MISCELLANEOUS

Resolution acuity versus recognition acuitywith Landolt-style optotypes

Sven P. Heinrich & Michael Bach

Received: 22 May 2012 /Revised: 17 May 2013 /Accepted: 11 June 2013# Springer-Verlag Berlin Heidelberg 2013

AbstractBackground International standards define acuity as the re-ciprocal of the threshold gap size of a Landolt C optotype.However, the literature is inconsistent as to what type ofacuity is measured with Landolt Cs. The present study ad-dresses this question more directly than previous studies byquantifying the effect of an inherent luminance artifact inLandolt-style optotypes.Methods Two groups of modified optotypes were used. Inthe first group, each optotype had a single gap structure withthe same average luminance. Between optotypes, the gapstructures differed in their degree of fineness. In the secondgroup of optotypes, a standard gap was always present,defining the orientation of the optotype. Additional gapstructures of the same average luminance, but different fine-ness, were inserted at the remaining potential gap locations,thereby balancing luminance across potential gap locations.Visual acuity measures were obtained for each optotypevariant, using a computer-based test employing a staircaseprocedure.Results Similar acuity values were obtained for all optotypesof the first group, and for standard Landolt Cs, irrespective ofthe fineness of the gap structure. With luminance-balancedoptotypes of the second group, measured acuity was halved,compared to standard optotypes.Conclusions The results support the view that it is recognitionacuity, rather than resolution acuity, which is measured withstandard Landolt-style optotypes, with the imbalanced lumi-nance distribution serving as a cue. Luminance-balanced

optotypes may help to obtain a more veridical estimate ofresolution acuity, although recognition acuity may be morerelevant in daily living.

Keywords Visual acuity . Shape perception . Landolt C .

Resolution . Recognition

Introduction

Visual acuity is typically estimated by requiring the subjectto identify optotypes of different sizes. If the subject cannotperceive the optotype clearly, the subject should indicatewhat he or she thinks is the most likely optotype (“forcedchoice”). The size of an optotype is usually given in terms ofthe size of its critical detail. The critical detail of a Landolt Coptotype is its gap. International standards [1] define acuityas the reciprocal of the gap size of a threshold Landolt C. Itseems plausible, however, that it is not the gap as such that isrecognized at stimulus sizes near threshold. Rather, the ob-server perceives a blob with a slight irregularity that resultsfrom differences in local luminance. The origin of this lumi-nance difference is obvious, because the gap luminance isnecessarily different from the luminance of the remainder ofthe ring. In order to infer the orientation of the optotype, it isthus sufficient to assess the luminance irregularity, withoutactually resolving the gap [2]. Or, as Liu et al. [3] put it,subjects could simply judge “which side of the stimulus hasless ink”. One way of quantifying this irregularity is tocompute the spatial frequency spectrum of the optotypes.The anisotropy in the low-frequency content may help inguessing the orientation of a Landolt C [4, 5]. Among thespatial frequencies with an anisotropy, it is not necessarilythe one with the largest amplitude or power on which sub-jects base their decision [6].

As pointed out by Pirenne [7], “there are in fact as many‘visual acuities’ as there are types of test objects”. These

The authors have full control of all primary data, and agree to allowGraefe’s Archive for Clinical and Experimental Ophthalmology to reviewtheir data upon request.

S. P. Heinrich (*) :M. BachSektion Funktionelle Sehforschung, Univ.-Augenklinik Freiburg,Killianstr. 5, 79106 Freiburg, Germanye-mail: sven.heinrich@uniklinik-freiburg.de

Graefes Arch Clin Exp OphthalmolDOI 10.1007/s00417-013-2404-6

acuities are typically classified into several categories, in-cluding “resolution acuity” and “recognition acuity”. Rea [8]defines resolution acuity as “the ability to detect that thereare two stimuli, rather than one”, while recognition acuity is“the ability to correctly identify a visual target, as in differ-entiating between a G and a C”. The literature is inconsistentas to what type of acuity is assessed with Landolt Coptotypes. Some authors associate these optotypes with res-olution acuity [9–13], while others rather assume that recog-nition acuity is measured [14–16].

An extensive discussion of recognition acuity versus reso-lution acuity with reference to a number of older publicationsis provided by Schober [17]. He concludes that shape percep-tion plays a larger role in Landolt C discrimination than theability to resolve the gap. On the other hand, a study byAnderson and Thibos [18] on Tumbling E optotypes favorsthe opposite view. The authors compared thresholds for thediscrimination of leftwards- versus upwards-oriented E stim-uli to thresholds for horizontal versus vertical discriminationthree-bar gratings optotypes of the same size. They found nosizable differences. This suggests that adding the fourth bar ofthe E (orthogonal to the three grating-like bars) does notfacilitate optotype discrimination, despite creating a lumi-nance imbalance. Assuming that these results can be trans-ferred to the question at hand, we should expect Landolt Cs toyield resolution acuity.

In the present study, we disentangle recognition and reso-lution in the case of Landolt-style optotypes more directlythan in previous studies, and we quantify the difference inacuity values that is associated with the distinction betweenrecognition and resolution. We do this by demonstrating thatthe outcome of an acuity test is not directly related to theability of the subject to resolve the critical detail. Rather,optotypes differing in the fineness of their critical detail yieldsimilar acuity estimates if their luminance distributions areindistinguishable at near-threshold sizes. Using luminance-balanced optotypes that largely eliminate the luminance dif-ferences between the actual gap position and the other poten-tial gap positions, we assess to what degree the luminancecues affect the measurement of acuity. This is essentially anapplication of the principles laid down in Aulhorn’s [19]seminal work on the relationship between light perceptionand recognition acuity.

Below, we will use the term “primary position” for the gapposition at which the gap that determines the orientation ofthe optotype is located (this corresponds to the position of theonly gap in the standard Landolt C). “Secondary positions”are all other positions of a given optotype that could be takenby the primary gap, but are not taken in the current instanceof the stimulus. For example, a typical four-orientationLandolt C oriented rightwards has its primary gap positionon the right side and secondary positions on the top, bottom,and left sides. The need for this terminology will become

clear below when the luminance-balanced optotypes aredescribed.

Methods

The study was approved by the local review board and ad-hered to the tenets of the Declaration of Helsinki. All tensubjects provided written informed consent prior to the exper-iment, and participated wearing their habitual refraction. Theoptotypes were presented using a custom psychophysics pack-age based on Igor Pro (Wave-metrics Inc.). A small OLEDmonitor (12.8 mm×9.0 mm) (eMagin Corporation, Bellevue,WA, USA) displaying 852×600 pixels was placed 2 m awayfrom the observer. This provided enough spatial resolution toaccurately display all details of the optotypes’ gap structureswhile at the same time optotype sizes remained wellbelow the screen size. Optotype and background lumi-nance were approximately 2 cd/m2 and 480 cd/m2 respective-ly. The monitor was calibrated such that the luminance of graystimulus parts, if present, was close to the average of the twoluminance values.

Subjects indicated the orientation of the optotype by press-ing a key on a keypad. Starting with a gap of 0.0 log arcmin,the optotype size was adjusted trial-by-trial based on an adap-tive staircase procedure during a sequence of 50 trials, usingweighted upwards and downwards steps. This technique al-lows for targeting arbitrary points on the psychometric func-tion [20]. For the first 15 trials, the staircase procedure targetedthe threshold (56.25 % correct responses), and for theremaining trials, the staircase procedure branched intotargeting two points in the transition region of the psychomet-ric function below and above the threshold (38.75 % and73.75 % correct responses respectively). This ensured thatnot only the threshold, but also the slope of the psychometricfunction could be determined reliably. The sequence ofoptotype styles was randomized between observers, and beforethe actual test runs, a training run with 30 trials was performedfor each optotype style to avoid practice effects that wouldintroduce additional variability between conditions [21].

The present study used optotype styles with critical detailsthat spatially differ with respect to the gap structure withoutdiffering in average luminance. Specifically, the followinggap structures were used (Fig. 1):

1. Single. The gap consists of a single opening, as in astandard Landolt C.

2. Double. Two small openings, each of half the size of thesingle gap, separated by a black segment of the samewidth.

3. Triple. Three small openings, each of one third of thesize of a single gap, separated by black segments of thesame width.

Graefes Arch Clin Exp Ophthalmol

4. Gray. Instead of having background luminance, the lu-minance of the gap was set to the mean of backgroundand stroke luminance along a distance of twice the widthof a single gap.

5. Thin. Instead of having an opening, the optotype strokewas thinned by 50 % along a distance of twice the widthof the single gap.

Irrespective of the actual spatial extent of these structures, wewill quantify their size in terms of the size of a single gap thatwould yield the same average luminance. We will also continueto generically use the term “gap” in singular even if the respectivestructure consists of multiple openings or has no opening at all.For a given gap size, these structures differ among each otherwith respect to their fineness. For a given resolution of the visualsystem, the respective optotypes created from these differentstructures should therefore yield different acuity estimates ifoptotype identification is based on resolving (in a strict sense)the critical detail. On the other hand, the luminance distribution inthe gap region is very similar for all different gap structures. Thus,if optotype identification relies on the recognition of the blurredshape, no sizable difference between gap structures is expected.

The optotypes used in the experiments were square ratherthan circular. This shape was previously used by other authors[22, 23], and possibly first suggested by Thorington in 1908(as referenced by Ewing [24]). In the present study, the ad-vantage of the square shape was that it avoided luminance

artifacts that result from the gaps having parallel edges thatwould cut the contour line of the circular Landolt C ring non-radially. Because the modified gap structures take up morespace than the single standard gap, these artifacts wouldbecome more pronounced than in the original Landolt C.

Two groups of optotypes were included into the set of stimuli.For demonstrating the similarity of results for different criticaldetails, the first group of optotypes had exactly one of the listedstructures as critical detail at the primary position, while allsecondary positions were closed (unbalanced optotypes; Fig. 1,top). As a reference, we also tested a square optotype with only asingle standard gap at the primary position, and a standard roundLandolt C. The second group of optotypes was luminance-balanced, with a standard single gap as critical detail at theirprimary position, and one of the other gap structures inserted atall three secondary positions (balanced optotypes; Fig. 1, bot-tom). Altogether, ten different optotype styles were included inthe experiment. Figure 2 shows examples of how some of theseoptotypes appear with dioptric blur. Both single and double gapunbalanced optotpyes become indistinguishable, showing thesame luminance asymmetry. The balanced optotype, on the otherhand, is almost symmetric when blurred by the same amount.

Analysis

For each optotype style, the psychometric function was deter-mined from the response data through a maximum likelihood

Landolt C single double triple thingray

unbalanced

balanced

Fig. 1 Optotype styles used in the present study. The top row shows‘unbalanced’ optotypes, including the standard round Landolt C. Theseoptotypes have a gap structure on one side only. The bottom row shows

‘balanced’ optotypes, which have a single gap on one side and gapswith a different structures on the other three sides, such that the meanluminance is the same on all four sides

0.65 0.70 0.75 0.80 0.85 0.90 0.95

Fig. 2 Dioptrically blurred examples of three optotype styles, computedvia a Fourier-optical model [25] assuming a gap size of 18 arcmin and adefocus of +6 D. Isolumes were added for easier discrimination. With anunbalanced single gap (left) and an unbalanced double gap (middle), theoptotypes are virtually identical when blurred. Although they have nodiscernible gap, their luminance distribution is asymmetric. With the

balanced optotype (right), the luminance distribution is nearly symmetric.The numbers in the legend of the isolumes indicate gray level on a linearscale. Values of 0.0 and 1.0 would correspond to black and white,respectively. Note that the the reproduction of gray levels of the blurredoptotypes in print or on a screen without gamma correction is likely to beinaccurate

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fit of a cumulative gaussian. As acuity is defined as thereciprocal of the threshold gap size, we evaluated subjectperformance in terms of the threshold gap size for a givenoptotype, measured in minutes of arc (arcmin). Logarithmicvalues were used for analysis.

Besides quantifying the effect of balancedness, we testedthe following main hypotheses explicitly.

1. Gap size thresholds for unbalanced optotype do notdiffer sizably among each other, irrespective of the fine-ness of the gap structures.

2. Gap size thresholds for balanced optotypes are sizablyhigher than for unbalanced optotypes.

We defined ‘sizeable’ as exceeding 0.1 log arcmin thresholddifference, which is at the lower end of the range of test–retestvariabilities typically found in Landolt C acuity tests [26–28].We furthermore assessed whether there is a difference betweenbalanced and unbalanced optotypes in the widths of their re-spective psychometric functions. The width of a psychometricfunction is inversely proportional to the slope [29].

Results

In most subjects, psychometric functions were similar fordifferent unbalanced optotypes, and differed between bal-anced and unbalanced optotypes (see Example in Fig. 3).

Gap size thresholds

Unbalanced optotypes all yielded similar acuity estimates,irrespective of the gap structure, which were slightly betterthan those obtained with a standard round Landolt C, whilevalues obtained with balanced optotypes were clearly worse(Fig. 4, left). Before testing the specific hypotheses, weperformed an omnibus two-way repeated measures ANOVA(balancedness (2)×gap structure (4), single-gap unbalanced

optotype not included in ANOVA design). This identifiedboth factors, balancedness and gap structure, as well as theinteraction between them, as significant (P<0.0001 for each).Pairwise comparisons showed that the balanced double gapoptotype yielded higher thresholds than other balancedoptotypes (P≤0.004 for all comparisons, significant with cor-rection for multiple testing), whereas there were no significantdifferences between other balanced optotypes.

To quantify the effect of balancedness, we used the un-balanced single-gap optotype as a reference. The medianacuity values obtained with the other unbalanced optotypeswere only marginally worse, by 0.02 log arcmin whenpooled across gap structures. Acuities with balancedoptotypes were considerably worse, namely by a median of0.38 log arcmin. Excluding the balanced double-gapoptotype, which differed significantly from the other bal-anced optotypes (see above), the difference between bal-anced and unbalanced optotypes was 0.35 log arcmin. Theconfidence intervals (Fig. 4, left) support our main hypoth-eses, namely that threshold gap sizes for the various unbal-anced optotypes differed by less than 0.1 log arcmin from theunbalanced single-gap optotype, and that the respectivethreshold for the various balanced optotypes differed bymore than 0.1 log arcmin from the balanced single-gapoptotype. We confirmed this further by performing the re-spective t tests for each optotype (P≤0.001 for every com-parison, significant with correction for multiple testing).

Widths of the psychometric function

The widths of the psychometric functions showed consider-ably less differences between unbalanced and balancedoptotypes than the thresholds (Fig. 4, right). In absoluteterms, pooled across gap structures, the difference was 0.04log arcmin in the median, which is significant (two-wayrepeated measures ANOVA, balancedness P=0.018, gapstructure, P=0.41, interaction P=1.0, single-gap unbalancedoptotype not included in the ANOVA design).

Discussion

The present study was designed to test two main hypotheses,both of which were confirmed.

1. The results obtained with unbalanced optotypes show thatacuity estimates are similar for critical structures thatdiffer in their degree of fineness, which suggests that itis not actually the fineness of the gap structure as suchwhich determines whether the optotype can be recognizedby a given subject. This can be explained by very similarluminance distributions near threshold, and implies that itis not the resolution threshold which is measured with

Fig. 3 Examples of psychometric functions of one subject. Thresholdsfor unbalanced optotypes did not depend on the type of gap structure.The psychometric function for the balanced optotype, however, wasshifted towards larger sizes and was less steep

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unbalanced optotypes. With balanced optotypes, acuitymeasures are largely uncontaminated by luminance cues.

2. The difference between balanced and unbalancedoptotypes of 0.35 log arcmin equals a factor of about2.25 on the non-logarithmic acuity scale. This reflectsthe need for resolving details of the gap structure in orderto identify the orientation of a balanced optotype, whichis unnecessary for recognizing unbalanced optotypes.

The finding that balanced optotypes with a doublegap yield the highest threshold estimates further sup-ports the second point. Because the double gap is closerto the single gap in spatial extent than are the other gapstyles, identifying the single gap among double gaps innear-threshold optotypes is most difficult. It is exactlybecause resolution acuity is the dominating factor, thatthe outcome of an acuity test with balanced optotypesdepends on the spatial similarity between primary andsecondary gaps when luminance cues have largely beeneliminated.

Additional corroboration comes from the comparison toprevious studies that have assessed grating acuity, which is

not affected by luminance or shape cues. These studies haveshown that the threshold stripe width of a grating (i.e., halfthe period) is 1.4–2 times the threshold size of the LandoltC gap [14, 30, 31]. Although this factor is somewhat small-er than the difference between balanced and unbalancedoptotypes in the present study, the values are compatibleif one considers that gratings have the advantage of beinglarger than the gap structures in the present study.

The widths of the psychometric functions are also higher forbalanced optotypes, albeit the effect is less pronounced than theincrease in threshold. Wider, i.e., less steep, psychometric func-tions imply more variability in the perceptual or decisionalprocess. Speculatively, this could be the result of resolutionacuity being more affected by fluctuations in optical qualitythan recognition acuity. Such fluctuations may result fromchanges in accommodation, pupil diameter, and tear film[32–34].

The present study focused on Landolt-style optotypes thatare similar to the internationally standardized Landolt C [1]. Itis unclear at present why the situation for Tumbling Eoptotypes [18], which we mentioned in the introduction, ap-pears to be different. A priori, it seems likely that letter or digit

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Fig. 4 Gap size thresholds (left)and widths of the psychometricfunctions (right) for the variousoptotype styles, relative to therespective standard LandoltC values. On the abscissae, thestyle of the primary (only) gap isindicated for the unbalancedoptotypes, and the style of thesecondary gap is indicated for thebalanced optotypes. Individualsubjects are represented by roundnumbered markers. The boxplotsrepresent median andinterquartile range with the notchindicating the 95 % confidenceinterval for the median.Thresholds for balancedoptotypes are considerablyhigher than those for unbalancedoptotypes. The psychometricfunctions are also slightlywider for balanced optotypes

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optotypes would be similar to Landolt-style optotypes withrespect to the distinction between recognition acuity and res-olution acuity. This prediction is supported by the finding thatletter acuity is not directly predicted by the diameter of theblur circle in case of defocus [35]. However, it appears to beless straightforward to develop a generally applicable methodto create balanced letter or digit optotypes, as balancing wouldneed to strive for equalizing the luminance distributions with-in the set of letters while preserving the characteristics thatmake each letter identifiable. Could so-called “vanishingoptotypes” [36] offer a solution? These resemble high-passfiltered letters that have the same average luminance as thegray background and yield thresholds that are 0.11–0.34 logarcmin worse than those obtained with conventional letteroptotypes [37]. Similar modifications have also been usedwith Landolt Cs [5, 38, 39].

Although the concept of vanishing optotypes addressessome of the same problems as the balanced optotypes usedhere, there are important differences. As their name suggests,vanishing optotypes become invisible if the acuity is insuf-ficient to resolve the high-frequency spatial structure of theoptotype. If this point is reached, there is nothing to see forthe subject on which optotype identification could be based.The fact that the vanishing optotype’s outline represents acertain letter or an oriented Landolt C is largely irrelevant,and merely provides a means to construct a forced-choicetask. The balanced optotypes in the present study, on theother hand, do not vanish near threshold. Thus, they continueto be available for inspection by the subject. The task re-quires the subject to actually resolve the primary gap in orderto distinguish it from the secondary gaps.

In summary, the present study confirms more directly thanprevious studies that it is recognition acuity that is measuredwith Landolt C optotypes. This may be seen as a good thing,because recognition, rather than resolution, is the visual skillthat is typically needed in daily life. However, resolutionacuity as assessed with balanced optotypes may be a moredirect measurement of ‘low-level’ visual performance, andas such it may possibly be a more sensitive marker ofophthalmic pathophysiological processes while being lesssusceptible to cognitive influences.

Acknowledgments We are grateful to Felix Scharff for his help withcollecting data, and we thank our subjects for their participation. The studywas supported by the Deutsche Forschungsgemeinschaft (BA 877/18).

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