Documenta Ophthalmologica 58, 71 - 77 H984). �9 Dr W. Junk Publishers, The Hague. Printed in the Netherlands.

R e l a t i n g v e r n i e r a c u i t y a n d S n e l l e n a c u i t y in s p e c i f i c c l i n i c a l

p o p u l a t i o n s

JAY M. ENOCH, EDWARD A. ESSOCK* and RICK A. WILLIAMS

School of Optometry, University of California, Berkeley, CA 94720, USA *Present address: Department of Ophthalmology, Tufts University School of Medicine, Boston, Mass., USA

Key words: vernier acuity, Snenen acuity, cataract, amblyopia

Abstract. The relationship between vernier acuity and Snellen acuity in a group of cataract patients was examined. The vernier stimulus consisted of two small spots of light, vertically separated by a variable-sized gap. The Snellen stimulus was a standard projected Snellen chart. The form of the relation between vernier and Snellen acuity was found to depend upon the vernier gap size used. Specifically, when the smaller gaps of 4 or 8 min of arc are used, the two types of acuity are linearly related. When the gap is 16 or 32 min of arc, (or if best vernier performance irrespective of gap is considered) vernier acuity is related to Snellen acuity by a power function with an exponent less than one, within this clinical population. Thus, with increasing degrees of retinal image degradation caused by cataract, optimum vernier acuity is impaired at a slower rate than Snellen acuity. Our results in cataract patients are compared to results obtained by others within a population of strabismic and anisometropic amblyopes.

Introduction

It is a pleasure to participate in this special volume honoring Prof. Bruno Bagolini. The senior author has known Prof. Bagolini since his days as a student with Prof. Hermann Burian at Iowa. Prof. Bagolini has always brought a high level of scientific vigor and integrity to his elegant studies of amblyopia, strabistnus and binocular vision. He has inspired a generation of students and provided outstanding leadership to his department and nation. In our contr ibut ion to this volume, we report some comparisons between vernier acuity and Snellen acuity tests in cataract patients and in amblyopia.

In our studies of vernier acuity in patients with degraded optical media ( 1 - 5 ) , we have noticed an interesting relationship between vernier acuity and Snellen acuity. With increasing degrees of optical stimulus degradation caused by cataract, vernier acuity generally worsens at a slower rate than does Snellen acuity, with the specific relationship depending on the particular vernier stimulus employed. We were interested in comparing our results in cataract patients to previous results obtained by others in strabismic and

anisometropic amblyopia (6). The size of the gap (in visual angle) between the two features of the

vernier alignment target is an important factor in the analysis of the vernier acuity data. Earlier studies ( 1 - 3 ) have shown that increased stimulus degradation differentially affects vernier performance at small and large gaps. This is illustrated in Figure 1 where vernier threshold as a function of

72

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Figure 1. Threshold in seconds of arc for alignment of a vernier stimulus consisting of two small spots of light (see inset) is shown as a function of the vertical gap (in minutes of arc) separating the two spots. Results are shown for four patients with cataracts varying in severity of image degradation from relatively mild (20/40 and 20/50 Snellen acuity) to severe (20/100 and 20/1000 Snellen acuity). Degradation of the retinal image by cataracts increases vernier threshold at small gap sizes to a greater degree than at larger gap sizes, thereby increasing the 'optimum' gap for which best performance is achieved. A related effect shown by these curves is an increase in the steepness of the slope of the performance curve across the smaller gaps with increasing cataract severity.

gap size is shown for four cataract patients with varying severities of stimulus degradation. With increasing stimulus degradation, the vernier alignment becomes more difficult, and also the gap size at which best performance occurs (the 'opt imum gap') increases (2, 3).

In this paper the relation of vernier acuity and Snellen acuity under condit ions of stimulus degradation is examined individually for different vernier gap sizes.

M e t h o d s

Subjects

Fifteen volunteer cataract patients were tested. Each pat ient 's cataractous eye

was tested, and in 12 cases, the companion eye was also tested. Of these 12 eyes, 5 had an intraocular lens (IOL) (20/25 acuity or better) , 6 had cataracts less severe than in the other eye (3 of these had 20/25 acuity or bet ter) , and one eye displayed no sign of cataract (20/15).

The exam of the referring ophthalmologist indicated that no visual problems other than cataracts were known to exist for any of these patients (either eye). To date, ten of the patients have undergone cataract surgery, and for these ten eyes (generally, the most severe cataracts in the group), postoperative examination verifies the lack of any apparent visual anomalies�9

The age of the patients ranged from 62 to 86 years and the mean age for the sample of 27 eyes was 68.1 years.

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Apparatus and stimuli

The vernier stimulus pattern consisted of two small (2 rain arc by 1 rain arc) dots of light (100cd/m 2) that were separated by a vertical gap (Figure t, inset). The size of the vertical gap separating the comparison dots was

variable and constituted the parameter of interest in this report. The upper dot was laterally offset by a small amount (multiples of 6 sec arc steps) to the left or right of the lower dot. Detection of the direction of this offset (i.e. 'offset threshold') was the dependent measure.

The two-dot vernier target was viewed in a very dim room on a dim background (less than. 1 cd/m 2) at a distance of 5.7 m.

Procedure

Patients were first examined objectively, and then carefully, subjectively refracted in the experimental room. The refraction was conducted in a dimly- lit room with a high contrast (99%), bright background (32 cd/m 2) projected Snellen chart (AO Project-O-Chart). Stimulus conditions were selected to optimize Snellen chart performance (i.e. low glare, high contrast), and patients were encouraged to read the chart lines slowly and with care. This procedure was employed to obtain best estimates of the patient's visual performance at his/her limit. Our Snellen acuity estimates therefore do not necessarily reflect the acuity level that might be obtained in busy clinic conditions, or patient performance in the glare-filled, normal, visual world. That our Snellen acuity estimates were consistently a line or two higher (i.e., smaller letter size) than estimates typically obtained elsewhere should be kept in mind when considering the results.

The patient was instructed to indicate the direction of the vernier offset by depressing one. of two response buttons. A computer automatically gave response feedback, recorded the response and presented the next trial. Trials differed in the magnitude and direction of offset presented. The computer determined offset direction randomly, and offset size by a staircase procedure. In this staircase, two correct responses on successive trials produced a decrement of the offset size by one step on the next trial, and one incorrect response produced an increment of one step on the next trial. By this procedure, the staircase yields an estimate of the 85.4% correct point on the underlying psychometric function. A staircase (nine reversals, approximately 20-30 trials) was begun anew for another gap size. Each patient was tested at several gap sizes in order to define the shape of the vernier acuity versus gap size function (see Figure 1). Further details about the psychophysical testing procedure are available elsewhere (3).

Results and discussion

The SneUen and vernier acuities from all 27 eyes with varying degrees of stimulus degradation were compared by plotting log Snellen acuity versus log

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Figure 2. Vernier acuity (in seconds of arc) is plotted on a log scale as a function of SneUen acuity (in seconds of arc), also on a log scale for our population of cataract patients. This log-log plot provides a means of investigating the nature of the relationship between vernier and Snellen acuity by simply fitting a straight line to the log transformed data. A best-fit line with slope equal to 1, implies a linear relation. A slope other than 1, indicates that vernier is related to Snellen acuity by a power function, the slope of the line being the exponent of the power function. Data for each gap size are analyzed independently for gaps of 4 min arc (a), 8 min arc (b), 16 min arc (c), and 32 min arc (d).

vernier acuity and determining the best fitting (least-squares) straight line (Figure 2 and 3). The log transformed data were well fit by a straight line (Table 1). The best fit line was determined separately for each gap (gaps of 4, 8, 16, 32 min of arc, and also the opt imum gap as defined above) using a least squares criterion. The slopes of the lines (Table 1) indicate that the relationship of Snellen acuity and vernier acuity differs considerably at the different gaps. At the smaller gaps of 4 and 8 min of arc (Figures 2a and b) the relationship is close to linear, as the slopes of the log transformed data are approximately 1. Thus for the stimulus condit ions of this study, vernier acuity threshold at a small gap size is approximately by a simple fraction of Snellen acuity threshold, irrespective of the amount of optical stimulus degradation. A linear fit to the untransformed data (4 and 8 min gaps) provides an estimate of the fractional relationship between vernier and

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Figure 3. The analysis described for Figure 2 was performed using each patient's optimum vernier acuity threshold (across all gap sizes). The equivalent SneUen values (calculated based on 20/20 SneUen being equivalent to 60 sec arc) are shown on both axes.

Table 1.

Gap (minutes of arc) Slope r

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Figure 4. The best-fit lines shown in Figures 2 and 3 are transferred to untransformed, linear axes to facilitate the comparison between the implied power functions. The 4 and 8 min arc curves (with slopes near 1 in Figures 2 and 3) are very nearly linear. On the other hand, the curves for 16 and 32 min arc gaps and the optimum gap are clearly decelerating power functions (i.e. exponents less than 1).

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Snellen acuity. Vernier acuity threshold is approximately 1/3 of Snellen threshold when the gap is 4 min of arc, and it is approximately 1/4 of the Snellen threshold when the vernier target gap is 8 rain of arc. Thus, at small gap sizes, Snellen and vernier acuity of the cataract patients we tested are linearly related across the wide range of optical stimulus degradation displayed here.

At the larger gaps, however, the relationship of log vernier acuity to log Snellen acuity is fit by a line with a slope considerably less than 1 (Figure 2c and d). This is also true at the optimum gap (Figure 3; also see Table 1). A slope less than unity indicates that on untransformed vernier and Snellen axes, the data are best-fit by a power function with an exponent which is less than one. The best-fitting relations determined on the log transformed data are replotted in Figure 4 on untransformed axes so that the relationships of the acuity measurements can be observed directly. Indeed, the relations are readily seen to vary from near-linear functions at the small gaps (4 and 8 min arc) to decelerating power functions at both the larger gaps (16 and 32 min arc) and the optimum gap. The pronounced flattening of the curves for the 16 rain and 32 min and the optimum gaps implies a resistance of vernier acuity performance to stimulus degradation by cataract. That is, at these gaps, as the level of optical stimulus degradation is increased, hyperacuity performance is impaired at a slower rate than is Snellen acuity.

These curves also show that the size of the gap that will least under- estimate vernier acuity differs for different levels of blur (reflected by the level of Snellen acuity). Consequently, analyzing the optically degraded vernier performance at a single gap size can greatly underestimate the best possible vernier performance. This is especially true for groups including severe levels of blur. If only a single gap is to be considered for vernier acuity testing, it is best to use a large gap size in order to more accurately assess vernier performance over a larger range of blur levels. Of course, to measure best vernier acuity performance, a number of gap sizes should be considered in order to determine the optimum gap. For this sample, best vernier acuity is related to best Snellen acuity by a power function of the form:

vernier acuity = k x (Snellen acuity) ~ [where k is a constant].

The results presented here also underscore an aspect of hyperacuity that is very important in a different context. This aspect is the relative effect of optical stimulus degradation on vernier and Snellen acuity alluded to above, and its application to clinical testing. Specifically, a given amount of stimulus degradation caused by cataract is proportionally less detrimental to best vernier acuity (i.e. at the optimum gap or even a large gap) than to best Snellen acuity. Not only is vernier acuity threshold lower than Snellen acuity threshold in an absolute sense, but it is increased by stimulus degradation at a s l ow er rate than Snellen acuity. This resistence of vernier

77

acuity to optical degradation is the basis for our use of hyperacuity in tests of visual status behind ocular opacities (2-4).

In the context of the effects of optical stimulus degradation on the relation of vernier acuity and Snellen acuity, it is interesting to consider a previous report by Levi and Klein (6) of vernier and Snellen acuities in patients suffering a neural degradation of the stimulus representation. They compared vernier acuity for a grating vernier stimulus (with no gap) and Snellen acuity with a Davidson and Eskridge 'E' chart for both anisometropic and strabismic amblyopes. They found that anisometropic amblyopes show a linear relation between vernier acuity and Snellen acuity (i.e., the slope of the best fit line on log-transformed axes is equal to 1) with the vernier acuity equal to approximately 1/4 Snellen acuity (acuities on a linear scale). This relation is similar to the relation we report at small gaps for the optical blur sample. Levi and Klein also report that strabismic amblyopes deviate from this relation, their log-transformed data being well-fitted by a power function with an exponent of 0.80. Further determinations of the way in which various types of vernier acuity, Snellen acuity, and grating acuity covary within separate clinical populations may shed light on how these visual abilities are mediated within the visual system.

Acknowledgements

This research has been supported in part by National Eye Institute Research Grants No. EY 03674, EY 03669 and Core Grant No. EY 03176 (all to JME), National Institutes of Health, Bethesda, Maryland.

References

1. Enoch JM and Williams RA (1983) Development of clinical tests of vision: Initial data on two hyperacuity paradigms. Perception and Psychophysics 33:314-322

2. Williams RA, Enoch JM and Essock EA (1983) The resistance of selected hyperacuity configurations to retinal image degradation. Invest Ophthalmol Visual Sci (in press)

3. Essock EA, Williams RA, Enoch JM and Raphael S (1983) The effects of image degradation by cataract on vernier acuity. Arch Ophthalmol (submitted)

4. Enoch JM, Williams RA, Essock EA and Barricks M (1983) Hyperacuity perimetry: Assessment of macular function through ocular opacities. Arch Ophthalmol (submitted)

5. Essock EA, Enoch JM, Williams RA, Barricks M and Raphael S (1983) Joint application of hyperacuity perimetry and gap test in assessment of visual function behind cataracts: initial trials. Arch Ophthalmol (submitted)

6. Levi DM and Klein S (1982) Hyperacuity and Amblyopia. Nature 298:268-270