lines is 0.1 log units:in other words, for each target size, the next line should beapproximately 1.26 times smaller.

The Snellen chart (Figure 3(b)) does not meet theserecommendations: the number of letters per line and step

1

size between the lines are variable, as is the horizontal andvertical spacing on the chart. There is also a markeddifference in the legibility of different letters on theSnellen chart: a W, for example, has far less separation

between the elements of the letter and is more difficultto identify than a letter L. In the 1950s, Sloan suggested theuse of 10 letters with a selection of vertical, horizontal,oblique, and round strokes which are each about as legibleas a Landolt C. These Sloan letters areC,D,H, K,N,O, R, S,V, and Z. Each of the Sloan letters has a stroke width of theMARand has a total height andwidth of five times theMAR.

The Bailey–Lovie chart, introduced before the recom-mendations of the National Academy of Sciences, con-forms to most of these requirements, although it only hasfive letters per line. Further, the letters on the Bailey–Loviechart are taller than they are wide: their height-to-widthratio is 5:4 and they are selected from the British Standardsset of letters (D, E, F, H, N, P, U, V, R, and Z). The ETDRSchart (Figure 3(c)), developed for the early treatment ofdiabetic retinopathy study (ETDRS), is similar in designbut does use the recommended 5� 5 Sloan letters.

A criterion of 7/10 letters being read correctly for a lineto be marked as seen was suggested by the National Acad-emy of Sciences. This threshold reduces the chance of theline being scored correctly by chance (by a blind observer)to around 1 in 9 000 000. On a chart with five letters per line,recording a visual acuity where four of the five letters areread correctly equates to a chance success rate of 1 in 46 000.There is a theoretical advantage if the observer knows thereare only 10 letters which can be presented on the chart: ifan observer guesses from all 26 letters rather than the tenSloan letters, the probability of the observer getting fourout of five letters correct reduces to about 1 in 100 000.

Target

(a) (b) (c)

2-DPSF

1-DPSF

Figure 1 Schematic illustration of the point-spread function of

three visual targets: (a) a point target; (b) two adjacent lines, too

close to be resolved; and (c) two adjacent lines, with sufficientseparation to be resolved. Middle row: two-dimensional

representation of the target point-spread function; bottom row:

one-dimensional representation of the point-spread function;

and red line indicates the sum of energy incident on the retina.PSF, point-spread function.

(a)

(b)

(d)

(c)

θ

θ

θ

θ

Figure 2 Examples of the limiting feature for four

commonly used resolution tasks: (a) two-point discriminationtask; (b) grating; (c) Landolt C; and (d) Sloan letter E (note that

white gap size is equal in width to black bar elements).

(a)

(c)(b)

Figure 3 (a) A forced-choice preferential looking testconsisting of a grating against an isoluminant background. Note

the peephole in the center for the clinician to observe the child’s

visual behavior; (b) the Snellen chart; and (c) The ETDRS chart.

ETDRS, Early treatment of diabetic retinopathy study.

2 Acuity

Test–retest variability of the Snellen chart is around�0.3 logMAR,while the ETDRS chart has far better repeat-ability (test–retest variability �0.1–0.2 logMAR). Despitethe many limitations of the Snellen chart, it is still widelyused in clinical practice.While this is likely to be largely dueto clinicians’ familiarity with the Snellen chart, there is also aperception that Snellen acuity measurement is quicker thanthat on the Bailey–Lovie or ETDRS charts.

Various modified versions of the ETDRS chart exist:for example, a version with an altered letter set (A, B, E,H, N, O, P, T, X, and Y) has been developed for use byreaders of most European languages, including those basedon Cyrillic or Hellenic alphabets.

For observers unable to report letters on a sight chart,other frequently used optotypes include the tumblingE chart (formerly and less politically correctly known asthe illiterate E chart), where a letter E is shown in each offour rotations; the HOTV chart, where only these fourletters are used; symbols such as the Lea or Kay pictures;and simple shapes, such as the Cardiff card.

Reporting Visual Acuity

Clinicians have traditionally used Snellen fractions torecord visual acuity, where the numerator is the testdistance and the denominator the target size. The targetsize is expressed, counterintuitively, as the distance fromwhich the target has an MAR of 1min of arc. Therefore, avisual acuity of 6/6 indicates that from 6m, letters withMAR 1-min arc are correctly identified, while a visualacuity of 3/36 indicates that from 3m, the targets identi-fied have a MAR of 1min of arc when viewed from 36m.The reciprocal of the Snellen fraction gives the visualacuity in MAR: so a visual acuity of 3/36 indicates aMAR of 12min of arc.

In much of Europe, the Snellen fraction is reduced intoa decimal fraction.

A further confusion with the Snellen system is that incountries not using the metric system, distances areexpressed in feet rather than meters, with 20/20 beingexactly equivalent to 6/6 but with a test distance of 20 ftrather than 6m. Although Snellen recommended adop-tion of the metric system in 1875 and, in 1980, the USNational Academy of Sciences favored adoption of astandard defined in meters, given the imminent adoptionof the metric system, the feet system is still widely used inthe USA, and among lay people in the UK.

The accepted standard for expressing visual acuityin clinical research, and increasingly in clinical practice,is to use the base 10 logarithm of the MAR (logMAR),such that 0.0 logMAR is equivalent to 6/6 or 20/20, and1.0 logMAR is the same as 6/60 or 20/200. Table 1 givesapproximately equivalent values inMAR, cycles per degree,Snellen fractions in meters and feet, decimal acuity, andlogMAR for a range of visual acuities.

Optical and Neural Limits on Visual Acuity

Visual acuity is limited by many factors: the optics andrefraction of the eye; the clarity of the optical media; thespacing and function of the retinal photoreceptors;the ratio of retinal ganglion cells to photoreceptors; andthe resolution of the primary visual cortex and higherareas of visual processing.

Each diopter of myopia reduces visual acuity: a –1.00DSmyope will typically have uncorrected visual acuity ofaround 0.5 logMAR (6/18; 20/60) and a two-dioptermyope will have vision of around 0.8 logMAR on a distancetest. Hypermetropia can often be relieved by accommoda-tion in young people, but each diopter of hypermetropia

Table 1 Visual acuity conversion tablea

MAR (min) Cycles/ degree Snellen (metric) Snellen (feet) Decimal Log MAR

60 0.5 1/60 20/1200 0.017 1.8

20 1.5 3/60 20/400 0.05 1.3

10 3 6/60 20/200 0.1 1

6.3 4.7 6/36 20/120 0.17 0.84 7.5 6/24 20/80 0.25 0.6

3.2 9.4 6/18 20/60 0.33 0.5

2 15 6/12 20/40 0.5 0.31.6 18.8 6/9 20/30 0.67 0.2

1.3 23 6/7.5 20/25 0.8 0.1

1 30 6/6 20/20 1 0

0.83 36 6/5 20/17b

1.2 �0.10.67 44 6/4 20/13

b

1.5 �0.2

0.5 60 6/3 20/10 2 �0.3

0.33 91 6/2 20/7 3 �0.4

aEach row contains approximately equivalent values of visual acuity. Log MAR values have been rounded to 1 decimal place.bOn US Snellen charts, these lines are 20/16 and 20/12 respectively.

Acuity 3

beyond the accommodative ability of the eye will reducevisual acuity by a similar amount to an equivalent degree ofmyopia. Astigmatism, particularly where the meridia ofastigmatism are oblique, will also reduce uncorrected visionsignificantly.

Other aberrations of the eye beyond defocus and astig-matism further limit visual acuity. Retinal image qualitycan be improved by viewing monochromatic stimuli (toreduce chromatic aberration) and by using a deformablemirror to correct coma, trefoil, and other higher-orderaberrations of the eye. Under these ideal conditions,Williams and colleagues have shown that subjects areable to resolve gratings of up to 55 cycles per degree,equivalent to a visual acuity of approximately –0.30logMAR (6/3; 20/10).

Assuming that an image is perfectly focused on theretina, the next limit on visual resolution is the spacing ofthe retinal photoreceptors. In order to detect a grating,alternate black and white bars must fall on adjacentphotoreceptors. This theoretical limit of vision, knownas the Nyquist limit, is equivalent to a grating with lightto dark separation of 1/√D, where D is the center-to-centerseparation of two photoreceptors. In the fovea, D is approx-imately 3mm, equivalent to a visual angle of approximately55 cycles per degree – almost identical to the value foundby Williams. This confirms that in people with goodvision, all of the limits on visual acuity are precortical.Amblyopia, where vision is reduced despite the absenceof any eye disease, is dealt with elsewhere in theencyclopedia.

Visual Acuity across the Retina

Nonfoveal vision is limited by many elements. First, theeye’s optics are not optimized for viewing off the visualaxis, and peripheral vision is subject to greater aberrationthan central vision. Second, the size of photoreceptorsincreases and their density falls with increasing eccentric-ity. The number of photoreceptors per retinal ganglioncell also increases, from less than one photoreceptor perganglion cell in the fovea to more than 20 photoreceptorsper ganglion cell in the far periphery. The volume ofvisual cortex devoted to noncentral retina is also propor-tionally lower. It is unsurprising, therefore, that visualacuity falls quickly with increasing distance from thefovea (Figure 4). This is one reason for the severelyreduced visual acuity of people with central vision lossfrom diseases such as age-related macular disease.

Visual Acuity over Life

Over the first year of life, visual acuity assessed by apreferential looking test appears to be reasonably stable

at around 6min of arc. Between a child’s first and thirdbirthday, visual acuity improves exponentially to reach1min of arc. A further small improvement in resolutionability to approximately 0.75min of arc is achieved by age5 years. In the absence of eye disease, this value remainsrelatively constant until the sixth decade. In a population-based study of nearly 5000 older adults, Klein found adecrease in visual acuity to a mean value of approximately2min of arc in those aged over 75 years. Of course, thisreflects the age-related nature of many diseases which affectvisual acuity, such as cataract, glaucoma, diabetic retinopa-thy, and age-related macular degeneration. Figure 5 plotsdata from the studies of Mayer and Klein.

Visual Standards

In most countries, there is a visual-acuity requirement forcar drivers. While the level and measurement techniquevaries between countries, the acuity limit is usuallyapproximately 0.3 logMAR. Commercial airline pilotsare required to have a binocular visual acuity of 0.0logMAR.

Best corrected binocular visual acuity of 1.0 logMARor poorer is used as a definition of low vision or partialsight in many countries, with acuity of worse than 1.3logMAR being described as severe sight impairment.

Hyperacuity

Some visual tasks can be performed with a far greaterdegree of precision than would be suggested by the MAR.Alignment tasks such as Vernier discrimination (wherethe offset of one line with respect to another is detected,Figure 6(a)) can be performed with misalignment of less

00 2010 40 605030

50

100

150

200

250

Eccentricity (�)

Lette

r vi

sual

acu

ity (

min

arc

)

Figure 4 Letter visual acuity measured in peripheral vision as a

function of degrees of eccentricity. Data from Anstis, S. M.(1974). Letter: A chart demonstrating variations in acuity with

retinal position. Vision Research 14(7): 589–592.

4 Acuity

than 5 s of arc – considerably less than the center-to-center spacing of a foveal photoreceptor. This is thoughtto be due to interpolation of the inputs of two or moreadjacent neural elements.

Dynamic Visual Acuity

Throughout this article, visual acuity has been discussedfor static targets. If the target is moved, central visualacuity decreases: the faster the target moves, the larger it

must be for it to be seen. If a target moves with velocity of40� s�1, the MAR is increased to about 2min of arc, whileat 80� s�1, acuity is about 3min of arc.

In peripheral vision, slow image motion (less than10� s�1) slightly improves visual acuity for peripherallypresented targets, perhaps because it breaks the phenom-enon of Troxler fading.

Target motion at the retina can be induced by targetmovement, by eye motion, or by head motion. Many eyediseases, particularly those of the macula, are associatedwith poor fixation stabilityof the eye.This poor eye stabilityincreases retinal image motion, and is significantly asso-ciated with poorer visual function. Small degrees of headmotion do not significantly decrease visual acuity undernormal conditions, but have a marked deleterious effect forsubjects viewing through telescopic spectacles. Therefore,subjects withmacular disease who have poor fixation stabil-ity and who view through telescopic low-vision aids have amarked impairment in their dynamic visual acuity.

See also: Chromatic Function of the Cones; Contrast

Sensitivity; Photopic, Mesopic and Scotopic Vision and

Changes in Visual Performance.

Further Reading

Anstis, S. M. (1974). Letter: A chart demonstrating variations in acuitywith retinal position. Vision Research 14(7): 589–592.

Bailey, I. L. and Lovie, J. E. (1976). New design principles for visualacuity letter charts. American Journal of Optometry and PhysiologicalOptics 53: 740–745.

Bennett, A. G. and Rabbetts, R. B. (eds.) (1989). Visual acuity andcontrast sensitivity. In: Clinical Visual Optics, pp. 23–72. Oxford:Butterworth-Heinemann.

Brown, B. (1972). Resolution thresholds for moving targets at the foveaand in the peripheral retina. Vision Research 12(2): 293–304.

Committee on vision. (1980). Recommended standard proceduresfor the clinical measurement and specification of visual acuity.Report of working group 39. Advances in Ophthalmology ¼Fortschritte der Augenheilkunde ¼ Progres en Ophtalmologie41: 103–148. Assembly of Behavioral and Social Sciences,National Research Council, National Academy of Sciences,Washington, DC

Crossland, M. D., Culham, L. E., and Rubin, G. S. (2004).Fixation stability and reading speed in patients with newlydeveloped macular disease. Ophthalmic and Physiological Optics24: 327–333.

Demer, J. L. and Amjadi, F. (1993). Dynamic visual acuity of normalsubjects during vertical optotype and head motion. InvestigativeOphthalmology and Visual Science 34(6): 1894–1906.

Klein, R., Klein, B. E., Linton, K. L., and De Mets, D. L. (1991). Thebeaver dam eye study: Visual acuity. Ophthalmology 98(8):1310–1315.

Liang, J., Williams, D. R., and Miller, D. T. (1997). Supernormal visionand high-resolution retinal imaging through adaptive optics. Journalof the Optical Society of America. A, Optics, Image Science, andVision 14: 2884–2892.

Mayer, D. L. and Dobson, V. (1982). Visual acuity development in infantsand young children, as assessed by operant preferential looking.Vision Research 22(9): 1141–1151.

010 100

1

2

3

4

5

6

Age (years)1

Vis

ual a

cuity

(m

in a

rc)

Figure 5 Variation in visual acuity over life. From Mayer, D. L.

and Dobson, V. (1982). Visual acuity development in infants andyoung children, as assessed by operant preferential looking.

Data from Vision Research 22(9): 1141–1151 and Klein, R.,

Klein, B. E., Linton, K. L., and De Mets, D. L. (1991). The beaverdam eye study: Visual acuity. Ophthalmology 98(8): 1310–1315.

(a)

(b)

Figure 6 Examples of hyperacuity tasks. Misalignment of thelower element is easily visible. (a) Vernier alignment; (b) dot

alignment: the offset of the middle dot with respect to the upper

and lower dot is easily discerned.

Acuity 5

Plainis, S., Tzatzala, P., Orphanos, Y., and Tsilimbaris, M. K. (2007).A modified ETDRS visual acuity chart for European-wide use.Optometry and Vision Science 84(7): 647–653.

Rosser, D. A., Cousens, S. N., Murdoch, I. E., Fitzke, F. W., andLaidlaw, D. A. (2003). How sensitive to clinical change are ETDRSlogMAR visual acuity measurements? Investigative Ophthalmologyand Visual Science 44: 3278–3281.

Thibos, L. N., Cheney, F. E., and Walsh, D. J. (1987). Retinal limits tothe detection and resolution of gratings. Journal of the OpticalSociety of America. A, Optics, Image Science, and Vision4: 1524–1529.

Westheimer, G. (1987). Visual acuity. In: Moses, R. A. and Hart, W. M.(eds.) Adler’s Physiology of the Eye: Clinical Application,pp. 415–428. St Louis, MO: Mosby.

6 Acuity