Investigative Ophthalmology & Visual Science, Vol. 30, No. 7, July 1989
Copyright © Association for Research in Vision and Ophthalmology
Horizontal Fusional Amplitudes
Evidence for Disparity Tuning
Ronald Jones and Gregory L. Stephens
The region of retinal disparity that is effective in maintaining binocular alignment of the eyes was
investigated by measuring the horizontal fusional amplitudes for fixation targets consisting of a small
central cross to which peripheral lines having various disparities were added. It was found that the
addition of peripheral targets significantly facilitated binocular alignment, but only if the peripheral
lines had less than about 0.5° of disparity. This result indicates that the fusional mechanism responsible for binocular alignment is only narrowly tuned for retinal disparity. In light of current evidence that
indicates that much larger disparities are capable of initiating vergence eye movements, the results
support suggestions that fusional vergence consists of functionally dichotomous vergence initiating
(coarse) and sustaining (fine) channels. Invest Ophthalmol Vis Sci 30:1638-1642,1989
Considerable evidence now exists that fusional
vergence consists of two functional components.' A
coarse, transient mechanism initiates the vergence
response to a retinal disparity, while a slower, spatial
feature-sensitive mechanism sustains binocular
alignment within the limits of Panum's area. The
vergence-initiating component responds most vigorously to large disparities, with the maximum velocity
of response occurring for disparities between 1 ° and
2°. 2 However, the disparity sensitivity of the vergence-sustaining component has not been determined directly. The purpose of this study was to define the range of target disparity that contributes to
the maintenance of binocular fixation.
The sustained fusional vergence response can be
isolated by measuring the effect on binocular alignment of forced vergence. Forced vergence refers to
the gradual introduction of changes in the vergence
required for binocular fixation independently of any
change in the stimulus to accommodation. The maximum amplitude of forced vergence that will permit
single clear binocular vision for a given fixation target
provides a measure of the strength of sustained fusion
for that target. Since the limits of single clear vision
From The Ohio State University College of Optometry, Columbus, Ohio.
Supported by grant EY-06577 from the National Eye Institute,
National Institutes of Health, Bethesda, Maryland, and by the Ohio
Lions Eye Research Foundation.
Submitted for publication: April 4, 1988; accepted January 19,
1989.
Reprint requests: Dr. Ronald Jones, College of Optometry, The
Ohio State University, 338 W. Tenth Avenue, Columbus, OH
43210.
are measured subjectively, it is possible that the vergence demand required for fixation may not match
the actual vergence eye movement response to the
stimulus.3"5 For this reason the response parameter
measured by forced vergence is better termed a fusional amplitude rather than a fusional vergence eye
movement response. We have measured the effects
on the fusional amplitudes of adding target detail in
front of and behind the plane of fixation. The results
demonstrate that fusion is sustained only by stimuli
that are near the horopter.
Materials and Methods
The fusional amplitudes for divergence and convergence were measured using a computer-controlled
haploscope (Fig. 1A). Subjects viewed separate CRT
displays (Tektronix Model 620, P31 phosphor; Beaverton, OR) with each eye by means of front surface
mirrors (M). The CRT faces were set at optical infinity by placing them at the focal points of the haploscope lenses (L). Dissimilar field stop (FS) shapes in
each arm of the instrument prevented fusion of the
edges of the fields so that only the displayed targets
provided fusional stimuli. (The field stop was square
for the right eye and diamond-shaped for the left.)
The targets for each eye were computer-generated
(using a Hewlett-Packard Model 1351A Graphics
Generator; Palo Alto, CA) and consisted of a central
fixation cross which could be bracketed by two vertical lines separated by 4° (Fig. IB). The lateral positions of the vertical lines also could be adjusted to
produce a retinal disparity of the lines with respect to
the fixation cross (Fig. 1C). The left line was posi-
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DISPARITY TUNING OF FUSIONAL AMPLITUDES / Jones and Stephens
tioned to have an uncrossed disparity of between 0°
and 1.5° and the right line a crossed disparity of equal
amount.
The positions of the entire left and right eye target
configurations could be slowly and smoothly displaced laterally under computer control to change the
convergence or divergence demand for binocular fixation (the rate of introduction of disparity was {h°/
sec). Subjects were instructed to fixate the central
cross and report any diplopia or blurring of the cross
by pressing a button that was monitored by computer. The limit of fusion for divergence was the
maximum divergence that the subject could tolerate
prior to seeing diplopia. The limit of fusion for convergence was determined similarly; the haploscope
targets were converged until either diplopia or blur
was reported by the subject. The appearance of blur
at the convergence limit was the more common occurrence and is explained by the recruitment of accommodative convergence to supplant fusional convergence when the limit of fusional convergence is
reached.6
The lateral phoria for each subject was measured
using the target configuration shown in Figure ID.
The lower line could be moved laterally by the subject by means of a joystick control. When the lines
appeared in vertical alignment, the subject pressed a
button monitored by computer. The amplitudes of
fusion for divergence and convergence were calculated by subtracting the phoria position from the
limits of fusion for divergence and convergence, respectively.
In each of the two experiments reported, the fusional amplitudes were measured using four different
target configurations. The order of presentation of
the four targets used a balanced-block design in
which all possible orders of presentation were employed in random order. (This provides 24 different
sequences of target presentation.) The balancedblock design assured that any fatigue or adaptation
effects would not influence the mean values. Subjects
measured their phorias at the beginning of each sequence and after each fusion limit measurement
within a sequence. All measurements were made in a
darkened room. The CRT faces were illuminated
with a small light source to provide a constant background luminance.
The procedure used in each of the 24 measurement
sequences was as follows: a phoria measurement was
made, then the first fusion targets were positioned at
optical infinity (and zero vergence demand) for 5 sec.
The targets were then diverged until the subject reported that the fixation cross appeared diplopic. The
targets were returned to the zero vergence demand
A\
Lsll Eye
CRT
M
*
A
vL
y
)
Right Eye
CRT
()
A.
B.
1
1
1
1
K-
—
-
C.
D.
LEFT EYE TARGET
RIGHT EYE TARGET
Fig. 1. (A) Schematic of the haploscope. (B) Stimulus fields for
the right and left eyes when fusional limits are being measured. (C)
Disparity of the bracketing vertical lines was created by displacing
the lines in opposite directions for the two eyes. The line to the left
of fixation appeared behind the fixation cross, the line to the right
offixationappeared in front of thefixationcross. (D) Target configuration for measurement of a subject's phoria position.
position for 5 sec and the phoria remeasured. A fusional limit and phoria measurement were then made
for each of the other three target types. An identical
sequence was used to measure convergent fusional
amplitudes. In this case the endpoint was indicated
by either the appearance of target blur or diplopia. No
more than eight sequences were completed per day,
four divergence and four convergence. Completion of
the experiments for each subject took approximately
2 weeks and required 192 fusional amplitude measurements, each preceded and followed by a phoria
measurement (240 total). Four subjects, including the
two authors, all experienced in this form of testing
and with normal binocular vision, acted as subjects.
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INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / July 1989
7 -i
6 -
A, y /
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y y
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y y /
5 -
4 -
y y
y y
y y
y y
y y
y y
y y
y y
y y
y y
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3 -
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1 -
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DIVERGENCE
CONVERGENCE
Fig. 2. Divergent and convergent fusional amplitudes for each of
four different target conditions. Fusional amplitudes for the crosshatched target conditions are statistically different from the zero
disparity condition.
Informed consent was obtained from each subject
before testing was begun.
Results
Experiment 1
One target consisted of only the central fixation
cross. The other three targets contained, in addition
to the cross, peripheral vertical lines with disparities
of0°, 0.25°, or 0.75°.
The results of Experiment 1 are shown in Figure 2.
Only the fusional amplitudes are presented, with data
from the four subjects averaged together.* Amplitudes were largest for the target having peripheral
lines with zero disparity. Adding disparity to the peripheral lines decreased the fusional amplitudes.
However, the smallest amplitudes were obtained for
the target consisting of only the fixation cross without
the peripheral lines.
The results were analyzed using Tukey's multiple
comparison method for two-factor analysis of variance.7 Subjects and target types were treated as independent sources of variance, and experimental effects
were evaluated by comparing the mean fusional amplitude values for all possible paired combinations of
* The phoria values for all subjects tended to be small and constant. Statistical analysis using the limits of fusion rather than the
amplitudes gave results identical to those presented.
Vol. 30
the four targets. The results for divergence and convergence were similar. Significantly larger fusional
amplitudes {P < 0.05) were obtained for the target
comprised of a fixation cross with peripheral vertical
lines of zero disparity than for either the target with
vertical lines of 0.75° disparity or the target with no
peripheral vertical lines. Moreover, there was not a
significant difference in the fusional amplitudes for
the 0.75° disparity target and the target having no
vertical lines. This pattern of results indicates that
peripheral features with disparities of 0.75° or larger
do not sustain fusion.
Experiment 2
Given the results of Experiment 1, that the addition of disparity to the peripheral targets decreased
the fusional amplitudes, a second experiment was
performed to better quantify the region of disparity
which could contribute to fusion. The targets used in
this experiment had bracketing vertical lines with
disparities of 0°, 0.5°, 1° or 1.5°. Other aspects of the
experiment were as before.
The results for the individual subjects and the
values for the four subjects averaged together are
plotted in Figure 3. Fusional amplitudes have been
normalized with respect to the amplitude obtained
for the zero disparity target. Differences between the
results for the various target types were again statistically assessed using the Tukey multiple comparison
method. The general effects were the same for all
subjects: the greatest amplitudes of fusion were obtained for the zero disparity target, with a sharp decrease in the fusional amplitudes as disparity of the
peripheral lines was introduced. The divergent fusional amplitudes obtained for the zero disparity target were significantly different from those for the 1 °
and 1.5° target conditions (P < 0.05), while the convergent amplitudes for the zero disparity target were
significantly different from all of the non-zero disparity conditions (P < 0.01). No other differences among
target types were significant. The shapes of these
curves again indicate that the sensitivity of sustained
fusion is sharply tuned to disparity. On average, most
of the contribution to fusion appears to be due to
target features having less than 0.5° of disparity.
Discussion
The results of this study are in agreement with previous reports which show that the addition of peripheral contours increases the effectiveness of the fusion
stimulus.35'8'9 Further, these results establish that peripheral target features must be on or near the plane
containing the fixation point to be effective. The re-
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DISPARITY (DEG)
DISPARITY (DEQ)
0.5
-40 "
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DISPARITY TUNING OF FUSIONAL AMPLITUDES / Jones and Srephens
No. 7
1.0
1.5
A.
Fig. 3. Fusional amplitude change (percent) as a function of peripheral line disparity for each of four subjects. A negative value indicates a
decrease in the fusional amplitude relative to the amplitude for the zero disparity condition. The values for the four subjects averaged together
are shown by the dotted line. Error bars indicate 1 standard error. (A) Divergence. (B) Convergence.
suits indicate that the disparity sensitivity of sustained fusion is sharply tuned about zero disparity,
the half-amplitude width being about 0.5°. This value
is consistent with the estimates of the width of disparity tuning for fine stereopsis determined by Norcia, Sutter and Tyler10 using evoked response techniques. The 0.5° value may also be comparable to the
direct measurements of the limits of the region of
stereopsis made by Ogle.'' At the eccentricity of the
vertical line targets used in our study (2°), a 0.5°
disparity is approximately at the limit of the range of
stereopsis for which there is a linear relationship between depth appearance and disparity magnitude
(Ogle's patent stereopsis, now usually termed fine
stereopsis12).
The finding of a relatively narrow range of disparity capable of sustaining fusion must be reconciled
with the fact that much larger disparities are capable
of initiating a fusional vergence eye movement response. The initiation of fusional vergence involves
transient wide-field disparity detection processes that
lack feature selectivity.13"15 On the other hand, sustained fusion is possible only when similarly shaped
binocular features are present. Our results support
the concept that there are functionally distinct initiating and sustaining phases of fusional vergence and
provide direct evidence that the sustaining phase of
fusional vergence has a relatively narrow range of
sensitivity to disparity. Thus we conclude that disparity vergence is divided into fine and coarse disparity sensitive components. Such a dichotomy has been
previously proposed for stereopsis.12
Schor16 has modeled fusional vergence control as a
system containing two stages of neural pseudo-integration (each described by a first-order differential
equation). The initial stage has a short decay timeconstant, and its output is in parallel with a second
stage having a relatively longer time-constant. It is
important to note that the disparity-induced fusional
responses measured in our study reflect the activity of
Schor's fast fusional vergence stage because the slow
mechanism was not activated during the short time
(<20 sec) needed for our measurements of fusional
amplitude. This was established for our subjects by
comparing the subjects' phorias before and after each
fusional amplitude measurement. These phorias did
not differ significantly, indicating that changes in the
output of the slow disparity vergence mechanism
were not significant under our test conditions. The
present results therefore are construed to indicate that
the initiating and sustaining mechanisms are subdivisions of Schor's fast fusional vergence stage.
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INVESTIGATIVE OPHTHALMOLOGY 6 VISUAL SCIENCE / July 1989
The partitioning of fast fusional vergence into two
components has previously been proposed by Krishnan and Stark17 to adequately explain the dynamic
behavior of fusional vergence. They have proposed a
systems control model that depicts fast fusional vergence as having parallel control elements of pseudointegration and pseudo-differentiation. (These elements act as low-pass and high-pass niters, respectively.) Our results would suggest that these elements
are differently tuned for retinal disparity, the integral
element (corresponding to the vergence-sustaining
mechanism) being narrowly tuned to small disparity,
the higher frequency response element (the vergenceinitiating mechanism) having a broad sensitivity to
disparity. This modification of the systems control
model leads to improved prediction of the dynamic
behavior of fusional vergence.18
Key words: binocular vision, eye movements, stereopsis,
fusional vergence, retinal disparity
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