The vergence eye movements are produced by a group of compound reflexes, only two of which are identifiable because they are measurable; these are fusional vergence and accommodative convergence. The fusional vergences are optomotor reflexes designed to improve and maintain the alignment of the eyes so that similar retinal images project on corresponding retinal areas, a requirement for single binocular vision that utilizes normal retinal correspondence. The accommodative convergence is a reflex linking convergence automatically to accommodation and supplying the most economical innervating method for achieving proper alignment simultaneously with a change in the dioptric power of the lens as attention shifts rapidly between a remote point and a proximal point. Another vergence reflex, or perhaps other vergence reflexes, influences the alignment but remains ill-defined and not measurable; this unidentifiable entity which exerts vergence influence on the alignment makes up the tonic vergence.

The following four stimuli produce the synkinetic near response:

1. A blurred retinal image focused posterior to the plane of the retina. Regardless of whether the object projecting as a blurred image is far away or near, accommodation is applied. Accompanying the accommodation are the other two components of the synkinetic near response.
   
2. Bitemporal disparate retinal images. Accommodative convergence is used to reduce the bitemporal disparity in some patients similar to the way fusional convergence is used. Bitem-poral retinal image disparity alone is enough to initiate the near response in some patients with exodeviations. Often a synkinetic near response to the bitemporal sharply focused retinal images occurs in the young exodeviating emmetrope even while fixating at a distance.
   
3. Awareness of near. A psycho-optic influence reflexly causes the subject to put forth the synkinetic response while attentive to proximal points in space. The opposite, awareness of far, causes relaxation of the synkinetic near response while the patient is attentive to remote points in space. The subject induced to respond counter to these psycho-optic drives (i.e., to relax the synkinetic near activity while looking at a near point through plus lenses or to stimulate this activity while looking at a far point through minus lenses) gives only a fraction of what the total response would be were he allowed to respond naturally in conformity with the awareness of near and far influences. Recognizing their inability to prevent all convergence during measurement of alignment at near positions while the subject looks through plus lenses, many investigators have labeled this inevitable convergence response “proximal convergence.” Clinically, a similar situation has been recognized while doing simulated distant alignment measurements on instruments requiring near fixation through plus lenses. In variably, such simulated distant measurements are more convergent than true distant measurements. However, such terms as “proximal convergence” and “instrument convergence” create a concept that these are separate entities within the spectrum of vergences rather than mere findings produced by the unnatural stimulation of the synkinetic near response.
   
4. Voluntary convergence. The synkinetic near activities usually occur at a subconscious level, as do reflexes. However, there is one outstanding exception. The synkinetic near activities that occur in response to a conscious desire to maximally converge the eyes are not reflex; this is voluntary convergence and is produced by fixating an imaginary near point. Associated with the convergence response are accommodation and miosis. Thus, voluntary convergence is a willed, forceful thrust of the entire spectrum of synkinetic near activities.
   

The accommodation and accommodative convergence components of the synkinetic near response are in perfect balance when each produces the satisfactory adjustments needed for clear vision and fusion over a wide range of fixation distances. If these activities are in proper relation, then the ratio of accommodative convergence to accommodation (AC/A) is normal. An abnormal AC/A is characterized by either a deficiency or an excess of accommodative convergence associated with each unit of accommodation; thus, the resulting abnormal ratio is either a low AC/A or a high AC/A.

The normal ratio is influenced by certain drugs that alter the AC/A as long as they are present; however, when the drugs are withdrawn the AC/A reverts to the premedication level. The normal ratio is altered by parasympathomimetic and para-sympatholytic drugs instilled into the eyes. Miotics potentiate the transmission of acetylcholine across the myoneural junction, allowing innervation to the ciliary muscle to produce a contraction greater than normal. This in turn results in a greater dioptric power change in the molding of the lens. However, associated with the innervation to the ciliary muscles is the same amount of innervation to the medial recti. Because the miotic has no effect on these muscles, there is no change in the quantity of convergence this amount of innervation produces. Consequently, the miotic alters the AC/A so that the response is more accommodation associated with an unchanged amount of accommodative convergence (i.e., the miotic lowers the AC/A).

Weak cycloplegics partially prevent innervation arriving at the myoneural junction of the ciliary musculature from producing the expected dioptric increase in the refractive power of the lens. This is due to the reduction in the motor units firing in the ciliary musculature because the cycloplegia competes with the motor end-plates for the acetylcho-line. Yet, the innervation simultaneously dispatched to the medial recti produces the normal convergence. The result is that the cycloplegic diminishes the accommodation response without changing the accommodative convergence (i.e., the cycloplegic raises the AC/A).

NORMAL AC/A

The normal AC/A in children is pliable, an attribute that allows adjustments in uncorrected myopia and exodeviation.

In uncorrected myopia, the patient tends to adjust the AC/A to a high ratio in order to obtain the maximal accommodative convergence and the deficient accommodation required for near vision. This compensation assists the myope to enjoy near binocularity. After the patient wears glasses for near vision for a few weeks, the high AC/A reverts to normal because it is no longer needed.

The young child with exodeviation tends to have a high AC/A which permits the patient to compensate maximally for the deviation and the bitemporal retinal image disparity it causes. After the exodeviation is corrected with surgery the ratio reverts toward normal because the high AC/A is no longer needed.

ABNORMAL AC/A

An abnormal AC/A may be either a high or a low ratio. A high AC/A causes more convergence for near fixation than for distance fixation, with the actual difference between them being determined by the severity of the AC/A abnormality, which may vary from slight to marked. A high AC/A may occur in a patient with orthophoric eyes for distance fixation as well as in the patient with an esodeviation or an exodeviation. The patient with a high AC/A who is either orthophoric or exodeviated for distance was described by Duane¹ as having a convergence excess. The patient with a high AC/A with exodeviation at distance has a divergence excess.¹

The high AC/A is invariably the etiologic factor causing the convergence excess, and in this setting the high AC/A is primary (i.e., it is primarily defective and not a secondary change in a normal AC/A). Depending on the refraction of the patient and the severity of this primarily abnormal AC/A, the eyes are straight, esophoric, or esotropic at distance, but regardless of the distant alignment, the esodeviation is invariably greater at near fixation. However, the high AC/A in the patient with exotropia with divergence excess usually is an altered normal ratio that exercised its attribute of pliability, becoming a high ratio to help offset the exodeviation. Yet, the primarily defective high AC/A can occur in any type of patient, even one with exotropia. It is possible that the patient with divergence excess may have either a high ratio that evolved from a normal one or a primarily abnormal high ratio, although the latter occurs infrequently. Most importantly, the primarily abnormal high AC/A is unpliable, unlike the normal AC/A. Surgically aligning the exodeviated eyes in a patient with divergence excess whose high AC/A is primarily defective results in a persistent esodeviation at near fixation, whereas the preoperative high AC/A adapted from a normal one promptly returns to normal postoperatively, nullifying any trend to near esotropia.

The primarily defective high AC/A that causes convergence excess tends to improve after the patient reaches 8 years of age. Improvement may gradually continue over the next several years, but usually a trace of high AC/A persists throughout life. Approximately 50% of the patients with the primarily high AC/A show this improvement trend while the remaining 50% retain their same high AC/A into adulthood. Miotics normalize the high AC/A but only while the drug is used; the miotic produces no permanent change in the AC/A. Surgery on the horizontal rectus muscles may improve the high AC/A somewhat; the greater the severity of the high AC/A, the greater is the effect of surgery on the ratio. There is no orthoptic technique that can improve the high AC/A.

A low AC/A causes less convergence for near fixation than for distance fixation, with the actual difference between them being determined by the severity of the AC/A abnormality, which may vary from slight to marked. A low AC/A may occur in a patient with orthophoric eyes for distance fixation as well as in a patient with esodeviation or exodeviation. The patient with a low AC/A who is either orthophoric or exodeviated for distance was described by Duane as having convergence insufficiency.¹ The patient with a low AC/A and esodeviation at distance has a divergence insufficiency.

The low AC/A in convergence insufficiency is a primarily defective ratio that never improves with age. Although weak cycloplegics temporarily improve the low AC/A, this is of no practical value because the blurred vision and asthenopia produce symptoms more disturbing than those caused by the low AC/A. Neither surgery of the horizontal recti nor orthoptics improve the low AC/A in convergence insufficiency.

The low AC/A in divergence insufficiency is a relatively rare clinical entity. A very few esodeviated children who fuse at near fixation but who are either esotropic or have a large esophoria at distance have been studied; however, surgery has not been performed in a sufficient number to determine if there is a trend for the low AC/A to improve after the distance esodeviation is eliminated. Divergence insufficiency is found as a gradually appearing phenomenon in a few elderly patients, but advancing divergence palsy in a child or young to middle-aged adult accompanied by recent onset of distance homonymous diplopia is the dangerous history that demands neurological work-up. Consequently, it is not known whether the low AC/A is the adjusted normal pliable AC/A that evolved to help offset the esotropia or whether it is a primarily defective, unpliable ratio that just happens to occur in small-angle esodeviation.

CLINICAL INVESTIGATION OF AC/A

Two simple methods of clinically investigating the AC/A are used extensively; however, regardless of which is used, the accommodation must be controlled while the study is conducted. Corrective lenses control the accommodation if the patient is other than emmetropic. Also, small-detailed fixating targets should be used rather than muscle lights. Prism and alternate cover measurements are made while the patient accommodates two different amounts. This enables the amount of convergence associated with accommodation to be evaluated.

One method of selecting the two separate quantities of accommodation for the patient is the dis-tance-near measurements method, which alters the fixation distance. The most practical fixation distances are 6 meters and 0.33 meter. A normal AC/A is indicated by similar prism and alternate cover measurements at these two fixation points; dissimilar measurements indicate an abnormal ratio (Table 1).

TABLE 1. AC/A as Determined by Prism and Alternate Cover Measurements

The other method of selecting the two separate quantities of accommodation for the patient is the lens gradient method, which maintains the same fixation distance while altering the accommodation with lenses. For example, 0.33 meter is used as the fixation distance, and prism and alternate cover measurements are performed first while the patient looks through +3.00 spheres and then without the lenses. Although the +3.00 spheres are a stimulus to relax the accommodation, the response is less than the stimulus because of awareness of near. Consequently, the values obtained by the lens gradient method in a patient with a normal AC/A are less than those obtained by the distance-near measurement method. Abnormal AC/A, whether high or low, is detected by either method, but the absolute values do not correspond. The lens gradient method is the preference of the researcher in this field, and the distance-near measurement method is the choice of the clinician. Usually, as students first encounter the AC/A, they want absolute figures delineating the range of normal. Accommodative convergence in prism diopters related to A in diopters by the lens gradient method is usually in the range of 3.7 to 4.2 in the normal person. However, this absolute figure for the lens gradient method is not particularly meaningful when the student evaluates patients and determines their optical treatment for abnormalities in their synkinetic near response. At this level, the student soon comes to appreciate the clearer overall clinical picture that the distance-near measurements method affords. However, for most scientific investigations, the various controls that can be added to the lens gradient method, such as measuring accommodation response with the Badal optometer stigmatoscope² rather than depending on the accommodation stimulus and such as recording the accommodative convergence change with fixation disparity techniques³ rather than with prism and alternate cover, make the lens gradient method the method of choice for the researcher studying the AC/A.

AMPLITUDE

Another parameter that can be used to assess accommodative convergence is its amplitude. The amplitude is a measure of the total prism diopter change in the alignment that is produced between totally relaxing the synkinetic near response and maximally applying it.

For example, an emmetropic child having a normal AC/A and an amplitude of accommodation of 14 diopters converges the eyes to a point 7 cm away when maximally accommodating. This quantity of convergence associated with the maximal accommodation is the maximal accommodative convergence. If the patient is orthophoric at distance and has an ideal AC/A, the amplitude of accommodative convergence equals the interpupillary distance in centimeters, times the amplitude of accommodation. Therefore, the amplitude of accommodative convergence usually ranges between 70Δ and 84Δ because the interpupillary distance of most children ranges from 5 to 6 cm. In contrast, a child with an amplitude of accommodation of 14Δ and a high AC/A that is relatively severe may have an amplitude of accommodative convergence of more than 150Δ. Another child with the same accommodation amplitude and a low AC/A may have an accommodative convergence amplitude of 40Δ or less.

Determining the amplitude of accommodation in any particular patient is not clinically helpful; its principal value is the concept it affords. As this discussion of the vergences continues, the fusional vergences will be evaluated entirely according to their amplitudes measured in prism diopters. Therefore, a method for relating accommodative convergence to the fusional vergence amplitude is important in order to appreciate all aspects of vergence; unfortunately, the AC/A does not supply this perspective. Once the amplitude of accommodative convergence is appreciated, one realizes that it is by far the strongest of all vergences.

The maximal amount of eye movement produced by fusional vergence is referred to as an amplitude. The amplitudes of horizontal, vertical, and rotary fusional vergence are measurable; the prism diopter is the unit of measurement except in incyclovergence and excyclovergence, which are measured in degrees.

HORIZONTAL

Convergence

Fusional convergence is a reflex that responds only to the stimulus of bitemporal disparity of the retinal images. Because exotropia is associated with heteronymous diplopia resulting from the bitemporal image disparity, fusional convergence can overcome the diplopia by eliminating the retinal image disparity and maintaining exophoria.

The fusional convergence amplitude is measured by the maximal response to stimulation. The two clinical methods for stimulating fusional convergence are to adjust horizontal prism power before the eye or to converge the tubes of a major amblyoscope. Starting from the position of rest and evoking maximal fusional convergence with either the prisms or the major amblyoscope, the examiner determines the amplitude by directly reading the maximal response end-point. Accommodation must be controlled during the testing; otherwise, the patient could subconsciously apply the synkinetic near response to overcome the bitemporal disparity in retinal images. Accommodation is controlled by having the patient read small letters or numbers as the eyes converge; consequently, a muscle light and a small dot on a card do not qualify as accommodative targets. The examiner recognizes the maximal response endpoint by noting the point at which the patient selects one of two options when the image disparity stimulus has just exceeded the fusional vergence amplitude.¹ The patient may apply the synkinetic near reflex in response to the image disparity that has just exceeded fusional vergence amplitude; however, this is associated with accommodation, and because the accommodation is monitored with a detailed accommodative target, the patient reports blurring.² The patient may cease to converge further and may recognize diplopia; at that moment the examiner can see the patient's eyes break from the point of maximal convergence they achieved by the vergence reflex and drift to their resting position. This is called the fusion break-point. The examiner then reduces the retinal image disparity by reducing the prism power or the convergence of the major amblyoscope tubes until fusion is restored and the target is seen clearly. This is the fusion restoration point.

Either method requires that the examiner first know the status of the patient's refraction and compensate for it with corrective lenses so the accommodation is controlled. The patient is instructed in the end-points and told to report “blurring” or “doubling” as soon as it appears. The blurring is best illustrated to the patient by the examiner inserting +0.50 spheres before each eye while the patient views small letters at a distance of 6 meters. Similarly, the doubling is demonstrated by quickly inserting a 10Δ base-out prism before one of the patient's eyes and withdrawing it rapidly before the fusional response can be made.

The best prism technique for measuring the fusional convergence amplitude utilizes the rotary prism, which smoothly and slowly builds up the base-out prism power. Loose prisms or a horizontal prism bar may be used, but with each increment in prism power there is a momentary break in fusion and a restoration cycle that does not occur with the rotary prism. Although the test may be performed at any distance, 6 meters and 0.33 meter are customary. The fixation target at distance is a vision chart with numerous small letters; a small pocket calendar is a good target for near fixation.

The major amblyoscope may be used to measure the amplitude at either 6 meters or 0.33 meter. The near measurement is made by inserting -3.00 spheres in the oculus of each tube. The arms are steadily and slowly moved in from the objective setting until the end-point is reached. The slides in each housing are fusion slides (similar slides) with plenty of detail to control the accommodation.

The normal fusional convergence amplitude at 6 meters is 15Δ for fusion break and 12Δ for fusion restoration. This is usually recorded as 15/12. At 0.33 meter the amplitude normally is 20–25/18–22. The explanation for the near amplitude being invariably greater than the distant amplitude probably is related to the awareness of near and the awareness of far. At 6 meters the awareness of far dampens the use of the synkinetic near response to counter the bitemporal retinal image disparity that continues to build beyond the fusional convergence amplitude; however, at 0.33 meter the awareness of near encourages its use. Despite attempts to discourage the synkinetic near response by using techniques to control accommodation, some use of it escapes detection because of the depth of focus of the eye. The eye may be overaccommodated up to 1.50 D for the 0.33 meter target yet, due to the depth of focus, the vision is still clear. Therefore, it is very likely that the amplitude at 0.33 meter is a combination of fusional and accommodative convergence whereas the amplitude at 6 meters is a purer fusional convergence amplitude.

The above are the normal fusional convergence amplitudes found in orthophoria. Alignments that require fusional convergence to compensate for their deviation have larger amplitudes, while those who have no need for fusional convergence have smaller amplitudes; therefore, the amplitude is large in exophoria and small in esophoria. Orthoptic techniques have a great capability to effect a significant response in enlarging the amplitude and improving alignment control and symptoms in exophoria.

Divergence

Fusional divergence is a reflex that responds only to the stimulus of binasal retinal image disparity. The homonymous diplopia of esotropia caused by the binasal retinal image disparity can be overcome by fusional divergence, converting the strabismus to esophoria.

Fusional divergence amplitude is investigated by measuring its maximal response to stimulation. There are two direct methods and one indirect method for determining the fusional divergence amplitude. The two direct methods are the same as those described for measuring fusional convergence except that the horizontal prism power is increased in the opposite direction and the major amblyoscope tubes are diverged rather than converged. The necessity for controlling the accommodation and the end-points of response are the same as described in measuring fusional convergence.

The indirect method of measuring fusional divergence entails manipulating the synkinetic near response, increasing the binasal retinal image disparity by producing small increments of accommodative convergence until the amplitude of fusional divergence is just exceeded. The esotropia measured at this point by the prism and alternate cover test is equivalent to the fusional divergence amplitude. This can be performed at distance fixation or at near fixation; while the accommodation is controlled, minus-power lens increments are inserted in a trial frame before each eye. When diplopia with a sudden break of the eyes from fusion into overt esotropia is produced, the lens increment has just exceeded the fusional divergence amplitude; the estropia measured by prism and alternate cover through this lens is an indirect measure of the fusion breakpoint. The fusion restoration point is the esophoria measured through the weakest reduction in the lens power that allows fusional divergence to overcome the diplopia.

The normal fusional divergence amplitude at 6 meters is 8Δ for fusion break and 6Δ for fusion restoration. At 0.33 meter the amplitude normally is 12/9 and probably contains a small amount of accommodative convergence relaxation that is lacking in the amplitude at 6 meters. These are the usual and normal amplitudes encountered in orthophoria, but patients having esophoria tend to have larger fusional divergence amplitudes. Also, in the exophoric patient the amplitudes may be smaller than normal because there is no need for fusional divergence. The amplitude of fusional divergence may be expanded by orthoptic training, but it does not expand as easily nor to as great a degree as does the fusional convergence amplitude.

Relationship Between Horizontal Fusional Vergence and Synkinetic Near Reflex

Regardless of the method used to measure the amplitude of horizontal fusional vergence, attention must be given simultaneously to the synkinetic near reflex because it is an optomotor reflex that evokes a horizontal vergence. Because either reflex (i.e., the horizontal fusional vergence or the synkinetic near reflex) is capable of overcoming horizontal disparity of retinal images, they must be differentiated from each other during investigation. Fusional convergence and accommodative convergence produce identical corrective eye movements, as do fusional divergence and relaxation of accommodative convergence. Therefore, a method that measures horizontal fusional vergence amplitude must eliminate the possibility of contamination of the results by accommodative convergence.

Fusional convergence and divergence are measured by two methods. In one method, accommodation is held constant while horizontal disparity of retinal images is produced by prisms or a haploscope. This method is called relative convergence. It is divided into two portions: (1) positive, which overcomes bitemporal retinal image disparity, and (2) negative, which overcomes binasal retinal image disparity. Positive relative convergence is fusional convergence and negative relative convergence is fusional divergence. In the other method, bifixation is maintained at a fixed distance while accommodation, and thus, accommodative convergence, is altered by plus and minus lenses. This method is called relative accommodation. Positive relative accommodation is produced by increasing accommodation, and negative relative accommodation is produced by decreasing accommodation. To maintain bifixation, positive relative accommodation requires fusional divergence and negative relative accommodation requires fusional convergence. If prism and alternate cover measurements are made first while maintaining maximal positive relative accommodation and secondly while maintaining maximal negative relative accommodation, the findings are equivalent to the fusional divergence and convergence amplitudes, respectively. Therefore, the examiner may employ either the technique of positive relative convergence or that of negative relative accommodation to measure the amplitude of the fusional convergence. Similarly, either the technique of negative relative convergence or that of positive relative accommodation may be used to measure the amplitude of the fusional divergence.

VERTICAL

Positive

Positive vertical vergence is a simultaneous elevation of the right eye and depression of the left eye, compensating for a left hyperdeviation by maintaining a left hyperphoria.

Negative

Negative vertical vergence is the opposite of positive vertical vergence, namely, maintaining right hyperphoria by simultaneous depression of the right eye and elevation of the left eye.

Vertical fusional vergence amplitudes are measured by producing vertical retinal image disparity with prisms or the major amblyoscope. To stimulate positive vertical vergence, either the image on the right retina is lowered or the image on the left retina is raised by increasing base-down prism power before the right eye or base-up prism power before the left eye. Stimulation of negative vertical fusion requires the opposite. The major amblyoscope accomplishes the same results by appropriately moving the tubes vertically in opposite directions before the right and the left eye. Directing the tube before the right eye downward and the tube before the left eye upward measures positive vertical fusional vergence; moving the tubes in opposite direction measures negative fusional vergence.

Accommodation does not have to be controlled during measurement of vertical vergence amplitude, because the synkinetic near reflex cannot influence the findings. The end-point of the fusional vergence amplitude is diplopia. A normal amplitude is 3Δ to 6Δ, depending on how slowly the measurement is made. Left hyperphoria patients have a greater positive than negative vertical vergence amplitude, whereas the reverse is true in patients having right hyperphoria.

TORSIONAL

Incyclovergence is simultaneous incycloduction of each eye to compensate for excyclodeviation and to maintain excyclophoria.

Excyclovergence is simultaneous excycloduction of each eye to compensate for incyclodeviation and to maintain incyclophoria.

The amplitude of torsional fusional vergences is measured on the major amblyoscope by rotating the housings in which the slides are placed until cyclodiplopia is produced. The only end-point of the torsional vergence amplitude is cyclodiplopia. The normal patient has an incyclovergence of 6° to 10° and an excyclovergence of 8° to 12°.

1. Duane A: A new classification of the anomalies of the eye, based upon physiological principles. Ann Ophthalmol I, October 1896, II, January 1897

2. Alpern M: Vergence and accommodation. Arch Ophthalmol 60:358, 1958

3. Ogle KN: On the accommodative convergence and the proximal convergence. Arch Ophthalmol 57:702, 1957