Variation of binocular-vertical fusion amplitude with convergence

Abstract

Purpose: The maximum binocular vertical disparity that can be fused with disparity vergence (vertical-fusion amplitude or VFA), varies with convergence angle. VFA is larger for convergence responses to near than to far viewing distances; however, the clinical norms for changes in VFA with convergence have not been established. VFA at several convergence angles was measured to obtain a quantitative description of the changes in VFA with convergence.

Methods: Fifty-six adults took part in the study. Horizontal and vertical disparity stimuli were presented on a computer monitor by using the red-green anaglyphic technique. Stimulus to convergence was altered either by changing horizontal disparity on the computer monitor (experiment I: nine horizontal disparities: 1.2-22.5 PD [Delta]) or by changing the binocular viewing distance (experiment II: five viewing distances: 25-300 cm). Convergence was held constant during an experimental session, while vertical disparity was incremented in steps of 0.05 Delta after a subjective report of fusion, until the subject reported diplopia. The maximum vertical disparity that could be fused was defined as the VFA.

Results: VFA increased linearly over the range of convergence stimuli (y = 0.10x + 1.62) and intersubject variability of VFA increased marginally with the amount of convergence. Linear regression equations with similar slopes and y-intercepts were observed in experiments I and II.

Conclusions: The results of the experiments provide a quantitative description of a linear relationship between VFA and convergence. The linear regression equation could be used in a clinical setting to establish norms and to screen for vertical vergence abnormalities.

Figure 1

a & b). Schema of two different convergence stimuli used in experiment I. The red-green concentric circles were generated on a computer monitor and their physical separation (SS) was reduced to increase the convergence stimulus (compare vergence angles in figures a & b). The convergence stimulus was larger in figure b than in figure a. c & d). Schematic representation of two different convergence stimuli used in experiment II. The physical separation of the red-green concentric circles was fixed while the viewing distance (VD) was reduced to increase the convergence stimuli (compare vergence angles in figures c & d). The convergence stimulus was larger in figure d than in figure c. The red concentric circle and red filter are shown in black while the green concentric circle and green filter are shown in gray. These figures show the state of two eyes prior to fusing the convergence stimulus. For the sake of clarity, the vertical vergence stimulus was 0 Δ in these figures.

Figure 2

Schematic representation of a vertical disparity used in experiments I and II. The schema represents the positions of the eyes before fusing the vertical disparity. The vertical disparity stimulus is given by the sum of angles α and β. The convergence stimulus is given by angle γ. The red concentric circle and red filter are shown in black while the green concentric circle and green filter are shown in gray. In the experiment, vertical disparities were generated by vertical displacing the red-green concentric circles in steps of 0.05 Δ.

Figure 3

VFA plotted as a function of the convergence stimuli for individual subjects in experiment I. a) Raw data of 30 individual subjects. b) Linear regression equations fit to the raw data of these individual subjects (thin gray lines) along with the group-linear regression equation fit (thick black line) and ± 99% confidence intervals (black dashed curves). VFA increased linearly with the convergence angle in all 30 subjects.

Figure 4

VFA plotted as a function of the convergence stimuli for individual subjects in experiment II. a) Raw data of 22 individual subjects who showed an increase in VFA with convergence stimuli (dashed gray lines) along with the raw data of the 4 outliers (solid black lines). b) Linear regression equations fit to the raw data of these 22 individual subjects (dashed gray lines) along with the group-linear regression equation fit (thick black line) and ± 99% confidence intervals (black dashed curves). The results of experiments I and II were both qualitatively and quantitatively similar to each other (compare figures 3 and 4).

Figure 5

Pooled data from experiments I and II. a) Raw data of 52 individual subjects who showed an increase in VFA with convergence. Solid red and blue lines show data from experiment I and II respectively. b) Linear regression equations fit to the raw data of these individual subjects (solid gray and dashed gray lines) along with the group-linear regression equation fit (thick black line) and ± 99% confidence intervals (black dashed curves). c) The mean (black line) and ± 99% confidence interval of the mean (dashed gray lines) of the VFA’s at each 1 Δ convergence bin. The mean and ± 99% confidence interval was obtained by averaging the individual linear regression equation estimated VFA obtained from 52 subjects.