OPTO 374 - Binocular Vision

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					OPTO 374   -   Binocular Vision                     1

COURSE:        OPTO 374           -   BINOCULAR VISION

UNITS:         2 + 0 = 2

TUTOR:         Dr Kelechi Ogbuehi


     by Arthur Bennett and Ronald Rabbetts

     by Mitchell Scheiman, and Bruce Wick,

     Hugh Davson

4)   OPTOMETRY by Keith Edwards and Richard LLewelyn
OPTO 374   -   Binocular Vision                          2


A.   Overview of Binocular Vision
         The Importance of binocular vision
         Advantages of binocular vision
         Disadvantages of binocular vision

B.   Normal Binocular Vision Phenomena
         Visual Direction
         Retinal correspondence
         Sensory fusion
         Motor fusion
         Fixation disparity
         AC/A ratio
         Binocular summation
         Ocular dominance
         Depth perception & stereopsis

C.   Problems with sensory fusion
         Rivalry and suppression
         Aniseikonia

D.   Neurophysiology & development of binocular vision
OPTO 374       -          Binocular Vision                                            3

Lecture 1

Vision is perhaps the most important of our senses, as reflected by the fact that
approximately 50% of our cerebral cortex is involved in visual processing. It provides us
with critical information about the world around us.

Vision is based on the retinal image formed in each eye, and monocular vision alone
provides us with much significant data.

In this course, we will mainly be concerned with binocular vision—that is, vision that
results from the combined input from two eyes.


Q.     Why is the study of binocular vision important to clinical optometry?

A.     Clinical applications of our study of this basic science include:

                  Managing patients with complaints of eye strain, headaches, difficulty
                   with reading, etc.
                  Pediatric optometry
                  Scientific basis for vision therapy
                  Monovision and contact lenses

Q.     What is the significance of binocular vision?

A.     Simply put, the purpose of binocular vision is to enhance the quality of vision that
       we have with each eye alone.
OPTO 374       -         Binocular Vision                                                4

One scientist (G.K. Von Noorden) said, ―with the exception of stereopsis, seeing with
both eyes is marginally, if any, better than seeing with one — absolute threshold,
differential threshold, and visual acuity being about the same.‖ It is important to note at
this juncture that as long as binocularity with normal (or near-normal) retinal
correspondence exists, binocular visual acuity is at least one line improved over that of
the better monocular visual acuity.

Q.       What are the advantages of binocular vision?

Major Advantages:

        Larger visual field. Without eye movements, the monocular field is about 145°
         wide. With both eyes, it‘s about 190° wide. In addition, there is considerable
         overlap between both monocular visual fields, and it is in this overlap area that we
         have stereopsis (depth perception).

        Stereopsis. Stereopsis is the highly accurate sense of depth perception that is
         unique to binocular vision, and is considered the most significant advantage
         gained by binocular vision.

Minor Advantages:

        Spare eye
         If one eye is lost to injury or disease, we will still be able to see well with the

        Binocular summation
         Certain aspects of vision are improved because of the additional input provided by
         the second eye. The improvement may be small, but it definitely improves the
         quality of vision.

         Examples include visual acuity, light detection thresholds or even seeing a
         camouflaged object.

         Within the binocular visual field, we can take advantage of two detectors, and the
         result is better sensitivity/detectibility of visual stimuli.

         Greater sensitivity makes things which are smaller, dimmer, quicker, etc. more
         detectible. This phenomenon is called binocular summation.
OPTO 374     -         Binocular Vision                                            5

      Enhanced visual performance. For example, better space perception, hand-eye
       coordination, more efficient, comfortable reading, etc.

       Parents of children, who have had their strabismus corrected, thereby changing
       from monocular to binocular vision, often report that their children‘s visual-motor
       skills, such as hand-eye coordination are vastly improved.

Are two eyes always better than one? If so, would multiple eyes (such as spiders have) be
better than two?

There are some disadvantages to binocular vision. The neurophysiology needed to
support and fuse the input from two eyes is more complex than if we just had one eye.
With greater complexity, there is more potential for problems.

Binocular vision has its own unique set of problems that arise when part of the binocular
system is not working correctly. Binocular visual anomalies are frequently the cause of
symptoms such as eye strain, or difficulty reading.

Many of these problems would not exist if we had only one eye. For example, binocular
stress can be caused by:

      Incorrect refractive balance
      Dissimilar retinal image sizes (aniseikonia) between the two eyes due to
       anisometropia or retinal disease
      Convergence problems
      Conflicts between the accommodation and convergence

In an extreme case, such as intractable diplopia, the only solution to a binocular problem
may be to prescribe an eye patch. In this case, the treatment is to prevent simultaneous
perception in the absence of binocular fusion. The effect is to render the patient
monocular because the binocular system is more trouble than it is worth.

Some people incorrectly assume that the only advantage to binocular vision is stereopsis
or that, without binocular vision, one has no depth perception. Actually, there are many
important monocular cues that allow a person to judge depth in the absence of binocular
OPTO 374     -         Binocular Vision                                             6

In fact, beyond a few meters from the eye of an observer, monocular cues are more
important (and stereopsis contributes little) to depth perception.
Lecture 2

Visual Direction

When a person with normal binocular vision looks at an object, both visual axes converge
such that they intersect at the object of regard.

When this object is at optical infinity (6 meters or greater), and the patient is emmetropic
or myopic, one or two types of vergence are responsible for the position of each eye.

      If the person is orthophoric (i.e. has no phoria), then only Tonic vergence is
       responsible for turning each eye to point at the target.

      Where a heterophoria is present, tonic vergence and fusional vergence are
       responsible for turning each eye to point at the target.

     Tonic vergence refers to the muscle tone of each of the six extraocular muscles.
     The tension in each muscle when it is completely relaxed helps to determine in
     which direction the eye will point when accommodation is completely at rest.

     It facilitates understanding to look at fusional vergence as a problem-solver. The
     problem here is a phoria. Fusional vergence is only used when there is a phoria,
     and just enough fusional vergence is used to correct that phoria.

     A phoria is therefore referred to as a “compensated (corrected) deviation”. If the
     phoria is so large that fusional vergence cannot correct it, the phoria is referred to
     as a “decompensated phoria”.

     When a phoria decompensates, and the emmetropic person looks at an object at
     optical infinity, only one visual axis is pointed at the target, the other visual axis
     points away from the target in a direction determined by the type of phoria the
     person is afflicted with.

     A decompensated phoria leads to a number of problems with binocularity.
OPTO 374      -         Binocular Vision                                             7

     It is important to note that when fixating an object closer than 6 meters (20 feet):

      tonic vergence;
      fusional vergence (if there is a phoria);
      accommodative vergence (whenever we have accommodation, we have
       accommodative vergence);
      and proximal vergence (which is an increase in convergence which occurs
       because a person knows that the object he/she is looking at is close to him/her);

         all combine to determine the direction in which each eye will point.

Retinal Correspondence
When a person with normal binocular vision looks at an object, the image of that object
falls on both foveas. In this case both foveas receive information from the same object.
The foveas are then said to be related (conjugate or corresponding). This is Normal
Retinal Correspondence (NRC).

Abnormal retinal correspondence occurs when the images from the object above fall on
the fovea of one eye, and on an extra-foveal point of the other eye. In this case, the fovea
of one eye is conjugate with the extra-foveal point of the other eye.

If we look at the schematic representation in fig 1b, we see that when the right fovea (FR)
and the left fovea (FL) are conjugate (in this diagram, with respect to the object point X),
the temporal side of the left retina is conjugate with the nasal side of the right retina (in
this example, with respect to the object point Z). Also, we see that the nasal left retina
corresponds with the temporal right retina (in this example, with respect to the object
point Y).

Panum's Area
Binocular vision as defined by Worth can be classified into three grades:

         Simultaneous Perception
         Fusion
         Stereoscopic Vision

Simultaneous Perception

This occurs in both binocular single visible (BSV) and binocular vision (BV) where the
images of the object of regard from both eyes are simultaneously perceived in the brain.
OPTO 374     -         Binocular Vision                                              8


Combining both these perceived images into a single image is fusion. Fusion can be
sensory or motor.

Sensory fusion is the automatic ability to fuse the images from both eyes into a single
perceived image.

Motor fusion is the ability to maintain sensory fusion through a range of vergence (which
may be horizontal, vertical or cyclo).


Fusion of these slightly different retinal images is the precursor to Stereopsis. Stereopsis
enables the perception of depth (3-D vision) and helps in the accurate judgment of
relative distance between two objects, and relative speed (or change of speed) of one
object with relation to another.

There are many cues to the perception of depth, but stereoscopic depth is the most

Stereoscopic cues are caused almost exclusively by retinal disparities.

Retinal disparities are small positional displacements between otherwise well-matched

In the visual system, because of the horizontal separation of the eyes, only horizontal
disparities convey depth information.

The concept of disparities is illustrated in figure 1a. Imagine looking outside your living
room through each of two windows which are located side by side. What you see through
the windows are almost identical, but the relative positions of the objects in the visual
scene are slightly displaced when looking through one window as compared to when
looking through the other one.

The horizontal shift in the objects‘ positions is what happens in normal vision, and is the
result of the difference in horizontal positions of both eyes.
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OPTO 374     -         Binocular Vision                                              11

Fusion and stereopsis only occur in binocular single vision.

The ability for the brain to fuse both retinal images is dependent on where the images of
an object of regard fall on both retinas.

We have already discussed the fact that, in normal retinal correspondence, when both
eyes look at an object, both visual axes intersect at the object of regard so the each image
falls exactly on the fovea of each eye.

Subsequently the brain is able to fuse these two images into one visual percept.

The question is: Can the brain fuse the images of both eyes if one image falls on the
fovea of, for example, the left eye, and the other image falls on an extrafoveal point of
the right eye?

The answer to the question above is YES, but only if the image on the right eye falls
within a circumscribed area known as Panum’s Fusional Area. If the image falls
outside of this area, then fusion is not possible. The first consequence of this is diplopia
which may or may not progress to cortical suppression.

Please note that any point on either retina (for example, a point X on the right retina)
has a relationship with a number of points within its Panum‟s area on the opposite
retina. Such that, if the image of an object falls on X on the right retina, as long as that
same image falls on any point within X‟s Panum‟s area on the left retina, fusion will
occur and stereopsis will be present.

The fusion and stereopsis which occur in this case, are not as good as that which
occurs when there is normal retinal (point-to-point) correspondence.

To conclude: In abnormal retinal correspondence where the image of an object falls
on the fovea on one retina and on an extrafoveal point of the opposite eye, fusion and
stereopsis will occur only if the extrafoveal point lies with Panum‟s area. If not, there
will be no fusion, no stereopsis and therefore there will be diplopia.

As we see in fig 1b, Y, X, and Z all lie on the same arc. We also know that each of those
points stimulate exactly conjugate points on the left and right retinae.

The term Horopter describes an arc, which contains all the objects that stimulate exactly
corresponding areas on the left and right retinae.
OPTO 374     -         Binocular Vision                                               12

Examining the schematic in fig lb, Panum's space is a narrow area surrounding the
Horopter within which objects stimulate corresponding retinal areas, and thus give rise to,
binocular vision.

What then is the difference between the Horopter and Panum's space?

In fig. 1b we see that Y, X, and Z stimulate corresponding retinal points to result in
binocular single vision. The object point X, for example, stimulates the corresponding
retinal points FL and FR to result in binocular single vision.

An object that falls within Panum's space, but not on the Horopter, will also stimulate
binocular single vision but it does this by stimulating retinal points that do not have an
exact corresponding relationship.

In fig. 1c, the object O is located in Panum's space and stimulates FL and a point P on the
right retina. Even though FL should correspond with FR, it corresponds with P but still
results in binocular single vision. Therefore, there is actually no such thing as
corresponding points. Instead, a point, for example on the left retina, corresponds with a
well-defined area on the right retina. Therefore what exists in reality is a point-to-area
relationship rather than a point-to-point relationship.

Re-examining fig. 1c thus, FL does not correspond with FR but with any point, for
example, within the highlighted circle. This highlighted circle is referred to as Panum’s
area (or Panum's fusional area).

Theories of Sensory Fusion

As we have learned, the important features for sensory fusion are retinal correspondence,
retinal image disparity detection and neural summation.

Studies of higher mammals have shown that about 80% of the striate cortex cells can be
binocularly stimulated. For this to occur properly however, corresponding retinal areas
must be in proper alignment, if not the individual visual fields from both eyes (because
they are competing for the brain’s attention) mutually inhibit each other.

It is the proper binocular stimulation of these cortical cells that leads to unification of
both ocular images into a single binocular percept. The theory of binocular vision just
described is the theory of Binocular Neural Summation.

Another (older) theory (Retinal Rivalry or Alternation theory) asserts that no fusion of
both ocular images actually occurs. The argument was that the binocular field was
composed of a mosaic of monocularly perceived patches such that the visual input from
one eye at times dominates the perceived image, and at times is suppressed. This theory
left many features of binocular vision (such as contrast sensitivity enhancement)
unexplained and has since been found to be essentially incorrect.
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OPTO 374     -         Binocular Vision                                              15

Lecture 3

Notes on the Horopter
Corresponding retinal points are a central problem in binocular vision because they are
the starting point from which stereopsis begins.

We can define corresponding points by equality of perceived visual direction, absence of
difference in perceived depth, or a zero motor value for the initiation of vergence
movement (to understand this motor value, remember that sensory fusion is the automatic
ability of the brain to fuse visual information from corresponding points in both eyes. If
this were not possible, then one eye would have to be turned in, out, up, or in to enable
sensory fusion to take place. We would then say that there is a non-zero motor value for
the initiation of vergence movement).

The three-dimensional surface of zero disparity points (in which the fixation point is
ideally included) is referred to as the Horopter.

It is too difficult to measure the entire Horopter for the whole visual field, so what we
earlier defined as the Horopter (which is really a horizontal cross-section of the actual
Horopter that is called the Longitudinal Horopter) is what we measure instead.

In a perfect situation, uniformly distributed retinal points would produce a circular
Horopter known as the Vieth-Muller Circle.

However in actuality, corresponding retinal points are not uniformly distributed. For
example, when the foveas of both eyes are exactly corresponding points, a point 3mm
temporal from the right fovea does not simultaneously correspond with the point 3mm
nasal to the left fovea. Instead, it corresponds with a point more than 3mm nasal to the
left fovea.

These ‗stretches‘ made on one retina before it is mapped onto the other, give the
Horopter a flatter shape and a tilt which make it more useful as a frame of reference for
depth judgments.

Some types of Horopter

Nonius Horopter

This is the Horopter which has been studied the most, and it is based on the judgment of
perceived monocular visual direction. In this case however, little is learned about
correspondence or binocular function.
OPTO 374     -          Binocular Vision                                            16

Maximum Stereoacuity Horopter

This is a longitudinal Horopter which has the disadvantage shared by all such Horopters,
that a large number of points are needed to establish the point of maximum Stereoacuity.
This Horopter is however based on a true test of binocular function.

Fusional Horopter

This Horopter also tests true binocular function and is of particular interest in anomalous

This Horopter is measured by first determining Panum‘s area and its middle is taken as
the Horopter.

Sensory Fusion
This is the achievement of single vision from the fusion of imperfectly matched retinal

All disparities (horizontal, vertical, magnification differences) are subject to fusion, and
the fusion of vertical disparities in particular has secondary effects on the perception of
depth from horizontal disparities.

In sensory fusion, the binocular visual system shifts monocularly perceived visual
directions into a compromise direction which is the same for both eyes. This new
direction is an illusion.

This sensory fusional shift is sometimes referred to as an allelotropia.

Panum‘s area (which we discussed earlier) can be re-defined as the range of retinal
disparities for which single vision may be achieved through sensory fusion.

Panum‘s area shows a considerable amount of variability in both normal and anomalous
correspondence. Both perceived depth and perceived visual direction can be shown to be
variable in normal binocular vision.

Panum‘s area is broader horizontally than for vertical disparities. Modern research shows
that Panum‘s area extends to over 30 horizontally, and to over 20 in all other directions.

Panum‘s area can be divided into two separate areas:

       i)        The area for the limiting disparity for spontaneous fusion
       ii)       The area for the limiting disparity for extended fusion
OPTO 374     -         Binocular Vision                                             17

The two limits for Panum‘s area can be described as follows:

Present a target so that its images fall on one fovea and on an extrafoveal point on the
other eye which is within sub-area no.i), and these images will be merged by sensory

If the image on the other eye falls on an extrafoveal point outside sub-area no.i), sensory
fusion will not occur and diplopia will be the result.

Now, if we first place the image (on an extrafoveal point of the other eye) so that it falls
within sub-area no.i), and then gradually move it outside (sub-area no. i), we will find
that binocular single vision will be maintained even though it would not have been
present if the image initially fell outside (sub-area no.i).

This difference in the extent of Panum‘s area depending on which way the stimulus is
presented is referred to as „hysteresis‟.

Both Panum‘s area and the expression of correspondence express hysteresis and more
than anything else, this suggests that their basis is similar.

The limits of Panum‘s area described earlier are those for the spontaneous fusion area.
The extended area limits can vary from those by as much as 2.60 in all directions.

Finally the current thinking about Panum‘s area is less of a threshold concept, and more
of an information processing concept. This is because Panum‘s area also varies in
dimensions according to such stimulus qualities as size, brightness and colour.

Sensory Fusion and Depth Perception

Sensory fusion and perceived depth are two separate responses to disparity. Either of the
two could occur alone in normal binocular vision. However, in the absence of depth
perception, sensory fusion is necessary to absorb undesirable differences in the retinal

Because fusion and depth may present independently, it is wrong to define stereopsis as
depth perception caused by the fusion of disparities within Panum‘s area.

Ocular Dominance

Of the cells responsive to binocular stimulation in the striate cortex, only 25% respond
equally to input from the right and left eyes, the others respond more actively to input
from either the right or the left eye.
This ocular dominance is particularly sensitive to the amount of binocular stimulation
received during infancy, therefore even small obstacles to sensory fusion at this critical
stage could lead to binocular anomalies such as amblyopia, suppression and deficient
fusional vergences.
OPTO 374      -         Binocular Vision                                              18

Lecture 4
Fixation Disparity

The cover test, selective screening tests (e.g the Maddox Wing), Distortion tests (e.g the
Maddox Rod), Prismatic dissociation tests (e.g. Von Graefe test), and tests with
independent objects (as with the synoptophore) are tests which assess the total imbalance
of the oculomotor system, with the eyes completely dissociated.

Fixation disparity is a phenomenon which requires only a small amount of dissociation of
the eyes, and therefore gives an insight as to the significance of the total imbalance of the
oculomotor system.

Even though binocular fixation is based on corresponding points, as we discussed in an
earlier lecture, this system is quite flexible. In figure 4.1 below, binocular single vision
would still occur provided the retinal image Q’L in the left eye falls within Panum‘s
fusional area on the left retina which surrounds the corresponding point (on the left
retina) of the point on the right retina (the fovea) on which Q’R falls.

This Panum‘s area phenomenon works for the fovea, parafovea (the area surrounding the
fovea) and for the retinal periphery. Therefore while one eye maintains central fixation, it
is possible for the other eye to deviate by only a fraction of 10 (about 15 minutes of arc),
and binocular single vision still be maintained.

This deviation in binocular vision is what is referred to as Fixation Disparity. This
deviation cannot be described as a heterotropic deviation since it is a deviation within
physiological limits from normal bifoveal fixation.

In heterophoric conditions, less pressure can be put on the fusional vergence mechanism
(and therefore more relief from adverse symptoms obtained) by allowing either eye
deviate slightly from the position of accurate bifoveal fixation.

The unit designed by Mallet (modified to its current form in 1983), is a simple way of
detecting a fixation disparity.

Figure 4.2 illustrates the principle of the Mallet unit.

The fixation target X is seen by both eyes but the lines above and below the X are
polarized 900 apart so that depending on which eye is wearing what filter, one eye sees
the upper line and the other sees the lower line. For this example, OS sees the upper line.

The Os seen to the left and right of the X are what we call foveal lock circles.
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OPTO 374      -        Binocular Vision                                                21

The right eye is properly fixated on the target (X), so the marker for the right eye points
to the center of the X.

The left eye, however, is turned outwards (exophoria) and therefore its fovea is turned
nasally, and projected temporally in the visual field.

For the left eye therefore, the images of both X and the top marker fall on the temporal
side of the fovea and thus should both be projected more nasally in the visual field when
compared to the visual axis.

However, fusion of the X images from both eyes causes the brain to project the X image
for the left eye as if it originated from the fovea (rather than an extrafoveal point temporal
to the fovea).

Therefore, relative to the projection of the X in the visual field, the marker for the left eye
is more nasal.

Another way of looking at it is that the marker for the left eye is to the right of the X
and therefore the deviation is „crossed‟ and thus we have an exo-deviation.

The fixation disparity for the object X is indicated by a misalignment of the two markers.

The image (in this case) of X is said to have ‗slipped‘ across the retina of the left eye,
hence the old (and inaccurate) term for fixation disparity - ‗Retinal Slip‟.

With the Mallet markers oriented in the vertical position, we assess horizontal fixation
disparity, and when they are in the horizontal position, we assess vertical disparity.

The advantage fixation disparity tests such as that described above is that they serve as a
guide to patients who may need prisms to relieve the symptoms of their phoria. A person
may have a large phoria and not require prisms because his/her fusional vergence can
compensate for the phoria, while another person with a much smaller phoria may require

The amount of prism required by a patient with a fixation disparity is the smallest amount
of prism that re-aligns the marker of the deviating eye. This prism is sometimes referred
to as the „Associated Phoria‟. The base of the prism is always in the same direction as the
deviation of the marker. In the example above, the marker was deviated inward, and
therefore the base of the relieving prism is base-in.

Any prism more than 2∆ should be divided equally between both eyes to avoid the more
noticeable aberrations of a single stronger prism. For example, 4∆ BI found for OS can
be divided into 2∆ BI in front of OD and 2∆ BI in front of OS.
OPTO 374      -         Binocular Vision                                                22

Dividing vertical prisms between both eyes is slightly more complicated. Four prism BD
in front of OD will be divided as 2∆ BD in front of OD and 2∆ BU in front of OS.

Perhaps it is simpler to remember that a crossed deviation is exophoria and an uncrossed
deviation is esophoria. Then remember that base-in corrects exophoria and base-out
corrects esophoria.

It is worthy of note that prisms always cause an apparent displacement of the object
toward their apex.

This means that when we use prisms to „correct‟ or „relieve‟ a phoria, we are not trying
to change the direction of the eye‟s visual axis, we are sending the object to coincide
with the visual axis of the eye.

In the example above, we are sending the object outward to coincide with the visual
axis of OS.

The other way to determine the horizontal prismatic relief for a patient would be to
measure the dissociated phoria for a patient and then measure the positive or negative
vergence limits (depending on if the phoria is exo- or eso-) at the same distance, and then
determine if prisms are required (and how much) using Sheard‘s criterion.

This method is longer more cumbersome and the fusional limits assessed are not usually
accurate (the limits reduce with practice) the first time they are measured.

The fixation disparity test must be measured with the patient‘s prescription. Uncorrected
refractive errors can cause or exacerbate the symptoms of uncompensated phorias.

For horizontal phorias, adjusting the spherical part of the prescription may be used as a
stopgap measure to provide relieve from heterophoric symptoms. A greater plus power
will relieve symptoms of esophoria (by relaxing accommodation), and a greater minus
power will relieve symptoms of exophoria by stimulating accommodation.

When assessing vertical fixation disparity, take care to ensure that the trial frame or
phoropter is level (not tilted down or up in front of one eye). An unlevel trial frame or
phoropter may induce a vertical phoria.

An alternative and more sensitive test to use to assess vertical fixation disparity is the
Turville infinity balance technique, using two sets of two concentric circles as targets.
One set is seen by each eye. The advantage of this technique is that there is no foveal
lock (only a parafoveal lock) and therefore it is easier to elicit an existing vertical fixation
OPTO 374      -        Binocular Vision                                                23

Please note that horizontal fixation disparity cannot be assessed using the Turville

Some patients only just manage to attain fusion, and yet they have no symptoms. The
reason for this is that fine details of the image falling near the fovea are suppressed. In the
clinic, this is manifested as the frequent disappearance of one of the markers. This does
not indicate suppression and may just be due to retinal rivalry.

In some cases, the suppression area is only to one side of the fovea. So that if the Polaroid
visors are reversed (and thus the marker now falls on the opposite side of the fovea) it
will be visible to the patient.

At other times, diplopia may occur (the patient sees to Xs). In such cases, a dissociating
technique is used to estimate the prism required. This prism is then incorporated into the
patient‘s prescription and then refined using the fixation disparity test.

Sometimes a patient may require a prism for one distance, and not require it for another.
In this case, the prism needed for one distance is used to measure the disparity at the
other to determine what course of action to take.

In the case of anisometropic bifocal wearers, the need for specialized dispensing may be
assessed by measuring the vertical disparity with the patient looking through the reading
portion of his/her lenses.

An alternative method for assessing suppression uses near targets of various sizes at 35
cm. Some letters are seen by one eye and others by the fellow eye. The very big letters
may be seen by both eyes but when the letters get smaller, one eye may be suppressed.

Patients with such ‗small-letter‘ suppression should not be prescribed with prisms even if
neither of the Mallett markers was suppressed.

Figure 4.3 shows a Mallett-Hamblin near-vision suppression test (also used with
polarized filters).

The fixated disparity should not be recorded as a phoria. So that 2∆ right exophoria
should be recorded as 2∆ Base in R.

No horizontal fixation disparity:    X
No horizontal heterophoria:         O
No vertical fixation disparity:           X
No vertical heterophoria:         O
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OPTO 374     -        Binocular Vision                                              25

Lecture 5

Problems with accommodation can be divided into four broad groups:

      Accommodative insufficiency
      Accommodative excess
      Accommodative infacility
      Ill-sustained (poor stamina) accommodation

The four groups listed above often arise from functional causes such as overwork or
deficient physiology but they could also have non-functional etiologies (causes) which
include emotional-, refractive-, ocular disease induced-, systemic disease induced-, and
drug induced- etiologies.

Two more categories of accommodative dysfunction which do not have functional
etiologies are:

      Unequal accommodation
      Paralysis (Paresis) of accommodation


       Definition:    Accommodative insufficiency has been defined as the inability to
                      afford clear vision of targets at a fixed distance which is usually
                      the habitual near-work distance

                      The amplitude of accommodative is abnormal low for the patient‘s

                      Convergence insufficiency and accommodative infacility are
                      closely associated with accommodative insufficiency.

       Symptoms:      Headaches, eyestrain, diplopia, reading problems.

       Presentation: This problem is normal in presbyopic and pre-presbyopic patients,
                     but rarely in younger patients. There are however documented
                     cases in which accommodative insufficiency has been caused by
                     influenza infection, tropical disease infection and by low-grade
                     viral encephalitis. In all the cases, there were no obvious signs, just
                     a recent history of a bout (or bouts) of infection.
OPTO 374   -        Binocular Vision                                               26

                    Any pathological or traumatic conditions which affect the Ciliary
                    muscle, the oculomotor nerve or the crystalline lens itself may
                    cause accommodative insufficiency.

                    The use of sympathomimetic (e.g. phenylephrine) and
                    parasympatholytic (e.g. tropicamide) drugs sometimes causes
                    symptom- producing lowered amplitudes of accommodation.

     Treatment:     Bifocals are usually prescribed to relieve the patients near
                    symptoms, and follow up of the patient is necessary to monitor
                    his/her progress or to detect the underlying organic cause (if it is
                    still present.

     Notes          Assessing Accommodative Amplitudes

     Many formulas exist to calculate the average Amp. of Accomm. Expected for a
     particular age. Perhaps the most accepted one is that by Hofstetter which
     calculates the minimum expected amplitude for a particular age:

     Min. Exp. Amp. = 15 - 0.25 X age in years

     After assessing the monocular amplitudes for your patient, you can then grade
     his/her Amp. of Accomm. According to the table below:

     Table 5.1      Grades/Ranks of Amplitude of Accommodation

                  Rank                     Patient’s Amplitude

    5   (Very Strong)                   1.00 D or more above average amplitude
    4   (Strong)                        0.50 D above average
    3   (Adequate)                      Average amplitude for the age
    2   (Weak)                          2.00D below average
    1   (very weak)                     4.00 D or more below average
OPTO 374      -         Binocular Vision                                         27

The two sub-types of accommodative insufficiency will be discussed here:

      Relative Accommodation
      Lag of Accommodation

Relative Accommodation

This is a type of accommodative insufficiency where the positive relative accommodation
(PRA) is low.

The PRA (minus lens to blur) is performed at 40 cm by adding plus lenses to blur a
previously clear target. The patient must be wearing his/her CAMP (Corrected Ametropia
Most Plus) lenses. The CAMP lenses are the highest plus (or least minus) lenses which
correct each eye to 6/6.

The PRA test is done binocularly by increasing the minus lenses (in 0.25D steps) equally
for each eye until the first sustainable blur.

The NRA (negative relative accommodation) is the opposite of the PRA and is performed
by adding plus lenses to blur the print at 40 cm.

Both the NRA and PRA should be close to 2.50 D. So, NRA is about + 2.50 D and PRA
is about – 2.50 D. NRA and PRA should be very nearly equal (a maximum of 0.50 D
apart in value) if the CAMP prescription is correct. A PRA or NRA above 2.50 D is
highly suspicious, especially when it is combined with a depression of the opposite
relative accommodation limits.

Table 5.2         Grades/Ranks of Negative – and Positive – Relative Accommodation

                      Rank                    PRA (-) and NRA (+)

       5   (Very Strong)                   2.50 D or more
       4   (Strong)                        2.25 D
       3   (Adequate)                      1.75 to 2.00 D
       2   (Weak)                          1.50 D
       1   (very weak)                     < 1.50 D

A value for either NRA or PRA of less than 1.75 D should be considered a failure of that
OPTO 374     -        Binocular Vision                                             28

It is important to note however that relative accommodation is often limited by deficient
vergence ranges. An esophoric patient with a high AC/A ratio and poor fusional
divergence will likely have a reduced PRA.

Lag of Accommodation

This is a clinical form of accommodative insufficiency whereby the ‗response
accommodation‘ is less than the ‗stimulus accommodation‘ ((explain).

Accommodative lag can also be regarded as an inaccuracy of accommodation in the same
way that fixation disparity is regarded as an inaccuracy of vergence.

Accommodative lag can be measured in the clinic using Nott Retinoscopy and the
Monocular Estimate Method (MEM) Retinoscopy.

Nott Retinoscopy

      This is a binocular test and it is carried out (on any one retinoscopic
       meridian/axis) using the phoropter at 40 cm.

      The patient fixates at the near target at 40 cm. The examiner is behind this
       target and performs Retinoscopy through a hole in the near card.

      If the examiner is directly close behind the near card and there is a lag of
       accommodation, he will see a „with „movement. By moving back slowly, and re-
       scanning the same eyehe should eventually get a „neutral‟ reflex.

      The examiner then uses the phoropter nearpoint rod to estimate his distance
       from the patient. If this „neutral‟ point is 67 cm from the patient, the stimulus
       accommodation = 100/67 = 1.5 D.

       But the patient is looking at a target at 40 cm where the stimulus
       accommodation is 2.5 D.

       The accommodative lag in this case is 2.5 - 1.5 = 1D

MEM Retinoscopy

      The monocular estimate method retinoscopy can be performed at any near
       distance and can be performed without the phoropter or even a trial frame.

      This test is called „monocular‟ even though it is performed under binocular
       viewing conditions.
OPTO 374      -         Binocular Vision                                             29

      The advantage of this method is that the target is mounted directly on the

      Any of the principal meridians of the patient is scanned.

      A „with‟ movement will be observed if there is a lag of accommodation.

      This movement is neutralized using a plus lens. Take care not to have the lens
       in front of the patient‟s eye (at any one time) for more than 1 second. Because,
       after one second, accommodation sets in and can contaminate the lag result.

Table 5.3         Grades/Ranks of Accommodative Lag

                      Rank                      Accommodative Lag

       5   (Very Strong)                   + 1.25 D
       4   (Strong)                        + 1.00 D
       3   (Adequate)                      + 0.75 D
       2   (Weak)                          + 0.50 D
       1   (very weak)                     + 0.25 D


       Definition:      This is another inaccuracy of accommodation in which excess
                        accommodation is used to focus a near object.

                        It is the opposite of accommodative lag, and is referred to as an
                        accommodative ‗lead‘.

       Symptoms:        Asthenopia, blurred dist. VA, headaches, diplopia, ineffective
                        performance at the near point (for example reading material may
                        be held too close to the patient‘s face.

       Presentation: The classic cause of accommodative excess is latent hyperopia or a
                     spasm of accommodation (which may result in Pseudomyopia).

                        Maintaining and sustaining accommodation because of the
                        presence of inadequate stimulation (e.g. night myopia) is another
                        type of excess accommodation.
OPTO 374   -          Binocular Vision                                               30

                      Accommodative excess can also occur when excess convergence is
                      required to maintain fusion (because of the CA/C ratio - the CA/C
                      ratio is the opposite of the AC/A ratio and is the amount of
                      convergence-accommodation associated with 1 ∆ of convergence),
                      for example in the case of a patient with exophoria in which
                      positive fusional convergence is insufficient to maintain fusion.

                      Only the MEM retinoscopy method can be used to diagnose excess
                      accommodation, which is considered ‗strong‘ if the neutralizing
                      lens needed is – 0.25 D or greater. A plano neutralizing lens is
                      considered ‗adequate‘, and a +0.25 lens (accommodative lag) is
                      considered ‗weak‘.


               Definition:    This is the inability of a patient to change focus rapidly.

                              It is also called inertia of accommodation.

               Symptoms:      The main symptom with such patients is a reduction of
                              visual efficiency. Such patients will for example, complain
                              often of ‗blurring‘ when they look from ‗a book to the
                              blackboard‘ or vice-versa.

               Presentation: The test for accommodative infacility is to select an
                             appropriate near target (6/9 equivalent), and with or
                             without the CAMP lenses, change the accommodative
                             stimulus by adding +2.00 D lenses, and then adding – 2.00
                             D lenses when the patient reports the target is clear with the
                             + 2.00D lenses.

                              The examiner keeps changing from one set of lenses to the
                              other for a period of one or two minutes. Twenty changes
                              in one minute = 20/2 = 10 cycles/min.

                              The equipment to use is the Bausch and Lomb comparator
                              (Correct eye scope) or similar device.

                              The test is performed first monocularly, and then
                              binocularly. To check for suppression, Vectographic targets
                              and polarizing glasses are used so that the left eye sees on
                              set of targets, and the right eye sees another set of targets.
OPTO 374    -          Binocular Vision                                             31

                               Typical values range from 15 to 22 cycles per minute for
                               young adults, for monocular tests.

                               Binocular tests (without checks for suppression) are usually
                               to 3 to 5 cycles slower than monocular tests.

                               With tests/checks for suppression, binocular facility speeds
                               could be up to 60% slower.

                Treatment:     This involves exercising accommodative facility using the
                               same equipment used for diagnosis.

Table 5.4       Grades/Ranks for Accommodative Facility with ± 2.00D Lenses

                     Rank                 OD or OS         Binocular (with Supp. check)

     5   (Very Strong)                    > 18                       > 10
     4   (Strong)                         14 – 18                    8 – 10
     3   (Adequate)                       10 – 13                    6–7
     2   (Weak)                           6–9                        4–5
     1   (very weak)                      <6                         <4

                A test score of less than 10 cycles/min for monocular, a differences of
                more than 3 cycles/min between both eyes, or a binocular test with
                suppression check result of less than 6 minutes is considered a failure and
                the patient should be referred for vision training.


      Definition:      This is the inability to sustain adequate accommodative facility for
                       sustained periods (usually one minute or more).

                       Like accommodative infacility, it may be caused by normal
                       physiological variation in the population, poor general health,
                       infectious diseases, medication, or excessive visual demands.
OPTO 374        -          Binocular Vision                                        32

Table 5.5           Grades/Ranks for Accommodative Stamina with ± 2.00D Lenses

                    Rank                  OD or OS         Binocular (with Supp. check)

        5    (Very Strong)               ≥ 108 seconds              ≥ 60 secs
        4    (Strong)                      84 – 108 secs            48 – 59 secs
        3    (Adequate)                    60 – 83 secs             36 – 47 secs
        2    (Weak)                        36 –59 secs              24 – 35 secs
        1    (very weak)                 < 36 secs                  < 24 secs

AC/A Ratio

Most clinical systems used in vergence analysis base their diagnosis on the interaction
between the 4 Maddox vergence components of: Tonic Vergence, Fusional Vergence,
Accommodative Vergence, and Proximal Vergence.

When vision is shifted from distant to near objects, accommodation is brought
significantly into play making accommodative convergence a critical factor in vergence
disorders that affect near vision.

The AC/A ratio is the amount of accommodative convergence which is associated with
accommodation. So that if accommodation increases by 2D, and accommodative
convergence increases by 12 ∆, the AC/A ratio is 6 / 1.

The AC/A ratio may be assessed using either of the following methods:

           Calculation Method
           Gradient Method.

Calculation Method

AC/A        =   IPD (cm) + [(Hn – Hf) / (An – Af)]
OPTO 374      -         Binocular Vision                                           33


An = Accommodative demand at near (in Diopters)

Af = Accommodative demand at far (in Diopters)

Hn = Objective angle of deviation (phoria) at near using for example the prism cover
     test (in ∆)

Hf = Objective angle of deviation at far (in ∆)

Note Eso deviations have positive values, and exo deviations have negative values.

A clinically useful simplification of the general formula above was offered by M.C.
Flom in 1963. It is:

AC/A =       IPD (cm) + M (Hn – Hf) where M is the near fixation distance in meters.

The normal calculated AC/A range is from 4/1 to 7/1. An AC/A greater than 7/1 is
high, and one less than 4/1 is considered low.

The magnitude of the AC/A is directly proportional to the size of the IPD. The larger
the IPD, the larger the AC/A.

A 0/1 value for AC/A is improbable and a negative AC/A ratio (e.g. -2/1) is impossible.
So, if you get either of these values, you must re-check the PD, and the near &
distance phorias.

Gradient Method

        Using the CAMP lenses (plus the lens ADD if necessary), the patient‘s phoria at
         40 cm is measured.

        Add +1.00 to each eye and re-test the phoria (plus lenses will relax
         accommodation and therefore increase exophoria).

        If the exophoria for example changes from 10∆ exo. to 5 ∆ exo. the AC ratio is
         5/1. This is because the phoria has changed by 5∆ for a 1D change in the stimulus
         to accommodation.
OPTO 374    -        Binocular Vision                                          34

      The gradient AC/A may also be assessed using a – 1.00D lens.

      Some investigators prefer to use +2.00D or -2.00D lens to assess gradient AC/A
       especially in younger patients.

      The gradient AC/A may also be assessed at distance

      The normal value for gradient AC/A ranges from 2/1 to 5/1.

The calculated AC/A is more reliable than the gradient AC/A, but the gradient AC/A is
more clinically relevant because it shows directly the effect of added lenses on the
patient‟s angle of deviation.
OPTO 374        -          Binocular Vision                                            35

Lecture 6
Graphical Analysis

We can take our findings for: near and distance phorias; amplitude of accommodation;
base-in- and base-out- limits at distance and near; and positive- (PRA) and negative-
(NRA) relative accommodation, and fit them into a graph to get either:

                   A zone of clear single vision
                   or A zone of single vision

From an inspection of this zone, we may infer the presence or absence of binocular vision
anomalies, assess the relationship between accommodation and vergence, and between
the patient‘s phoria at any distance and the fusional vergence ranges for that distance.

Figure 6.1 is an incomplete graphical analysis graph (explain abscissas, ordinates and
symbols) depicting:

                   The phoria line
                   The demand (Donders‘) line

The phoria line basically is derived by plotting the measured 6m and 40 cm heterophoria
values on the graph, and then drawing a straight line which passes through both points
from the ―prism scale at 6 m‖ to the level of the amplitude of accommodation for the

To plot the demand line, we need to assess the relationship between accommodation and
accommodative convergence.

To do this, we first have to accept that the patient is either emmetropic or a fully
corrected ametrope whose accommodation at optical infinity is reduced to zero.

Next we state the formula for calculating the total convergence at a particular distance,
which is:
               CT = Distance P.D.          X 100 prism diopters
                        Target distance from C (C.O.R.)

The angle of total convergence refers to the angle subtended at the object of regard by the
intersection of the visual axes of both eyes (illustrate).

Thus for an emmetropic patient whose distance PD is 60 mm, his total convergence for
an object at 6 meters or greater is 0 ∆, while his total convergence for an object at 100 cm
is 6 ∆.
OPTO 374       -          Binocular Vision                                          36

Once we have derived the total convergence for a subject at 100 cm (because the stimulus
accommodation at 100 cm is 100 / 100 = 1 D), we can then multiply this value by the
stimulus accommodation at any other distance to get the total convergence at that

Therefore in the case of the subject above, for an object at 40 cm, his total convergence
will be: 2.5 X 6 = 15 ∆.

Once we have the values for total convergence at any two distances, we can plot
Donders‘ line. Donders‘ line is a straight line which passes through these two points, and
connects the ―prism scale at 6 meters‖ with the horizontal line that denotes the amplitude
of accommodation of the subject.

More precisely, Donders‘ line is a series of points which show the expected demands on
accommodation and convergence (at various fixation distances) in normal binocular
single vision.

Once we have plot the phoria and Donders‘ (demand) lines, we need to plot the limits for
the zone of clear single binocular vision (ZCSBV). To do this, we need four data point
values, which are:

                  Base-in – to – blur    @ 6 meters
                  Base-out – to – blur   @ 6 meters
                  Base-in – to – blur    @ 40 centimeters
                  Base-out – to – blur   @ 40 centimeters

Whenever we do not have a blur point value (such as is usually the case for BI to blur @
6 meters), we use the break point value.

After we get the values corresponding to the four points above, we will need to draw two

The first line connects the BI to blur points for 6 meters and 40 cm, and is drawn to touch
both the ―prism scale at 6 meters‖ and the horizontal line that denotes the amplitude of
accommodation of the subject.

The second line connects the BO to blur points for 6 meters and 40 cm, and is drawn to
touch both the ―prism scale at 6 meters‖ and the horizontal line that denotes the
amplitude of accommodation of the subject.

The region of the graph enclosed by these two lines, the line which denotes ―prism scale
at 6 meters‖, and the horizontal line that denotes the amplitude of accommodation of the
subject, is referred to as the ZCSBV. This zone is depicted in figure 6.2.
OPTO 374   -   Binocular Vision   37
OPTO 374     -         Binocular Vision                                             38

To get the zone of single binocular vision (ZSBV), we use the four break points at 6
meters and at 40 centimeters.

Note that there is a difference between the ZCSBV and the ZSBV. During either of the
prism tests, at the blur point, we have reached the limits of fusional convergence (or
divergence). The visual system then persuades accommodation to increase (or to relax).
If this happens, the image will remain single but will become blurred (this is referred to
as single binocular vision. The image is not clear, but blurry). If accommodation fails
to increase or relax then there will be no blur point and the image will immediately

It therefore becomes quite clear that the ZCSBV is similar in shape to the ZSBV, but it
is narrower.

The ZCSBV as shown in figure 6.2 approximates a parallelogram slanting rightward, due
to the influence of the AC/A, which serves as the axis of the zone.

The right side of the ZCSBV fans out (illustrate) primarily due to the influence of
proximal convergence for near point targets, but it may also be due in part, to the effect
of convergence (prism) adaptation.

Normally there is no blur point for fusional divergence (negative relative convergence or
base-in – to – blur) at 6 meters. If a blur point is found, it indicates the presence of a
latent hyperopia, or possibly an over-corrected myopia. This blur point usually indicates a
spasm of accommodation.

The PRA and NRA values can also be plot on the graph. Both points are plot on the
vertical dotted line which joins the zero point on the ―prism scale at 40 cm‖ with the 15∆
point on the ―prism scale at 6 meters‖.

The binocular plus acceptance (NRA) is influenced by positive relative convergence, and
tends to be reduced if PRC is reduced. It should fall on or very close to the base-out line
on the graph. The NRA represents a reduction in the stimulus to accommodation equal to
the lens added in front of the eye. So that an NRA of +1.00 D should be recorded on the
graph on the vertical dotted line where this line intersects with the horizontal line that
represents a stimulus accommodation of 2.50 – 1.00 (this test is done at 40 cm) = +1.50

The converse holds true for binocular minus acceptance (PRA).

Now that we have discussed the relevant points of the graphical analysis form, it is
important to have an idea what the norms are for the various tests such as NRA, PRA,
base-out limits at 6 meters and at 40 cm etc.
OPTO 374     -         Binocular Vision                                             39

Table 6.1              Clinical Norms of Morgan

    Name of Test                    Average Value                     Normal range

1) Distance Phoria                        1 ∆ Exo                 Ortho to 2 ∆ Exo
2) BO to blur @ 6 meters                  9∆                      7 ∆ to 11 ∆
3) BO to brk .@ 6 meters                  19 ∆                    15 ∆ to 23 ∆
4) BO to recv @ 6 meters                  10 ∆                    8 ∆ to 12 ∆
5) BI to brk. @ 6 meters                  7∆                      5 ∆ to 9 ∆
6) BI to recov @ 6 meters                 4∆                      3 ∆ to 5 ∆
7) Near Phoria                            3∆                      Ortho to 6 ∆ Exo
8) BO to blur @ 40 cm                     17 ∆                     14 ∆ to 20 ∆
9) BO to brk. @ 40 cm                     21 ∆                     18 ∆ to 24 ∆
10) BO to recv @ 40 cm                    11 ∆                     7 ∆ to 15 ∆
11) BI to blur @ 40 cm                    13 ∆                     11 ∆ to 15 ∆
12) BI to brk @ 40 cm                     21 ∆                     19 ∆ to 23 ∆
13) BI to recv @ 40 cm                    13 ∆                     10 ∆ to 16 ∆
14) BMA (PRA)                             - 2.37 D                 - 1.75 to - 3.00 D
15) BPA (NRA)                             + 2.00 D                + 1.75 to + 2.25 D

Criteria for Lens and Prism Prescription

The criteria we use for lens or prism prescription are:

      Morgan‘s Criterion
      Clinical Wisdom
      Sheard‘s Criterion
      Percival‘s Criterion

The criterion used for prescription depends on the clinician‘s training, clinical experience
and biases. However, Sheard‘s criterion is probably the mostly popular one used.
OPTO 374      -        Binocular Vision                                                40

Morgan‟s Criterion

What happens in this case is that the table of normals above is used to prescribe for the

For example, a patient has 10 ∆ exophoria at 40 cm. Morgan‘s table however tells us that
the normal range is ortho to 6 exophoria.

We relieve exophoric symptoms with BI prisms.

We prescribe the smallest prism that will bring this patient within Morgan‘s normal
range. This prism is 10 – 6 = 4 ∆ Base-in.

Clinical Wisdom

Here, we prescribe a prism which is one-third of the measured angle of deviation. Thus if
a 6 ∆ exophoria is determined, we will prescribe 2 ∆ BI.

However in cases of symptomatic esophorias or vertical phorias, the full correction is

It is better to divide the prisms equally between both eyes.

Sheard‟s Criterion

Sheard‘s criterion states that for comfort, the appropriate fusional vergence limit should
be twice the value of the measured phoria. So that if the measured phoria is 5 exo, we
would be concerned with the base-out to blur value (since exophoria is a tendency
towards divergence, we are concerned to know if the convergence reserves for the
patient, at the same distance are sufficient). If this value is 10 ∆ or greater, then Sheard‘s
criterion has been satisfied and we do not require to prescribe prisms. If it is less than
10 ∆ then we will need to prescribe prisms using the following formula:

       Sheard ∆ = (2 X phoria - Fus. Verg.) / 3.

If the phoria is eso, we are concerned with the BI to blur for the same distance. If there is
no blur point, we look at the break point, compare it to the phoria and determine if
Sheard‘ criterion is satisfied or not.

Explain graphical prism prescription using Sheard‟s criterion.
OPTO 374     -         Binocular Vision                                              41

Percival‟s Criterion

This criterion is unique because it ignores the position of the phoria line. He postulated
that the important factor is the demand line and its position within the ZCSBV.

His criterion asserts that this line should be in the middle-third of the with of the ZCSBV
at any point. This means if you took the horizontal line that indicated a stimulus
accommodation of 2D, to assess whether or not Percival‘s criterion is satisfied, you
would need to:

       Measure the length of the line from where it touches the BI to blur line, to where
        it touches the BO to blur line.
       Next divide this line into three lines of equal length. So that if the line is 6 mm
        long, divide it into three lines, 2 mm long each.
       Percival criterion is satisfied if the demand line cuts through the central of the
        three lines. If not, we need to prescribe prisms according to the following

                 Percival ∆ = (1/3L - 2/3S)

        Assuming the demand line cuts through the rightmost line, so that it lies closer to
        the base-out line than the base-in line. The horizontal distance from the base-in
        line to the demand line is the Longer (L) line. The distance from the base-out line
        to the demand line is the Shorter (S) line
OPTO 374     -         Binocular Vision                                             42

Lecture 7
These are disjunctive eye movements that involve the eyes moving by equal amounts in
diametrically opposed directions (explain).

The neural pathway for the vergence innervation is from area 19 to both third nerve
nuclei in the mid-brain.

Although not universally accepted as the only valid classification of vergence, it is widely
agreed that Maddox‘s classification of four vergence components – Tonic vergence;
Accommodative vergence; Fusional vergence; Proximal Vergence – is useful for clinical

It must however be taken into account that other factors (such as the phenomenon of
prism adaptation) must be taken into account in vision therapy.

Near Point of Convergence (NPC) or Absolute Convergence

This can be measured in the clinic using the tip of a pen or pencil, but it is recommended
that a target that stimulates accurate accommodation be used. A small isolated letter E
which subtends a visual angle of 1.5 minutes of arc (20/30) at 40 cm has become the
clinical standard.

The target is initially placed at about 40 cm from the subject and moved close to the nose
at a rate of 3-5 cm per second. We are looking for when the subject first reports a blur,
when the subject first reports that the target has doubled, and when the subject reports
that the target has become single again (recovery point). The break point is recorded as
the point of absolute convergence.

This point can be expressed in centimeters or in prism diopters (as total convergence)
using the formula given in the previous lecture. The only addition is that a constant value
must be used for the distance of the center of rotation of an eye from the spectacle plane.
This value is 27 mm.

Figure 7.1 depicts the total convergence by both eyes at the target at the NPC. Let us
assume that the NPC (breakpoint) is 7 cm from the spectacle plane for a patient whose
IPD is 60 mm, the total convergence for this patient is:

                     6cm X 100            =   61.85 
                     (7 + 2.7) cm
OPTO 374   -   Binocular Vision   43
OPTO 374     -         Binocular Vision                                            44

The normal blur point has a range of between 10 and 15 cm, and the normal break point
should be 8 cm or less. A break point of greater than 10 cm should be regarded as a
failure and should be the cutoff point for referral.

Sometimes the subject will not report a break point (usually because one eye is being
cortically suppressed). In this case, the examiner should watch for when one eye turns
away from the target or does not converge sufficiently to maintain binocular fixation of
the target.

The examiner could also use a penlight a few centimeters above the target and watch for
when the corneal reflex position changes significantly from normal. This is a modified
Hirschberg test.

NPC testing allows for the assessment of Sufficiency (vergence amplitude), facility
(flexibility), and stamina.

Sufficiency assessed the break point and if it is normal.

Facility assesses the recovery point. Note that the target does not have to be clear, just
single for the examiner to record a recovery point value. The recovery point should be 11
cm or less. A recovery point of beyond 11 cm should be considered a failure and a cutoff
point for referral.

Stamina assesses repeatability of the test. This is assessed by repeating the NPC test four
times. The NPC values should stay the same or improve (the exercise of repeating the test
makes the patient‘s convergence range improve). If the sufficiency reduces each time the
test is repeated, then the subject has failed the stamina test.

Note that tonic and proximal vergence are present in the neonate, accommodative
vergence is present a few weeks after birth. Fusional vergence is the last of Maddox‟s
vergence components to develop and it has not been determined when it occurs.

However, it is believed that the seven year old child has similar Sufficiency, Facility
and Stamina values to the adult. This is provided the child is attentive and has
performed the test satisfactorily.
OPTO 374     -         Binocular Vision                                             45


The classification of vergence anomalies most widely used in optometry today is the
Duane-White classification. This system of classification is based on the tonic deviation
of the eyes and the AC/A, and it is used to describe both heterotropic and heterophoric

Duane initially proposed that a subject be classified into one of his four original
categories of anomalies if the difference between their 6 m and 0.4 m phoria exceeded

Nowadays, a difference of 5 is used as the cut off point to denote patients with
abnormally high or low AC/A ratios.

Duane‘s four original classifications were:

      Convergence insufficiency (CI)
      Divergence Excess (DE)
      Divergence Insufficiency (DI)
      Convergence Excess (CE)

In addition we will also discuss:

      Basic Exophoria (BX)
      Basic Esophoria (BE)
      Basic Orthophoria with restricted zone
      Normal Zone with symptoms

Convergence Insufficiency

This is characterized by a low AC/A ratio, which results in an increased exophoria (5 or
greater) at near than at distance. Some CI patients present with a high exophoria at 6 m
(low tonic convergence) in addition to a low AC/A.

Also associated with CI are a low positive relative convergence (PRC) value, and a low
near point of convergence (NPC).

The treatment of choice is vision training, but such patients may also benefit from prism
prescriptions in the near glasses only.

Increasing minus lenses will do very little in these cases because of the low AC/A.

Presbyopic exophoria falls within this group of vergence disorders
OPTO 374   -   Binocular Vision   46
OPTO 374     -         Binocular Vision                                              47

Divergence Excess

This is also an exophoric anomaly in which a large exophoria at distance is combined
with a high AC/A to give a significantly lower exo at near.

Some patients have a simulated (pseudo) DE. After measuring the initial far and near
phorias, both eyes are occluded (prolonged occlusion) for 10 minutes. The near phoria
should then be repeated and will be found to have increased. Such a case is a simulated
DE and is believed to be caused by a spasm of fusional convergence.

These patients respond well to vision training, but not as well as the other types of exo

A minus add could also be given to the patient to take advantage of the high AC/A to
control the distance phoria.

Base in prisms may also be useful to reign in the symptoms from the distance phoria, but
the fear is that esophoria may then be induced at near if the prisms are too high.

Divergence Insufficiency

This is a case of esophoria as are convergence excess and basic esophoria, and it is the
least prevalent of the eso-deviations

The fact that it has ―Divergence‖ in its name means that it is a problem which occurs with
distance viewing. A divergence insufficiency then indicates a reduced divergence at
distance, which would suggest a high esophoria at distance. This phoria (as with all
phorias at distance) are caused by the muscle tone of the patient‘s eyes.

In a typical divergence insufficiency case, we would have a high esophoria at distance
combined with a low AC/A ratio (the AC/A ratio combines with tonic vergence, and to a
smaller extent proximal vergence to determine the near phoria position) to yield a low
esophoria at near. For example, such a patient could have 12 esophoria at distance and
3 esophoria at 40 cm.

Such patients may lapse into occasional esotropia at distance, and they are generally
difficult to manage. One treatment approach is to prescribe base-out prisms for distance
viewing, but care should be taken to avoid inducing excessive exophoria at near.

Vision training is also a treatment modality. The aim is to increase the patient‘s
divergence ranges.
OPTO 374     -         Binocular Vision                                             48

Convergence Excess

―Convergence‖ means that the problems presents with near viewing. An excess
convergence in this case must mean that the AC/A ratio is high with a normal phoria at
far (since no problems are indicated at distance, we must assume that the distance phoria
is normal. We also know that the AC/A combines with tonic vergence to determine the
near phoria. So if the tonic vergence is normal, to get a convergence excess, the AC/A
ratio must be high).

An example of such a condition is a 7 esophoria at near and orthophoria at distance.

Blurring of prints and asthenopia at near are the typical presentation and CE is usually
associated with latent Hyperopia, making it necessary to perform a cycloplegic refraction
for all CE patients.

Treatment modalities include vision training to fusional divergence ranges and plus-add
lenses for reading.

BO lenses are only prescribed when there is a significant phoria at distance as well.

Basic Exophoria

This refers to a situation where the exophoria at far is normal (because the tonic position
is normal), combined with a normal AC/A ratio so that both far and near exophorias are
equal or almost equal.

In the case of a BX patient with symptoms (which may occur at distance or at near), the
therapy of choice is vision training. Base-in prisms may also be used (just so long as
there is minimal prism adaptation) to reduce the demand on fusional convergence at
distance and/or near (and therefore, the symptoms of asthenopia would also be reduced.

Basic Esophoria

This is characterized by a significant esophoria at far combined with a normal AC/A ratio
so that the esophoria at near is about the same as that at distance. An example of such a
case is a subject with 10 esophoria at 6 m and at 40 cm.

Associated findings include a low PRA, a low PRA and a high NRA.

The preferred treatment in these cases is a BO prism prescription for the distance at
which the symptoms are being experienced. If the symptoms are experienced at both
distances then the BO prisms are incorporated into single vision lenses to be used for all

Vision training to increase divergence ranges may be undertaken it takes awhile (several
months) to get results, and these results are ephemeral more often than not.
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OPTO 374   -   Binocular Vision   50
OPTO 374     -         Binocular Vision                                              51

Basic Orthophoria with Restricted Zone

In this case the phorias at distance and near are normal, but the PRC and/or NRC are
reduced. Often, accommodative facility and AC/A are reduced as well.

Symptoms include patients complaining of fatigue after prolonged concentration on a
near task, particularly when fixation distance has to be changed frequently.

The cause of restricted zone could be poor general health or a side effect of the use of
therapeutic or other drugs. RZ could also be caused by uncorrected astigmatism,
uncorrected anisometropia, and aniseikonia. It may also be caused by accommodative
and or vergence dysfunctions.

Treatment first and foremost involves considering and solving/treating the underlying
cause so a careful case history is necessary. Treatment is optical when the origins of RZ
are refractive and it is vision training when the origins of RZ are accommodative and or
vergence dysfunction. In the latter case, the aim of vision training is to expand the entire

Normal Zone with Symptoms

Here even though the ZCSBV is normal, the patient present with symptoms that sound
binocular. Careful questions need to be asked by the examiner, and perhaps investigative
examinations taken to eliminate the likely causes of such a disorder before the examiner
concludes that the patient has psychogenic problems such as hysteria, malingering or
emotional instability.

Some questions which need to be investigated are:

         Is there a latent Hyperopia or pseudomyopia? Test for this with a
         cycloplegic refraction.

         Is there a latent phoria? Test for this with prolonged occlusion – READ UP

         Is there poor accommodative or vergence stamina? Test these parameters at
         the end of the day

         Are the symptoms really of binocular origin? Patch the non-dominant eye
         and ask the patient to keep a record of the resulting symptoms. If they improve
         with patching, some binocular dysfunction is indicated. If they stay the same
         or worsen, there may be general health problems, drug reactions or
         psychological stress.
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OPTO 374     -        Binocular Vision                                            53


Note that the list of anomalies described here is by no means an exhaustive list of
binocular anomalies that the optometrist could be expected to encounter.

For one thing, the diagnosis of binocular dysfunctions discussed is fundamentally
based on Maddox‟s vergence categorization. It is also on this categorization that
graphical analysis is based.

Graphical analysis however ignores dysfunctions of accommodation which are not
accommodative insufficiency whereas vision efficiency analysis includes the
assessment of accommodative lag, facility and stamina.

Originating in the 1950s, the analysis of the fixation disparity curve tends to reinforce
graphical analysis and supplement the vergence evaluation of graphical analysis, even
though both these analysis systems emphasize different aspects of vergence and
accommodative interactions.

The most recent proposals suggest that clinicians should use the version of vergence-
accommodation analysis proposed by Hung-Semmelow. Basically this takes into
consideration the effect of proximal vergence on the near point phoria position (which
classical case analysis ignores).

It is also suggested that parameters such as phoria and AC/A ratio should be measured
under “closed-loop” conditions (such as the conditions under which fixation disparity
is measured) because these conditions more accurately reflects the relationship
between accommodation and convergence.

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