Relating vernier acuity and Snellen acuity in specific clinical populations

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.     

On the failure of spatiotemporal interpolation: a filtering model

A vernier target moving discontinuously between discrete spatial stations is seen as having a spatial offset if its component bars are presented at spatially aligning stations with a temporal delay (the interpolation effect). In agreement with previous work, we find that the threshold for detecting this virtual spatial offset is the same as that for detecting an explicit spatial offset, provided that certain spatial and temporal constraints are met. Interpolation is a completely efficient process provided that the spatial interval between stations in the movement trajectory is less than 3-4 min arc, but thereafter it shows a gradual decline in efficiency. This paper presents a model of the decline in efficiency which arises, we suggest, not because of a failure of sampling to represent the original stimulus, but because of a progressive mismatch between the sampled signal and the bandwidth of the spatial filters involved in interpolation. Our model is compared with the constant velocity model of Fahle & Poggio [Proc. R. Soc. Lond. B 213, 451-477 (1981)].     

Electrophysiological correlates of vernier and relative motion mechanisms in human visual cortex

Vernier onset/offset thresholds were measured both psychophysically and with the steady-state VEP by introducing a series of horizontal breaks in a vertical square-wave luminance grating. Several diagnostic tests indicated that the first harmonic component of the evoked response generated by periodic modulation of offset gratings taps mechanisms that encode the relative position of spatial features. In the first test, a first harmonic component was only found with targets that contained transitions between collinear and noncollinear states. VEP vernier onset/offset thresholds obtained with foveal viewing were in the range of 15-22 arc sec. Control experiments with transitions between symmetrical, noncollinear patterns (relative motion) did not produce first harmonic components, nor did full-field motion of a collinear grating. A second series of experiments showed that VEP thresholds based on the first harmonic component of the vernier onset/offset response had an eccentricity dependence that was very similar to that found in a psychophysical discrimination task that required a left/right position judgment (vernier acuity). Other recordings showed that the first harmonic of the vernier onset/offset VEP was degraded by the introduction of a gap between stimulus elements, as is the displacement threshold. The vernier onset/offset target also produced a second harmonic component that was virtually identical to the one produced by a relative motion stimulus. Displacement thresholds based on these second harmonic components showed a more gradual decline with retinal eccentricity than did the first harmonic component elicited by vernier offsets. The second harmonic of the vernier onset/offset VEP was relatively unaffected by the introduction of gaps between the stimulus elements. The first and second harmonic components of the vernier onset/offset VEP thus tap different mechanisms, both of which support displacement thresholds that are finer than the resolution limits set by the spacing of the photoreceptors (hyperacuity).     

Visual memory for vernier offsets.

Human ability to perceive and remember precise spatial relationships was investigated in a vernier acuity task. An initial ("standard") vernier stimulus with a variable offset was presented for 100 msec. After a delay of 1, 4, or 8 sec, another vernier target (the "variable" stimulus) followed, also for 100 msec. Observers compared the offsets of the two stimuli with each other. For very small offsets, discrimination between smaller and larger offsets was very precise, in the hyperacuity range. Thresholds increased linearly with the spatial offset of the standard stimulus, suggesting that the precision of the mechanism solving this spatial task scales with offset size. Control experiments suggested that this effect was not due to variations in retinal eccentricity. Thresholds also increased with increasing delay between the presentations of the two stimuli. By varying the delay, we directly measured the fading of the spatial memory trace.     

Visibility of motion in infant vernier displays, using adult subjects

Motion is frequently incorporated in stimuli used for psychophysical testing of vernier acuity in infants and young children. In such stimuli, detection of the vernier offset is necessary in order to perceive the motion. Research described in this report tested whether the perception of a vernier offset is sufficient to signal the stimulus motion in adults. We measured how motion detectability changed as a function of vernier offset for two adult subjects, using a stimulus similar to that employed by other authors to measure vernier acuity in infants and children. Motion visibility varied with offset size, achieving a detectability of motion ( d ') of 0.95 (comparable to two-alternative forced-choice thresholds) at stimulus offsets of 16–19 s arc. In comparison to the motion, the stimulus offset itself was much easier to see, being detectable on 95–100% of trials with the smallest offset, 6.6 s arc. This distinction, between the visibility of motion and the visibility of the vernier offset itself, should be considered when interpreting vernier results using such displays, especially in infants and children for whom motion may be the attractive cue.     

Evoked potentials elicited by brief vernier offsets: estimating vernier thresholds and properties of the neural substrate

The characteristics of the neural generator producing an evoked potential in response to the brief presentation of a vernier offset was investigated in three experiments. In the first study, averaged evoked potentials (EPs) recorded in response to a single vernier offset stimulus consisting of a horizontal line which changed from colinearity to noncolinearity for 100 msec every 1.5 sec were compared to responses elicited by other vernier configurations consisting of: stimuli with multiple offsets; stimuli presented in different orientations; targets with different offset features; and with the simple displacement of a colinear line. The results showed that a single vernier offset elicited a robust response if the offset was located in the central zone (1 degree) of the target. Other features of the target configuration were unimportant. Displacement of a colinear line over the same range without an offset evoked little, if any, response. In the second study, EPs were recorded in response to a single offset target which varied in magnitude from 21 to 82 sec of visual angle on different trials. The latency and amplitude of the EP response varied systematically with the amplitude of the vernier offset. Plots of EP amplitude against log of the offset magnitude were linear over the range of offsets employed. Straight lines fitted to the data and extrapolated to zero amplitude provided estimates of vernier threshold. These estimates agreed closely with psychophysical measures taken with the same targets and confirm the initial observations by Levi et al. (1983). In the third experiment, irrelevant contours were added to the vernier target in various spatial and temporal configurations. The addition of stationary, contiguous contours to the vernier target reduced the amplitude of the EP response when the contours were within 4-8 min of the offset, producing progressively less EP attenuation with increasing distance from the offset. However, brief presentation of the irrelevant contour (e.g. a single line passing through the offset) with an onset asynchrony relative to the vernier offset stimulus appropriate to assure simultaneity of the line-elicited EP and the offset-elicited EP yielded an enhanced response, i.e. to two responses added algebraically. The long latency of the offset evoked response and the summation results of the EPs generated by an offset and by a briefly presented linear contour suggests independence of the neural generators producing the response to these two targets.     

Integration regions for vernier acuity in the cat: comparative aspects of cortical scaling

The spatial region involved in vernier acuity (integration region) was behaviorally determined in cats and compared with published human data and cortical scaling parameters for the two species. Integration region was estimated from vernier thresholds obtained with: (1) gaps of various sizes between the contiguous ends of the offset contours (gap effects); and (2) irrelevant contours placed at various distances from the vernier offset (interference effects). The gap studies showed that thresholds decreased as the gap grew from 0 to 4-7 min but then increased progressively with separations greater than 7 min. In the interference studies, thresholds were increased 2-6 times when the irrelevant contours were located within 40 min of the offset. Comparing these data with available human measures showed large species differences. Converting the interference distances for both species into cortical distances using published estimates of cortical magnification factor did not resolve the discrepancy. However, a comparison of the cat data with published human data, taken at an eccentricity at which the estimated human cortical magnification factor equals that of the cat, i.e. 7 deg, showed the effects of gap size and interference distance on vernier thresholds to be remarkably similar between the two species. This similarity supports the hypothesis that positional acuity depends upon mechanisms in striate cortex, and also suggests that such acuity may be mediated by a generic neural mechanism common to mammals.     

Selectivity of the evoked potential for vernier offset

Hyperacuity thresholds of a few arc seconds can be achieved psychophysically for a variety of spatial localization tasks. The present experiments show that evoked potentials can be elicited in response to the introduction of vernier offsets, but not by the introduction of other cues to hyperacuity such as bisection or relative pattern motion, although each of these cues is equally salient psychophysically. Moreover, vernier acuity measurements and the evoked potentials elicited in response to vernier offsets are strongly degraded by the introduction of flanking stimuli 2-4 min from the vernier target. This suggests that the hyperacuity VEP is a cortical correlate of a very specific type of hyperacuity, that produced by vernier offsets (colinearity failure).     

A comparison of the effects of ageing upon vernier and bisection acuity

While most positional acuity tasks exhibit an age-related decline in performance, the effect of ageing upon vernier acuity continues to be the subject of some debate. In the present study we employed a stimulus design that enabled the simultaneous determination of bisection and vernier acuities in 36 subjects, aged between 22 and 84 years. This approach provided a means for directly testing the hypothesis that ageing affects bisection acuity but not vernier acuity by ensuring that differences in stimulus configuration and in the subject's task were kept to an absolute minimum. Optimum thresholds increased as a function of age for both bisection and vernier tasks. Inter-subject threshold variability also increased with age. Issues surrounding the comparison of absolute vernier thresholds across different studies are discussed and two important methodological factors are identified: the precise statistical method used to estimate thresholds, and the magnitude, in angular terms, of the smallest spatial offset of the elements of the vernier stimulus which can be displayed. Comparison with previously published data indicates that the discrepancy between this study and most previous investigations with respect to the effect of age upon vernier performance can be at least partly accounted for by differences in the minimum displayable vernier offset. Vernier thresholds do increase with age. The increased variability of vernier thresholds in older subjects would appear to limit the diagnostic value of the test as a means of enabling normal ageing to be distinguished from visual loss due to pathology of the eye or visual system.     

Isolation of stimulus characteristics contributing to Weber's law for position

To examine the independent contribution of various stimulus characteristics to positional judgements, we measured vernier alignment performance for three types of Gabor stimuli. In one, only the contrast envelope of the upper and lower stimulus elements was offset, with the luminance-modulated carrier grating remaining in alignment. In the second, only the carrier grating was offset. In the third, both carrier and envelope were offset together. Performance was examined over a range of element separations. When both cues are available, thresholds for small separations are dominated by carrier offset information and are inversely proportional to carrier frequency. At large separations, thresholds are governed by the spatial scale characteristics of the envelope. For broad-band stimuli such as lines, bars or dots typically used for vernier acuity, their higher frequency content can be used when separations are small, but as separation increases a smooth transition between the scales that determine threshold results in the continuum known as Weber's law for position. That is, with increasing separation, larger scales must be used, and thresholds increase in direct proportion to 1/frequency.     

Temporal phase discrimination depends critically on separation

Temporal phase discrimination was measured as a function of spatial separation of the stimulus components. In contrast to many previous studies, phase discrimination thresholds were measured directly, rather than inferred from the ability to discriminate synchronous from antiphase stimuli, or from segregation or shape tasks. For abutting bars, relative phase thresholds were closely proportional to temporal frequency. The proportionality corresponded to a threshold temporal offset of 2.5-9.5 ms, across subjects. Introduction of a small gap (0.125 degrees or greater) led to a dramatic (3- to 7-fold) increase in thresholds for temporal phase discrimination, and thresholds were no longer proportional to temporal frequency. Insertion of a third bar filling the gap resulted in a recovery of the low thresholds, provided that its modulation was consistent with apparent motion across the three bars. Below 8 Hz, phase discrimination thresholds across three bars were equivalent to thresholds for two abutting bars. Above 8 Hz, phase discrimination thresholds for the three bar combination were lower than thresholds for two adjacent bars, implying that phase information was integrated across all three bars.Phase discrimination thresholds do not appear to reflect the properties of a single mechanism. Especially at high temporal frequencies, low thresholds for phase discrimination are closely tied to the presence of apparent motion. Temporal phase discrimination is markedly impaired by a small separation of stimulus components. Moreover, the inability to detect phase differences across gaps corresponds to the loss of phase-dependence of vernier acuity thresholds across gaps.     

Vernier in Motion: What Accounts for the Threshold Elevation?

Vernier acuity is susceptible to degradation by image motion. The purpose of this study was to determine to what extent vernier thresholds are elevated in the presence of image motion because of reduced stimulus visibility, due to contrast smearing, or to a shift in the spatial scale of analysis. To test the visibility hypothesis, we measured vernier thresholds as a function of stimulus velocity (0–6 deg/sec), for various levels of stimulus visibility, each normalized to the detection threshold at the respective velocity. Contrary to the prediction of the visibility hypothesis, vernier thresholds worsen as the velocity increases, even when the stimuli are equally visible. To test the shift in spatial scale hypothesis, we determined spatial frequency tuning functions for vernier discrimination and line detection tasks, using a masking paradigm. We measured vernier and line detection thresholds as a function of spatial frequency of a sine-wave mask (0.5-32 c/deg), and for stimulus and mask velocities ranging from 0 to 4 deg/sec. Peak masking for both vernier discrimination and line detection, which indicates the most sensitive band of spatial frequencies for each task, shifts systematically toward lower spatial frequencies as the velocity increases. The progressive increase in spatial scale largely accounts for the worsening of vernier thresholds for moving stimuli. Differences between peak masking for vernier discrimination and line detection were found at 0 and 1 deg/sec, suggesting that different mechanisms mediate the two tasks, at least at low velocities. The masking results are consistent with previous findings that directionally selective motion detectors mediate detection of moving stimuli, but suggest that these detectors do not analyze vernier offsets. We conclude that the elevation of vernier threshold for a moving stimulus is accounted for primarily by a shift of sensitivity to mechanisms of lower spatial frequency, and not by decreased stimulus visibility. Copyright © 1996 Elsevier Science Ltd.     

Sensitivity to stimulus onset and offset in the S-cone pathway

Previous work [Vassilev, capital A, Cyrillic., Mihaylova, M., Racheva, K., Zlatkova, M., & Anderson, R. S. (2003). Spatial summation of S-cone ON and OFF signals: Effects of retinal eccentricity. Vision Research, 43, 2875-2884; Vassilev, A., Zlatkova, M., Krumov, A., & Schaumberger, M. (2000). Spatial summation of blue-on yellow light increments and decrements in human vision. Vision Research, 40, 989-1000] has shown that spatial summation of brief S-cone selective stimuli depends on their polarity, increments or decrements, suggesting involvement of S-ON and OFF pathways, respectively. This assumption was tested in two experiments using a modified two-color threshold method of Stiles to selectively stimulate the S-cones. In the first experiment we measured detection threshold for small 100ms S-cone selective increments and decrements presented within three types of temporal window, rectangular, ramp onset/rapid offset and rapid onset/ramp offset. The ramp-onset threshold was higher than the ramp-offset threshold regardless of stimulus sign. In the second experiment we measured reaction time (RT) with near-threshold stimuli spatially coincident with the background to avoid spatial contrast. RT distribution for S-cone selective 500ms increments and decrements was unimodal and followed stimulus onset. An increase of stimulus duration to 1000 and 2000ms resulted in the appearance of responses following stimulus offset. The results suggest that, for brief S-cone selective increments or decrements, the human visual system is more sensitive to stimulus onset than to stimulus offset. Only for longer stimuli is the offset important, probably due to slow adaptation at a postreceptoral level.     

Exposure duration affects the sensitivity of vernier acuity to target motion

Threshold vernier acuity was measured under different conditions of target movement and exposure duration. In the case of a simple two-line vernier target, image motion up to about 3 deg/sec had little effect upon threshold for a briefly exposed (150 msec) target, which is relatively poor even for a stationary stimulus, but produced a decrement in acuity for a continuously exposed stimulus. This finding was repeated in a second experiment, which used a centroid cue to vernier offset, and which compared the effects of horizontal and vertical target orientation. It is suggested that image motion and reduced exposure duration restrict the proportion of the light spread function that can be usefully sampled by the neural networks responsible for hyperacuity.     

The imprecision of stereopsis

In comparison to lateral judgments of distance, stereoscopic judgments are not precise. Although stereoacuity thresholds for targets presented in the fixation plane can equal the best thresholds for the monocular hyperacuities, i.e. a few sec arc, the increment thresholds for disparity are substantially larger than the increment thresholds for lateral separation (width). We measured the minimum detectable change in the three-dimensional distance separating two features, one presented in the fixation plane, and the other some distance in front of it, i.e. with a significant standing disparity between the two features. For briefly-presented targets (150 msec), the Weber fraction for disparity was 10-20% over the range from 1 to 20 min arc, while the Weber fraction for width was only 2-3% under comparable conditions. The disparity thresholds were substantially improved for a longer duration target (1000 msec), but they were still a factor of two worse than the monocular width thresholds. In a related experiment, the vernier acuity for a standard vernier target was profoundly degraded by pairing the offset upper line presented to one eye with a disparate line in the other eye; the vernier threshold was elevated for disparities ranging from 3 to 30 min arc. This finding shows that the more precise monocular signals are actively suppressed in fused or partially-fused stereoscopic images.     

Vernier acuity is less than grating acuity in 2- and 3-month-olds

Vernier acuity and grating acuity were measured longitudinally starting at 1 or 2 months of age in 22 infants, using a two-alternative, forced-choice preferential looking technique. For vernier acuity, the motion-sound display was employed. For grating acuity, a preferential looking method was employed. Steps of the stimulus (vernier offset and spatial frequency of the grating) and procedures were basically identical between the two acuity tests. The range of stimuli was set so as to compare the two acuities at younger ages. Results show: vernier acuity is less than grating acuity at 11-12 weeks of age or younger, and the developmental rate of vernier acuity is greater than that of grating acuity in the first half-year of life. To interpret the data, it was speculated that: the mean sampling distance (center-to-center distance between receptive fields) may influence vernier acuity more than grating acuity, whereas the size of the receptive field may influence grating acuity more than vernier acuity: when the mean sampling distance is large relative to the size of the receptive field, vernier acuity may be less than grating acuity. Thus, the neonatal visual system, just as the visual system in the periphery and in strabismic amblyopia, may be characterized by spatial undersampling.     

Position acuity with opposite-contrast polarity features: Evidence for a nonlinear collector mechanism for position acuity?

Vernier acuity for opposite-contrast polarity stimuli clearly poses problems for local contrast models of relative position processing. In Expt 1 we show that vernier thresholds for abutting, or closely separated features of opposite-contrast polarity, are degraded across a wide range of stimulus strengths and configurations; but for widely separated stimuli they are more or less independent of contrast polarity (confirming and extending previous work). In Expts 2 and 3 we use a one-dimensional spatial noise masking paradigm to investigate to what extent the same mechanisms masked by this noise contribute to the relative position processing of same and opposite polarity stimuli. The orientation tuning functions determined using this paradigm are quite different for same and opposite polarity targets, for both line vernier acuity, and closely spaced two-dot alignment. However, for widely separated targets (24 min arc or more), they are similar. Over a range of separations from 3 to 30 min arc, for same and opposite polarity dots, masking is strongest at a spatial frequency of about 10 c/deg. Our results are consistent with the notion that signals from early (and relatively high spatial frequency) linear filters are collected in a second-stage nonlinear mechanism, which collates information along an orientation trajectory. We suggest that different properties of the mechanisms at each level of processing, can constrain positional acuity at small and large separations.     

The effects of a luminance-modulated background on the grating-evoked cortical potential in the cat

Averaged grating-evoked cortical potentials were recorded from area 17 of awake cats. Peak latency of early components of the visual-evoked potential (VEP) response to stimulus onset increased as a function of spatial frequency, while amplitude tended to be largest at intermediate spatial frequencies. Latency increased and amplitude generally decreased to lower spatial-frequency stimuli (less than 0.25 cycle/deg) in the presence of a uniform flickering field (UFF). The UFF had a relatively small or opposite effect on peak latency and amplitude for higher spatial-frequency stimuli (greater than 0.50 cycle/deg). The VEP response to stimulus offset was present only at low spatial frequencies and was virtually eliminated by the presence of the UFF. The effects were similar whether the target and UFF background were simultaneously presented or briefly separated; however, the UFF had no effect when the two were spatially separated. The effects of the UFF background on VEP onset response increased with increasing temporal frequency from 2-8 Hz; offset responses were affected similarly at all temporal frequencies. These effects are similar to those observed in humans and suggest that two spatio-temporally tuned mechanisms contribute to the early VEP response. In the cat, the mechanisms seem to correspond to X and Y cells in the dorsal lateral geniculate nucleus.     

Effects of spatial separation and retinal eccentricity on two-dot vernier acuity

Experiments investigated how vernier acuity for dot targets is affected by dot spatial separation and retinal eccentricity. Beck and Schwartz [Vision Res. 19, 313-319, 1979] found that the vernier thresholds increased linearly with interdot separation from 7.5 to 30 min arc. Experiment 1 showed that the vernier thresholds increased linearly with interdot separation from 0.5 to 8 deg arc. Experiments 2 and 3 showed that moving the dots into the periphery while keeping the interdot separation constant increased the threshold little if at all. The results are interpreted as supporting the hypothesis that there is (1) an encoding of dot positions in retinal coordinates, and (2) that the relative positions of the dots are made explicit in terms of the slope of the virtual line joining them. The increase in threshold with dot separation indicates that the visual system is unable to directly access and compare the retinal positions of the dots. The constancy of the threshold with eccentricity indicates that the visual system encodes the retinal positions of two well-separated dots as accurately in the periphery as in the fovea.     

Spatial attention improves performance in spatial resolution tasks.

This study used peripheral precueing to explore the effect of covert transient attention on performance in spatial resolution tasks. Experiments 1 (Landolt-square) and 2 ('broken-line') measured gap resolution and Experiment 3 measured vernier resolution. In all three tasks the target was presented alone in a large number of possible locations, ranging from 1.5-6 degrees of eccentricity in the vertical or horizontal axes. The precue indicated the target location but did not convey information regarding the correct response. Performance decreased as the gap size or the vernier offset size decreased and as target eccentricity increased. Precueing improved performance in terms of RT and accuracy in all three tasks; the eccentricity effect decreased in the cued trials of the gap resolution tasks. These findings support the idea that the performance improvement at attended locations results, to some extent, from an enhanced spatial resolution at the cued location, and not just from distractor exclusion, diminished uncertainty, or decisional factors.