May 2005
Volume 46, Issue 5
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Visual Psychophysics and Physiological Optics  |   May 2005
A VEP Measure of the Binocular Fusion of Horizontal and Vertical Disparities
Author Affiliations
  • Julia Hale
    From the Department of Ophthalmology, Bristol Eye Hospital, Lower Maudlin Street, Bristol, United Kingdom; and
  • Richard A. Harrad
    From the Department of Ophthalmology, Bristol Eye Hospital, Lower Maudlin Street, Bristol, United Kingdom; and
  • Suzanne P. McKee
    The Smith-Kettlewell Eye Research Institute, San Francisco, California.
  • Mark W. Pettet
    The Smith-Kettlewell Eye Research Institute, San Francisco, California.
  • Anthony M. Norcia
    The Smith-Kettlewell Eye Research Institute, San Francisco, California.
Investigative Ophthalmology & Visual Science May 2005, Vol.46, 1786-1790. doi:10.1167/iovs.04-0954
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      Julia Hale, Richard A. Harrad, Suzanne P. McKee, Mark W. Pettet, Anthony M. Norcia; A VEP Measure of the Binocular Fusion of Horizontal and Vertical Disparities. Invest. Ophthalmol. Vis. Sci. 2005;46(5):1786-1790. doi: 10.1167/iovs.04-0954.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

purpose. Because of the lateral separation of the orbits, the retinal images differ in the two eyes. These differences are reconciled into a single image through sensory and motor fusional mechanisms. This study demonstrates electrophysiologically the effects that normal horizontal and vertical fusional processes have on the processing of monocular position signals.

methods. VEPs were recorded in 16 healthy adults in response to a vernier onset–offset target presented to one eye. The vernier offsets appeared and disappeared at 2 Hz and were introduced into bar targets that were oriented either vertically (horizontal offsets) or horizontally (vertical offsets). The magnitude of the offsets was varied over the range of 0.5 to 10 arc min. VEP amplitude was measured as a function of the size of the dynamic offset under monocular viewing conditions and in the presence of two different static targets presented to the other eye. One of the static targets matched the dynamic test, except that it had no vernier offsets. The other static target, the static pedestal, matched the dynamic test, but contained a set of static vernier offsets in locations corresponding to the locations of the dynamic offsets presented to the other eye.

results. VEP amplitude was a monotonically increasing function of vernier offset size under monocular viewing conditions. The addition of the static target without offsets in the other eye resulted in an increased amplitude VEP response. The addition of the static target with vernier offsets resulted in a decrease in VEP amplitude for both horizontal and vertical disparities.

conclusions. The normal process of fusion results in a single visual direction. To obtain a single visual direction, the visual system must synthesize a binocular visual direction that differs from the monocular components. One of the conditions (the static pedestal with offsets) produces binocular visual direction shifts that degrade the appearance of vernier onset-offset, and reduce VEP amplitude for both horizontal and vertical disparities. This characteristic evoked response marker is a promising tool for measuring binocular fusion objectively in patients with strabismus.

Although under ideal conditions, stereoscopic judgments can be very precise (<10 arc sec), increment thresholds for disparity have been found to be substantially larger than increment thresholds for lateral separation (width) 1 —that is, there has to be a larger change in disparity than that for a comparable lateral displacement, if that change is to be detected. McKee et al. 1 also found that vernier thresholds are profoundly degraded if a vernier target in one eye is fused with a disparate target in the other eye that produces a large difference in apparent depth. The presence of fusion means that this finding cannot be explained by rivalry suppression, which has been shown to occur only in the absence of fusion. 2 It appears therefore, that the viewing of fused stereoscopic images can result in a loss of information from each monocular image. In other words, more precise information about monocular stimuli may be killed in the interest of binocular fusion, in keeping with other studies that have asserted that normal stereopsis obscures monocularly available information. 3 4 5 6  
McKee and Harrad 7 also measured psychophysical thresholds for a vertical vernier target presented to one eye that was stereoscopically paired with a disparate vernier target presented to the other eye, in both normal and stereoanomalous observers. In their two normal observers, vernier thresholds that were in the range of 6 to 10 arc sec when measured monocularly rose by a factor of 6 to 10 when the offset was paired with a disparity-creating pedestal in the other eye. Vernier thresholds were elevated for both horizontal and vertical disparities and the rise in threshold was symmetrical for presentation of the vernier target to either eye. Because fusion resulted in a loss of sensitivity, McKee et al. 1 have referred to the phenomenon as “fusional suppression” to distinguish it from other forms of sensitivity loss caused by dichoptic stimuli, such as that which occurs during binocular rivalry or dichoptic masking. 
An electrophysiological correlate of the psychophysical threshold elevation measured by McKee et al. 1 has recently been demonstrated. 8 In that method, a set of 5-arc min vernier offsets were introduced and withdrawn periodically from a field of vertically oriented bars. The evoked response to this target was measured in the presence of matching targets in the other eye. One of the matching targets led to the appearance and disappearance of a set of bars segmented in depth from a uniform-depth background. The second set of bars added a disparity to the moving portion of the display, yielding a stimulus that was always segmented into two depth planes. The evoked response in the latter case was smaller than in the former case, analogous to the psychophysical threshold elevations. 
In the present study, we used variable disparity tests to mimic the psychophysical paradigm of McKee et al. 1 The results show that response reductions were present for both horizontal and vertical disparities, consistent with previous psychophysical observations. 
Materials and Methods
Observers
Sixteen healthy adult observers with normal monocular and binocular vision and no previous history of amblyopia, patching, or intermittent strabismus consented to participate. Each observer had a corrected logMar (logarithm of the minimum angle of resolution) visual acuity of 0 (20/20) or better in each eye and normal stereopsis on testing (TNO plates; Richmond Products, Boca Raton, FL). We defined normal stereopsis as ≤60 arc min; however, the participants all had a stereoacuity of ≤30 arc min. Local ethics committee approval was obtained, and each observer gave fully informed consent. The research complied with the principles of the Declaration of Helsinki. 
Stimulus Generation and Apparatus
Stimuli were generated and signals analyzed by an in-house software package run on two computers (both Macintosh G4; Apple Computer, Cupertino, CA). One computer was used to generate dichoptic stimuli on two monitors (GS771; ViewSonic, Walnut, CA; 800 × 600 pixels; vertical refresh, 72 Hz). Separate monocular half images were drawn into the red and green bit planes of the graphics card, but the monitors were cabled to present a green image to each eye. The monitors were viewed via a mirror haploscope, so that each screen projected only to the ipsilateral eye. The viewing distance was 49 cm. Stimulus mean luminance was measured as 28.4 cd/m2 with a photometer (OptiCAL; Cambridge Research Systems, Ltd., Kent, UK) placed on each screen. Stimulus contrast was set at 80%. The stimuli were viewed under dark background conditions. 
The active VEP display, described in Figures 1 and 2 , comprised a circular image of 14° diameter. Computer-generated nonius lines for alignment in both the horizontal and vertical planes were presented around the aperture, and the stimulus was further surrounded by a fusible pattern of small circles that aided accurate superimposition of the images. The observers were asked to align the nonius lines physically, by movement of the mirrors, and to check their position between stimulus trials regularly. It has been shown that well-trained observers can detect nonius misalignment of as little as 1 arc min. 9  
VEP Stimulation Protocol
Three stimulus conditions were presented to each eye, as illustrated schematically in Figure 2 . These all consisted of the same dynamic “test” stimulus presented to one eye, with one of three static targets presented to the other eye. The monocular condition consisted of an oscillating vernier onset–offset stimulus presented to one eye and a blank field presented to the second eye. In the second condition (binocular 0 disparity), the oscillating vernier stimulus was paired with a static bar pattern instead of a blank field. The third condition (binocular 5 arc min) was the same as the second, except that the static bar pattern also contained vernier offsets. When presented alone, the static patterns did not produce a VEP response, but when fused with the temporally modulated pattern, they modified the observer’s perception of the stimulus in terms of its position in both the lateral and depth domains. 
The dynamic test pattern consisted of vertical (or horizontal) randomly generated black and green bars of spatial frequency 1 ± 0.49 cyc/deg, with 80% contrast. The pattern was divided into bands that spanned the direction perpendicular to the orientation of the bars. The bands were 1° thick and separated by 1°. An oscillating vernier pattern was created by laterally shifting these bands back and forth, into and out of alignment with the static part of the pattern, at a frequency of 2 Hz. Over a trial period of 10 seconds, the vernier offsets increased in size in 10 equal logarithmic steps from 0.5 to 10 arc min. 
When the test stimulus was combined with a blank mean luminance half image, the observers perceived purely lateral displacement. When combined with the static pattern having no vernier offsets, the direction of displacement of the vertical bars also had a component along the depth axis, so that the observers perceived the oscillating bands appearing and disappearing in depth from a collinear background. No depth was seen with vertical disparity presentations, although vertical movement of the offset regions was visible. 
In the other binocular condition, the static pattern was also divided into bands matching those in the dynamic pattern. These bands were assigned a constant lateral offset of 5 arc min in the direction opposite to that of the offset in the dynamic pattern. Thus, as the vernier oscillation swept from 0.5 to 10 arc min, the disparity of the bands swept from 5.5 to 15.5 arc min. When the pattern was vertical, observers perceived the same combination of lateral and depth motion as observed in the other binocular condition. However, in this condition, the bands never appeared to align with the background; rather, they appeared to be segmented from a static background and moving in depth. As before, no depth was seen with vertical disparities, but the stimulus retained its appearance of always being segmented. 
The three conditions were performed with the test in each eye in 13 observers who viewed crossed horizontal disparities and in 5 observers who viewed both horizontal and vertical disparities. Three observers were also tested with uncrossed disparities. For the vertical disparity conditions, the displayed images were unchanged, but the monitors were each rotated 90° in specially designed rotating cases. The only difference between these experiments was the direction of the disparity but, perceptually, fusion of the static offset bars with the test did not produce a sensation of depth for vertical disparities. 
VEP Recording Procedure
Once the mirrors were correctly aligned for stimulus fusion, the observer was directed to fixate on one of the static segments in the center of the stimulus circle. This ensured symmetrical retinal stimulation around fixation and discouraged tracking the changing disparities with convergence eye movements. Several test runs were performed to ensure that the observer was familiar with the procedure and comfortable with the mirror position. The investigator was in control of the start of each trial and monitored the EEG for excess noise or α-waves during recording. Between 20 and 30 trials, each lasting approximately 10 seconds were recorded for each condition in randomly ordered groups of five trials. The observer was not informed of the nature of the condition being presented. The observer was given a rest period after each 10 sets of five trials, or more frequently if needed. 
Signal Acquisition and Data Analysis
Recordings were made from three electrodes placed over the occipital pole at 01, 0z, and 02 of the international 10-20 system. A reference electrode was placed at Cz and a ground electrode at Pz. The EEG was amplified at a gain of 50,000 with amplitude band-pass filtering of 0.3 to 100 Hz at −6 dB on an amplifier (QP511 Quad AC; Grass-Telefactor, W. Warwick, RI). 
The raw EEG was submitted to a running spectral analysis over 1-second time intervals, providing a 10-point analysis of the 10-second sweep. For each 1-second epoch, spectral analysis was performed with a recursive least squares (RLS) adaptive filter technique, 10 in which VEP amplitude and phase (expressed as a complex number) were calculated for the first nine harmonics of the 2-Hz stimulus frequency. The complex numbers representing the amplitudes and phases were then coherently averaged over all trials for each stimulus condition and for each observer. Coherent averaging uses both amplitude and phase information. The T 2 Circ statistic 11 was used to estimate probabilities for each 1-second epoch of an averaged set of trials. Group response functions (e.g., Fig. 2 ) were obtained by computing the average over observers of the scalar amplitudes (without phase) for each 1-second epoch. 
Results
VEP response functions are shown in Figure 3for a group of 13 normal observers recorded from the Oz-Cz derivation. These data are representative of the data obtained on the other two channels. The results from the monocular viewing condition are shown as a gray line, the results of the binocular 0 arc min disparity condition are shown with solid symbols, and those from the binocular 5 arc min condition are shown with open symbols. Data are shown for the first (1F1 = 2 Hz), second (2F1 = 4 Hz), third (3F1 = 6 Hz), and fourth (4F1 = 8 Hz) harmonics. Based on previous research on the vernier onset–offset VEP, 12 the odd harmonics are known to be specific for the relative position of the static and moving elements, whereas the even harmonics are not. The even harmonic components are likely to be due to motion and contrast-transient–related activity, irrespective of direction or state of alignment. For each harmonic shown in Figure 2 , VEP amplitude increased as the size of the vernier offset increased. For the first harmonic, the amplitudes were larger relative to the monocular condition when the binocular 0-arc min pedestal was added to the other eye, but they were smaller when the binocular 5-arc min pedestal was added. The primary effect of the static pedestals is to change the maximum voltage attained. By 10-arc min disparity, the two binocular conditions yielded amplitudes that differed by approximately a factor of two for the first harmonic. A trend in the same direction is seen at the second and third harmonics, but not at the fourth and higher harmonics. 
Figure 4shows data from five observers who viewed both horizontal and vertical disparity versions of the display. Two of these observers contributed data to Figure 2 . Three of the observers were recorded for both crossed and uncrossed disparities. The dynamic test was presented to each eye, and the mean of the responses across eyes was plotted, with the error bars representing the average SE of the two recordings. As is seen in Figure 3 , the binocular 5-arc min condition resulted in a much lower response than did the binocular 0 condition. This difference was similar in magnitude with both horizontal and vertical disparities. Monocular response amplitudes (not shown for clarity) were in all cases intermediate between the binocular 0- and binocular 5-arc min conditions. Note that crossed and uncrossed terminology does not properly apply to vertical disparities. In this case, the two terms indicate the horizontal disparity of the stimulus before rotation of the displays. 
To compare the strength of the disparity pedestal effect as a function of orientation, we took 1F1 response amplitudes for each observer from the largest disparity oscillations (i.e., the rightmost data points in Fig. 3 ) and divided each binocular amplitude (0- and 5-arc min pedestals) by the corresponding monocular amplitude. We performed three-way repeated-measures multivariate ANOVA to test the effects of pedestal disparity (0 or 5 arc min), disparity orientation (horizontal or vertical), and eye tested (left or right). There was a large main effect of pedestal disparity (F(1,4) = 52.924; P = 0.002). This effect did not interact with disparity orientation, F(1,4) = 0.006; P = 0.943) nor did it interact with the eye tested (F(1,4) = 1.343; P = 0.311). There were no other significant effects or interactions. This analysis indicates that the effects of fusible pedestals are equivalent for both horizontal and vertical disparities. Averaged across orientation and eye, the binocular 0 condition yielded responses that were 1.22 ± 0.02 times the monocular condition, and the binocular 5 condition yielded amplitudes that were 0.73 ± 0.07 times those recorded monocularly. 
To quantify further the effects of the disparate pedestal, we fit the first harmonic disparity response data with Naka-Rushton (NR) functions of the form  
\[\mathrm{NR}_{i}\ {=}\ V_{\mathrm{max}}\frac{D_{i}^{n}}{D_{i}^{n}\ {+}\ D_{50}^{n}}\ {+}\ V_{\mathrm{min}}\]
, by minimizing the error expression,  
\[E\ {=}\ {{\Sigma}_{i{=}1}^{m}}\frac{(NR_{i}\ {-}\ V_{i})^{2}}{{\sigma}^{2}V_{i}}\]
, where V i and σ2 Vi are the mean and variance across trials of the VEP amplitude in response to the disparity D i . The index i ranges from 1 to m = 10, the number of disparity steps in the stimulus. V min represents the maximum voltage attainable, D 50 indicates the disparity at which amplitude reaches 50% of maximum, and V min is the minimum voltage corresponding to the electroencephalogram (EEG) noise level. 
The free parameters, V min, V max, D 50, and n were determined for all the subjects and stimulus conditions shown in Figure 3and for uncrossed horizontal disparity data from an additional nine subjects from Figure 2 . The results are summarized in Table 1 . The disparate pedestal produced a significant increase in D 50 (P < 0.001; paired t-test) and a significant decrease in V max (P = 0.001; paired t-test). The mean values obtained from fits to the individual observer’s response functions were nearly identical with the parameters obtained by fitting the group data functions shown in Figure 3(Table 2) . The exponents n were slightly lower in Table 2 , but the difference between the two pedestal conditions was well within the SEM difference across observers in Table 1 . This indicates that the response function in Figure 3is representative of the individual observer response functions. All individual observers showed a lower response when the disparate pedestal was presented as measured relative to that obtained when the nondisparate pedestal was presented. 
Discussion
The assignment of a single visual direction to objects is a critical aspect of binocular function. Because of the lateral separation of the eyes, the brain is confronted with three conflicting interpretations of the retinal images: the visual directions of each monocular representation and a third binocular visual direction. McKee and Harrad 7 suggested that a unique visual direction is obtained through local suppressive interactions between disparity detectors of different sizes. In their model, disparity-tuned units of different spatial scales at any given position are mutually inhibitory, with the magnitude of the inhibition being proportional to the unit’s activity. The addition of a large pedestal disparity optimally engages larger-scale units that in turn suppress fine-scale units. Fine-scale units in their model were needed to encode small vernier offsets, and thus they were able to explain the increase in threshold for offsets presented with a pedestal disparity. This model predicts that the magnitude of the suppression should be at a maximum for small disparities and should decrease as the test disparity approaches the size of the pedestal disparity, since, at that point, the same scale units would be engaged in symmetric mutual inhibition. In the psychophysical experiments, the test disparities were always much smaller than the pedestal disparity. The reduction in response amplitude we measured over the range of suprathreshold test disparities in the binocular 5-arc min condition is essentially constant as a proportion of either the monocular or binocular 0 amplitudes. The McKee and Harrad 7 model predicts that D 50 would shift rightward, but that V max would not be affected. We found clear effects on V max that are not consistent with this model. Based on our electrophysiological data, it appears that psychophysical threshold elevations result from a graded reduction of the vernier alignment signal represented primarily by the first harmonic response. 
In a prior study, we argued that the effect of a disparity pedestal, which creates a separation in depth between the dynamic disparity regions of our images and the static portions, may be analogous to the effect of gaps placed between two-dimensional vernier offset stimuli. 8 In the two-dimensional case, abutting stimuli produce a robust nonlinear response that decreases quickly as the image elements are separated. 12 13 14 We suggested that this interaction may also operate in three dimensions, with more interaction occurring for stimulus elements that are “coplanar.” The reductions of response in the binocular 5-arc min case would thus be expected, since the moving planes would be out of range of interaction with the static planes. In the case of vertical disparities, fusion shifts the relative positions laterally, but not in depth. As in the case of gaps, lateral misalignment also degrades the nonlinear lateral interaction (Hou C, et al. IOVS 2003;44:ARVO E-Abstract 4119), 15 which thus appears to be the maximum for collinear stimuli when there is no valid depth interpretation or for coplanar stimuli when there is. This interaction, like the cross-scale interaction of McKee and Harrad 7 could operate locally and in a feed-forward fashion. It is also possible that the interaction involves feedback from higher visual areas that maintain a global depth map of surface relationships. 
Although monocular vernier acuity is reduced with vertical disparities, 7 no sensation of depth is perceived. In this case, fusion brings about a change of visual direction, but since the horizontal disparity detectors are not activated, no depth is seen. 
Conclusions
The findings show that fusional suppression, as previously demonstrated psychophysically, 1 7 may be robustly demonstrated with the VEP. The phenomenon is equally strong for horizontal and vertical disparities and thus is not due to specifically stereoscopic mechanisms. Preliminary studies using the same methods indicate that adults with abnormalities of the binocular visual system such as strabismus and amblyopia show clear reductions in the strength of sensory fusion (Hale JE, et al. IOVS 2004;45:ARVO E-Abstract 3427), suggesting that the technique may be useful in the future for studying binocular interaction in both adult and pediatric patients. The method is an objective sensory measure and does not rely on a motor response, as does the 4-D base-out prism test. The parameters of the response function also provide a quantitative assessment of binocular function, unlike traditional measures of sensory fusion, such as the Worth 4 dot test or Bagolini glasses. 
 
Figure 1.
 
Stimulus configuration. One half-image of the actual display is shown. The display monitors of the haploscope were masked by a card containing a 25° circular aperture. VEP test stimuli and pedestals were presented behind the card in the central 14° of the display. The region between 14° and 25° contained a series of zero disparity circles as an aid to fusion. This region also contained four nonius targets presented just outside the 14° aperture at the top, bottom left, and right margins. These consisted of both horizontal and vertical elliptical nonius targets that were used for subjective alignment of the two monitors.
Figure 1.
 
Stimulus configuration. One half-image of the actual display is shown. The display monitors of the haploscope were masked by a card containing a 25° circular aperture. VEP test stimuli and pedestals were presented behind the card in the central 14° of the display. The region between 14° and 25° contained a series of zero disparity circles as an aid to fusion. This region also contained four nonius targets presented just outside the 14° aperture at the top, bottom left, and right margins. These consisted of both horizontal and vertical elliptical nonius targets that were used for subjective alignment of the two monitors.
Figure 2.
 
Schematic illustrations of the three stimulus conditions. In each recording condition (monocular, binocular 0 arc min, and binocular 5 arc min) a vernier onset–offset stimulus was presented. The offsets were introduced and withdrawn at 2 Hz, and the amplitude of the offset was swept from 0.5 to 10 arc min in 10 equal logarithmic steps. In the monocular condition, the other eye viewed a blank field; in the binocular 0 condition, the other eye viewed a bar pattern without offsets; and in the binocular 5 condition, the other eye viewed a bar pattern with a set of static 5-arc min offsets. The actual fields were circular, and there were seven moving bands (see Fig. 1 ). Vertical disparity conditions differed only in the orientation of the bar patterns.
Figure 2.
 
Schematic illustrations of the three stimulus conditions. In each recording condition (monocular, binocular 0 arc min, and binocular 5 arc min) a vernier onset–offset stimulus was presented. The offsets were introduced and withdrawn at 2 Hz, and the amplitude of the offset was swept from 0.5 to 10 arc min in 10 equal logarithmic steps. In the monocular condition, the other eye viewed a blank field; in the binocular 0 condition, the other eye viewed a bar pattern without offsets; and in the binocular 5 condition, the other eye viewed a bar pattern with a set of static 5-arc min offsets. The actual fields were circular, and there were seven moving bands (see Fig. 1 ). Vertical disparity conditions differed only in the orientation of the bar patterns.
Figure 3.
 
VEP amplitude as a function of disparity for monocular (gray line), binocular 0-arc min (▪), and binocular 5-arc min (□) pedestal conditions. Data are shown for the first four harmonics (1F1, 2F1, 3F1, and 4F1) of the 2-Hz stimulus frequency. In all cases, VEP amplitude increases as disparity increases. At the first harmonic (1F1), the binocular 0-arc min pedestal caused an increase in response amplitude relative to both monocular and binocular 5-arc min conditions. A trend in this direction was also seen for the second (2F1) and third harmonics (3F1) but not at the fourth harmonic (4F1). Average data from 13 observers.
Figure 3.
 
VEP amplitude as a function of disparity for monocular (gray line), binocular 0-arc min (▪), and binocular 5-arc min (□) pedestal conditions. Data are shown for the first four harmonics (1F1, 2F1, 3F1, and 4F1) of the 2-Hz stimulus frequency. In all cases, VEP amplitude increases as disparity increases. At the first harmonic (1F1), the binocular 0-arc min pedestal caused an increase in response amplitude relative to both monocular and binocular 5-arc min conditions. A trend in this direction was also seen for the second (2F1) and third harmonics (3F1) but not at the fourth harmonic (4F1). Average data from 13 observers.
Figure 4.
 
Horizontal and vertical disparity response functions for five subjects. Curves drawn though the data are the best-fitting Naka-Rushton functions. In each case, the 5-arc min pedestal produced a lower amplitude response than the 0-arc min pedestal.
Figure 4.
 
Horizontal and vertical disparity response functions for five subjects. Curves drawn though the data are the best-fitting Naka-Rushton functions. In each case, the 5-arc min pedestal produced a lower amplitude response than the 0-arc min pedestal.
Table 1.
 
Averages of Naka-Rushton Fit Parameters for Uncrossed Horizontal Disparity Data from 13 Subjects
Table 1.
 
Averages of Naka-Rushton Fit Parameters for Uncrossed Horizontal Disparity Data from 13 Subjects
No Pedestal 5-arc min Pedestal Mean Difference SEM P
V min 0.133 0.177 0.044 0.075 0.277
D 50 2.967 5.149 2.183 0.492 <0.001
n 2.535 2.633 0.098 0.332 0.382
V max 2.463 1.529 −0.935 0.249 0.001
Table 2.
 
Naka-Rushton Parameters for the Average Response Data in Figure 3
Table 2.
 
Naka-Rushton Parameters for the Average Response Data in Figure 3
No Pedestal 5-arc min Pedestal Difference
V min 0.154 0.174 0.021
k 2.965 5.044 2.079
n 1.974 1.893 −0.081
V max 2.358 1.468 −0.891
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Figure 1.
 
Stimulus configuration. One half-image of the actual display is shown. The display monitors of the haploscope were masked by a card containing a 25° circular aperture. VEP test stimuli and pedestals were presented behind the card in the central 14° of the display. The region between 14° and 25° contained a series of zero disparity circles as an aid to fusion. This region also contained four nonius targets presented just outside the 14° aperture at the top, bottom left, and right margins. These consisted of both horizontal and vertical elliptical nonius targets that were used for subjective alignment of the two monitors.
Figure 1.
 
Stimulus configuration. One half-image of the actual display is shown. The display monitors of the haploscope were masked by a card containing a 25° circular aperture. VEP test stimuli and pedestals were presented behind the card in the central 14° of the display. The region between 14° and 25° contained a series of zero disparity circles as an aid to fusion. This region also contained four nonius targets presented just outside the 14° aperture at the top, bottom left, and right margins. These consisted of both horizontal and vertical elliptical nonius targets that were used for subjective alignment of the two monitors.
Figure 2.
 
Schematic illustrations of the three stimulus conditions. In each recording condition (monocular, binocular 0 arc min, and binocular 5 arc min) a vernier onset–offset stimulus was presented. The offsets were introduced and withdrawn at 2 Hz, and the amplitude of the offset was swept from 0.5 to 10 arc min in 10 equal logarithmic steps. In the monocular condition, the other eye viewed a blank field; in the binocular 0 condition, the other eye viewed a bar pattern without offsets; and in the binocular 5 condition, the other eye viewed a bar pattern with a set of static 5-arc min offsets. The actual fields were circular, and there were seven moving bands (see Fig. 1 ). Vertical disparity conditions differed only in the orientation of the bar patterns.
Figure 2.
 
Schematic illustrations of the three stimulus conditions. In each recording condition (monocular, binocular 0 arc min, and binocular 5 arc min) a vernier onset–offset stimulus was presented. The offsets were introduced and withdrawn at 2 Hz, and the amplitude of the offset was swept from 0.5 to 10 arc min in 10 equal logarithmic steps. In the monocular condition, the other eye viewed a blank field; in the binocular 0 condition, the other eye viewed a bar pattern without offsets; and in the binocular 5 condition, the other eye viewed a bar pattern with a set of static 5-arc min offsets. The actual fields were circular, and there were seven moving bands (see Fig. 1 ). Vertical disparity conditions differed only in the orientation of the bar patterns.
Figure 3.
 
VEP amplitude as a function of disparity for monocular (gray line), binocular 0-arc min (▪), and binocular 5-arc min (□) pedestal conditions. Data are shown for the first four harmonics (1F1, 2F1, 3F1, and 4F1) of the 2-Hz stimulus frequency. In all cases, VEP amplitude increases as disparity increases. At the first harmonic (1F1), the binocular 0-arc min pedestal caused an increase in response amplitude relative to both monocular and binocular 5-arc min conditions. A trend in this direction was also seen for the second (2F1) and third harmonics (3F1) but not at the fourth harmonic (4F1). Average data from 13 observers.
Figure 3.
 
VEP amplitude as a function of disparity for monocular (gray line), binocular 0-arc min (▪), and binocular 5-arc min (□) pedestal conditions. Data are shown for the first four harmonics (1F1, 2F1, 3F1, and 4F1) of the 2-Hz stimulus frequency. In all cases, VEP amplitude increases as disparity increases. At the first harmonic (1F1), the binocular 0-arc min pedestal caused an increase in response amplitude relative to both monocular and binocular 5-arc min conditions. A trend in this direction was also seen for the second (2F1) and third harmonics (3F1) but not at the fourth harmonic (4F1). Average data from 13 observers.
Figure 4.
 
Horizontal and vertical disparity response functions for five subjects. Curves drawn though the data are the best-fitting Naka-Rushton functions. In each case, the 5-arc min pedestal produced a lower amplitude response than the 0-arc min pedestal.
Figure 4.
 
Horizontal and vertical disparity response functions for five subjects. Curves drawn though the data are the best-fitting Naka-Rushton functions. In each case, the 5-arc min pedestal produced a lower amplitude response than the 0-arc min pedestal.
Table 1.
 
Averages of Naka-Rushton Fit Parameters for Uncrossed Horizontal Disparity Data from 13 Subjects
Table 1.
 
Averages of Naka-Rushton Fit Parameters for Uncrossed Horizontal Disparity Data from 13 Subjects
No Pedestal 5-arc min Pedestal Mean Difference SEM P
V min 0.133 0.177 0.044 0.075 0.277
D 50 2.967 5.149 2.183 0.492 <0.001
n 2.535 2.633 0.098 0.332 0.382
V max 2.463 1.529 −0.935 0.249 0.001
Table 2.
 
Naka-Rushton Parameters for the Average Response Data in Figure 3
Table 2.
 
Naka-Rushton Parameters for the Average Response Data in Figure 3
No Pedestal 5-arc min Pedestal Difference
V min 0.154 0.174 0.021
k 2.965 5.044 2.079
n 1.974 1.893 −0.081
V max 2.358 1.468 −0.891
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