The role of accommodative convergence at
the limits of fusional vergence
John L. Semmlow and Diane Heerema
Two possible explanations are presented for the mechanism which limits the maximum fusional
vergence response. An experimental paradigm is developed to differentiate between these
alternatives. Experimental results indicate that the blur generally associated with strong fusional effort is due to convergence accommodation "overdrive." The important theoretical and
clinical implications of this finding are presented.
Key words: convergence accommodation, accommodative convergence,
zone of clear single vision, binocular fixation, near triad
he interaction of accommodative conT:
vergence, a blur-induced oculomotor component, with other vergence motor components was first formalized by Maddox1 in
1886, and has since become well integrated
into the theoretical structure describing vergence motor control.2'3 An analogous disparity-driven motor signal, convergence accommodation, interacts with accommodative
control of the lens but may also influence the
vergence system indirectly through the accommodative feedback pathway.4 That is, by
supplying an additional lens drive, convergence accommodation will alter the blur
stimulus to accommodation, thereby influencing accommodative convergence. Thus
accommodative and vergence motor controllers constitute a truly synkinetic system, and
any comprehensive theory of vergence control must account for accommodative inter-
From the Department of Electrical Engineering, Rutgers University, Piscatavvay, N. J.
Supported in part by Rutgers Research Council.
Submitted for publication Nov. 10, 1978.
Reprint requests: Dr. John L. Semmlow, Rutgers University, Department of Electrical Engineering, P.O.
Box 909, Piscatavvay, N. J. 08854.
970
actions. (An analogous statement could also
be made for a theory of lens control.)
As an example of the synkinetic interaction
between accommodation and vergence control systems we consider the mechanism
which limits the maximum fusional vergence
response. As fusional demand is increased a
limit is reached when blur occurs. In only a
minority of subjects is diplopia (double vision) encountered without being preceded by
target blur.3 The fusional stimulus level required to produce target blur (or diplopia) is a
function of accommodation, as indicated by
the slope of the right-hand boundary of the
zone of clear single vision in Fig. 1. The increase in fusional limit with increasing accommodative stimulation is usually related to
the accommodative convergence to accommodative stimulus (AC/As) ratio,5 supporting
the theory that accommodative convergence
adds linearly to other vergence components
to produce a net motor response.6' 7
The occurrence of blur at fusional limits is
most often explained as a recruitment of
accommodative drive and associated accommodative convergence to help forestall diplopia.3' 8' 9 The mechanism for this recruitment is unexplained, although a semivoluntary process is usually implied. An alternative
0146-0404/79/090970+07$00.70/0 © 1979 Assoc. for Res. in Vis. and Ophthal., Inc.
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Volume 18
Number 9
Accommodative convergence, fusional vergence 971
a
o
<
a
o
s
5
O
o
-5
5
10
15
20
25
VERGENCE (deg.)
Fig. 1. Idealized representation of the zone of clear single vision. The right-hand boundary
represents the positive (most overconverged) limit of fusion vergence and is generally taken as
parallel to the phoria line (dashed line). The top boundary shows an extension of the convergence limit which occurs in some subjects at maximum accommodative response.
explanation, originally suggested by Fincham
and Walton10 and later by Morgan,2 is that
the blur is produced by excessive convergence accommodation or "lens overdrive"
associated with a strong fusional effort. Given
a significant convergence accommodation to
convergence (CA/C) ratio (as suggested by
the findings of Fincham and Walton10), the
convergence accommodation expected near
fusional limits may overwhelm the feedback
regulation provided by the accommodative
control system.
Both of these hypotheses are consistent
with current experimental evidence, since
both predict a similar change in lens power
with increased fusional effort. However, the
two hypotheses imply opposite roles for
accommodative convergence near fusional
limits. Under the "recruitment" hypothesis
accommodative convergence should provide
positive convergence in support of the fusional effort. The "lens overdrive" hypothesis
requires active compensation from the accommodative controller in an effort to negate
the disparity-induced lens drive,10 hence the
associated accommodative convergence must
necessarily be in opposition to the ongoing
vergence response. Since these alternate hypotheses have important theoretical and clinical implications (presented in the Discussion
section), we propose an experiment to distinguish between them.
Since the two hypotheses imply opposite
roles for accommodative convergence at fusional vergence limits, the most direct test
would be simply to measure the accommodative vergence component under limit
conditions. However, since accommodative
convergence can be measured only during
monocular viewing conditions and fusional
stimulation requires binocular vision, such a
direct measurement is not possible. It is possible to indirectly measure accommodative
convergence by taking advantage of the
different response times of vergence components. Given simultaneous stimulation,
the disparity-driven vergence component responds with a shorter latency and faster dynamics than the blur-induced component.11
Thus, if a binocular stimulus were suddenly
switched from a condition requiring high fusional effort to one requiring no (or little) ef-
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Invest. Ophthalmol. Visual Sci.
September 1979
972 Semmlow and Heerema
STIMULUS
EXPERIMENT
RESPONSE
CONTROL
RESPONSE
-i/H
-5
0
10
1
II
H
12
TIME (sec.)
Fig. 2. Stimulus pattern and possible responses in an experiment to determine the origin of
blur associated with overconvergence. The expected response of a control experiment is also
fort, the fusional component would respond
first. The relative dynamics are such that the
fusional component would reach its final state
(presumably near zero because no fusional effort would be required) while accommodative
convergence was still near the level it held
during the condition of high fusional demand. Now, if binocular vision were suddenly interrupted, any resulting vergence
movement should be attributable to a continuing readjustment of the accommodative
convergence. The direction of this movement
(convergent or divergent) would indicate,
qualitatively, the state of accommodative
convergence immediately preceding the new
stimulus condition.
In particular, assume a subject is overconverged to nearly his fusional limit. His accommodative convergence component should
be either aiding or opposing the convergence
response according to the two hypotheses
presented earlier. If the stimulus target is
suddenly altered to relieve the fusional demand, that is, switched to a stimulus level
close to the subject's phoria position, then
both fusional and accommodative convergence components will begin to adjust to the
new stimulus conditions. If the "recruitment" hypothesis is correct, accommodative
convergence will be positive (convergent) in
support of the fusional demand and should
decrease (become less convergent) as its assistance is no longer required. If the "lens
overdrive" hypotheses holds, then accommodative convergence will be negative due
to accommodative compensation and should
increase as fusional vergence and the associated excessive lens drive is removed. Due to
the slower response of accommodative vergence these changes should continue even
after fusional vergence reaches its new state.
If one eye is blocked immediately after the
fusional movement is complete, any ongoing
accommodative convergence changes will
manifest as a monocular vergence movement
in the occluded eye.
In practice, precautions must be taken to
eliminate other monocular movements which
might obscure the accommodative convergence response (which may be small, since
the expected change will already have begun
by the time occlusion occurs). One source of
monocular movement would be the slow
drifting movements normally associated with
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Volume 18
Number 9
Accommodative convergence, fusional vergence
monocular vision.12 Since these movements
are random in direction and extent, averages
taken over a number of individual responses
will be used.
A more serious potential error is the confounding of accommodative vergence responses with the slow decay of residual fusional components. 13 These movements are
anticipated even when the final fusional
stimulus exactly equals the subject's monocular phoria position (which is difficult to
achieve experimentally), since previous work
has shown small fusional components are still
present in this situation.4 To compensate for
monocular movements not related to accommodative convergence, a control experiment will be performed wherein the right
eye is occluded 10 sec or more after the high
fusional demand has been reduced. During
the delay, both vergence components will
have time to readjust to their steady phoria
values. Because both experiments are identical except for the time after "fusional release" when occlusion occurs, any response
differences must be attributed to a difference
in the internal states of the two vergence
components. In addition, since in both experiments the fusional component will have
reached its final value before occlusion, any
response differences can be due only to a difference in the internal state of the accommodative convergence component. The general format of both experiments and possible
results are summarized in Fig. 2.
Methods
To allow for independent adjustment of both
accommodative and vergence stimulation, a special stimulus device, the dynamic binocular stimulator (DBS), shown in Fig. 3 and described
elsewhere,7 was modified to include a shutter
mechanism in the optical pathway of the right eye.
Subjects, positioned with a bite bar, viewed a
target consisting of a 1° red circle against a completely dark background with a small (6 min arc)
central spot to localize fixation. An optical relay
system permitted placement of a pinhole in a
plane optically conjugate to the subject's entrance
pupil providing an open-loop accommodative
stimulus (blur free regardless of the refractive
power of the subject's lens). Both accommodative
and fusional stimulation could be dynamically var-
973
Fig. 3. Overall layout of the DBS used to generate
the required stimulus conditions. The major components shown are: LI to L5, double convex, achromatic lenses; Ml and M2, front surface mirrors; M3 and M4, translating and rotating front
surface mirrors; B, beam splitter; P, iris diaphragm; T, visual target; D, dove prism.
ied, although in these experiments closed-loop accommodative stimulation was held constant at 2
diopters. Fusional stimulation ranged from 2° to
14° depending on the subject's fusional limits.
Movements of the right eye were dynamically
measured by means of the differential infrared
reflection technique.14 Although this technique
may be affected by certain artifacts,15 its sensitivity
is limited only by the optical sensitivity of the
light-detecting diodes. Based on detector noise,
our arrangement provides a resolution of about 10
min arc. The eye movement monitor was calibrated before and after each experimental run
with 2° calibration points placed on the stimulus
target.
Since the eye movements sought were expected
to be small, eye movement data were first recorded on analogue tape for computer averaging.
Averaging of individual responses will also tend to
eliminate the drifting movements normally associated with accommodative convergence, which
can be quite large.12 The averaging process was
synchronized with shutter activation in the control
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974
Invest. Ophthalmol. Visual Sci.
September 1979
Semmlow and Heerema
SUB: CP
SUB. D.D.
55
o T
Q.
T
o
UJ
>-
j
J_
DELAYEO
DELAYED
0.0
OCCLUSION
6.0
3.0
TIME (sec.
SUBJ.S.
8?
DELAYED
°- JL
0.0
OCCLUSION
3.0
6.0
0.0
6.0
TIME (sec.
OCCLUSION
Fig. 4. Upper curve of each graph represents the averaged movements of the right eye
produced by a steplike reduction in fusional stimulation followed by occlusion of this eye at the
time indicated by arrows. The lower curve represents the averaged response which occurs
when the occlusion is delayed 10 or more seconds after the reduction in fusional stimulation.
The accommodative stimulation is 2 diopters for both responses.
experiment and with both the shutter and fusional
stimulus in the main experiment. Individual responses containing substantial artifact such as
blinks or saccadic fixation changes were easily
identified and eliminated from the averaging
process.
Four subjects between the ages of 18 and 35
years were tested. All subjects had good binocular
vision, and all but one (J. S.) were completely
naive to the experimental objectives. Each experimental run was repeated (usually on separate
days) to provide confirmation of results.
Our experimental paradigm requires fusional
stimulation be rapidly switched from a high stimulus level, demanding a strong fusional effort, to a
level requiring little or no effort. The low stimulus
level was set at approximately the subject's monocular phoria position as determined by means of a
technique similar to the Maddox flash and described elsewhere.4 The high stimulus level was
set 2° to 4° below the subject's maximum fusional
limit, found with the use of steplike changes in
vergence stimulation. (Most subjects can reach
higher levels of overconvergence if fusional stimulation is increased slowly.)
Subjects were initially requested to maintain
fusion as vergence stimulation was alternated, in a
steplike manner, between the high and low stimulus values. A record of the dynamic fusional vergence response was taken to determine the time
required for the movement. This movement time
was used to trigger the occluding shutter so that
binocular vision could be interrupted immediately
following the dynamic response.
Subjects were instructed to maintain fusion as
best they could and not to be alarmed by a loss of
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Volume 18
Number 9
Accommodative convergence, fusional vergence 975
image in the right eye. After a subject had
achieved fusion under the high stimulus condition
the fusional demand was quickly relieved by
switching to the low stimulus condition. The resulting movements of the right eye were recorded.
After a delay period of from 0.6 to 1.8 sec (as
determined from the dynamic fusional response)
the occluding shutter was closed and eye movement recording continued for several more seconds. This procedure was repeated a number of
times so that the responses could be averaged.
The entire experiment was then repeated with a
10 sec delay between fusional relief and the interruption of binocular vision. Subjects were allowed
rest periods whenever they desired.
Results
The movements produced by "fusional relief" followed by occlusion are shown for all
four subjects in Fig. 4. The upper curves of
each graph resulted from immediate occlusion; the lower curves were obtained with
delayed occlusion. The vertical arrows indicate the time in both experiments when binocular vision was interrupted.
All four subjects showed the same general
response pattern with convergent (upward)
movements seen when occlusion immediately followed fusional relief. In general, the
time course of these responses was slower
than the normal accommodative convergence
step response. This was expected since the
driving stimulus (which is actually the change
in convergence accommodation) was slower
than a step and only the latter portion of the
response was seen. When occlusion is delayed, only the small divergence movements
reported elsewhere4 were observed.
As argued previously, a comparison of the
upper and lower curves of Fig. 4 indicates
that accommodative convergence was negative during the period of high fusional demand. This, in turn, implies that blur induced by strong fusional effort must have
been due to excessive convergence accommodation and supports the "lens overdrive"
hypothesis.
Discussion
Recently, increasing significance has been
placed on the role of disparity and associated
convergence accommodation in governing
the behavior of the near triad. The numerical
superiority of the CA/C ratio over the AC/As
ratio when expressed in like units10' 16 has led
several authors to suggest that disparitydriven signals dominate both vergence and
lens responses to near stimuli.4' 10' lu 17 The
results presented here extend these arguments by demonstrating the role of convergence accommodation in limiting the range of
fusional vergence (which is generally taken at
the point where blur occurs). More importantly, our results clearly show the indirect
influence of fusional stimulation on accommodative convergence. Hence, disparitydriven signals effect vergence motor control
via two pathways: one direct and the other
mediated through convergence accommodation, accommodative feedback, and accommodative convergence. Thus the CA/C ratio
may be clinically more significant in certain
problems of oculomotor imbalance than the
more commonly measured AC/As ratio.
The "lens overdrive" hypothesis also provides a straightforward explanation of the
additional fusional convergence seen in many
subjects at maximum accommodative response (the "spike" region of the zone of clear
single vision, Fig. 1). Due to the decreased
responsiveness of a strongly accommodated
lens, particularly in presbyopic subjects, the
influence of convergence accommodation is
substantially diminished. Thus fusional vergence can continue to increase without producing blur. In addition, accommodative
compensation should no longer be necessary
(since the lens is not responding to the
disparity-induced overdrive), and the vergence response should no longer be restrained by the negative accommodative convergence shown in our experiments. Currently, we are developing an experiment to
test this implication of the "lens overdrive"
hypothesis.
Another implication of our experimental
results relates to the theory proposed by
Fincham and Walton10 that accommodative
convergence is essentially a monocular manifestation of vergence recruitment normally
used to provide lens drive (through convergence accommodation). Here we have
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Invest. Ophthalmol. Visual Sci.
Septeinber 1979
976 Semmlow and Heerema
shown that accommodative convergence can
be opposite in sign to both fusional convergence and convergence accommodation,
demonstrating its independence from the
other vergence components and refuting the
above theory.
Our findings also have relevance for those
subjects who do not experience blur at fusional vergence limits. The convergence accommodation hypothesis would suggest that
such subjects have either a lower CA/C ratio
or a better regulated accommodative system
providing stronger compensation. Current
work is also directed toward investigating this
prediction.
Summary
Two alternative hypotheses for the mechanism producing blur during strong fusion effort have been discussed and an experiment
has been developed to distinguish between
them. By taking advantage of differences in
time characteristics of fusional and accommodative vergence responses, it was determined that accommodative vergence is negative when fiisional vergence is near its
maximum positive limit. Thus the accommodative system does not aid a maximal vergence effort as has often been suggested;
rather, it is compensating for the excessive
lens drive produced by convergence accommodation. Blur occurs when this compensation is no longer adequate.
This experimental finding demonstrates
the complex interactions of the accommodative/ vergence synkinesis. In particular,
vergence behavior is influenced not only by
the direct action of accommodative and fusional vergence (in conjunction with tonic
components) but also indirectly by the strong
influence of convergence accommodation on
the internal state of the accommodative
system.
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17. Crone, R.A.: The control of eye movements. In Diplopia, New York, 1973, American Elsevier Publishing Co., Inc.
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