Introduction
Humans and other animals with frontally located eyes attain binocular vision from the two retinal images through a series of sensory and motor processes that culminate in the perception of singleness and stereoscopic depth. Keen stereopsis is considered the paramount consequence of binocular vision because optimal performance depends on the normal functioning of all of the underlying vision processes, including central fixation with normal visual acuity in each eye, accurate oculomotor control to obtain bifoveal fixation, normal inter-retinal correspondence of visual directions, sensory mechanisms to produce haplopia (single vision), and neural mechanisms to extract selective depth signals from objects that are nearer or farther than the plane of fixation. Consequently, ordinary binocular vision represents a highly coordinated organization of motor and sensory processes and if any component in the organization fails, then binocular vision and stereopsis must be compromised to some extent. Clinically, the causes and significance of abnormal binocular vision are the primary emphasis, usually with a goal to alleviate any interference with clear, comfortable, single binocular vision. However, clinical applications must be established from an understanding of normal binocular vision. The topics included in this chapter were selected to provide the basic information on normal and abnormal binocular vision that forms the foundation for the clinical science of binocular vision.
Two eyes are better than one
It is obvious that an organism should gain an advantage by having two eyes rather than one. For example, it may be assumed that binocular vision is an important attribute because 75–80 percent of the neurons in primary visual cortex have inputs from both eyes. There are also several functional advantages to having two frontal eyes.
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The binocular field of view is larger than either monocular field. The normal visual field for each eye extends to approximately 60 deg superiorly, 60 deg nasally, 75 deg inferiorly, and 100 deg temporally from fixation. Thus, with binocular viewing, the horizontal extent of the visual field is increased from 160 deg to 200 deg, with a central 120 deg of overlap, or superimposition, of the monocular visual fields.
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Any image distortion due to optical or pathological defects in one eye can be masked by a normal image in the other eye. In general, the degree of dysfunction from a unilateral disorder or bilateral eye disease can be predicted from the performance of the un- or less-impaired eye.
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Pragmatically, having two eyes provides a resource to retain functional vision if an accident or disease causes the loss of sight of one eye.
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Normal binocular vision improves functional vision by binocular summation and stereopsis. Binocular summation, which is the improvement in visual sensitivity with binocular viewing compared to monocular viewing, provides only a small increase in sensitivity when measured by threshold responses, but may be a larger factor for performance measured with suprathreshold stimuli. Stereopsis, on the other hand, is the quantitative and qualitative improvement in relative depth perception that occurs with binocular viewing. At its most elementary level, keen stereopsis benefits both the predator, at the point of attack, and the prey, by unmasking the camouflage of predators.
Visual direction
Ordinarily, people are not aware that they are using two eyes, but rather, they have an impression of viewing with one eye located about midway between the two eyes (the egocenter, or cyclopean eye). Thus, the basic concept of visual space involves the relationship between the locations of objects in physical space and their perceived (subjective) spatial locations. These concepts are illustrated diagrammatically in Figure 36.1 , which presents representations of physical space in panel A and subjective space in panel B. Perceived directions of objects are based on several factors, including the retinal locations of their images. Each retinal image location is associated with a specific visual direction, called its local sign or oculocentric direction. The primary visual direction is the oculocentric direction of an object that is fixated along the primary line of sight and is imaged on the center of the fovea (represented by the diamond in Fig. 36.1 ). Secondary lines of sight are the oculocentric directions of other retinal image locations relative to the primary visual direction. As illustrated in Figure 36.1 , the perceived visual directions of non-fixated objects (represented by the circle and square) are relative to the visual direction of a fixated object (represented by the diamond). In the example, an image located to the left side of the fovea is perceived to the right of the fixated object, e.g. the visual direction of the square. The normal ability to distinguish differences in oculocentric directions is extremely accurate, as demonstrated by Vernier alignment thresholds, which are on the order of 5 arcsec for foveal viewing.
In a natural, dynamic world, objects are localized with respect to the head and body rather than to the line of sight and, therefore, retinal image information is not sufficient to define valid relationships between the physical and perceived locations of real objects. The perceived direction of an object in space relative to the body, its egocentric direction, is derived from the combination of its oculocentric visual direction with information about eye orientation in the head and head position relative to the trunk of the body. Egocentric localization is referenced to an egocenter midway between the two eyes and the combined information allows an individual to distinguish between retinal image motion caused by eye movements and movement of the object.
From a clinical point, egocentric direction is an important concept for understanding the alterations of normal subjective visual space of patients with a misalignment of the two eyes from strabismus. The general principles of egocentric direction are illustrated in Figure 36.2 . In the first examples ( Fig. 36.2A&B ), with normal binocular vision the retinal oculocentric directions from the two retinal images of an object at (panel A) or close to (panel B, circle) the plane of fixation are combined to produce a single direction (haplopia) relative to the observer’s egocenter. In contrast, for objects that are outside the range of single vision, either nearer or farther than the plane of fixation, a single object has two separate egocentric directions that correspond to the oculocentric direction of each of the retinal images relative to the perspective of the egocenter, i.e. diplopia, illustrated in Figure 36.2C .
Binocular eye movements are defined by combinations of version and vergence ocular movements (see Chapter 9 ). Versions are yoked or conjugate changes in the visual axes of the two eyes in the same direction and amount; vergence movements involve rotations of the visual axes in opposite directions. Only the version component of binocular eye position influences the perception of egocentric direction, which is sensed as the average position of the two eyes. The vergence component is nullified because vergence movements of the two eyes have opposite signs and their correlates cancel one another in the computation of the average of right and left eye positions. Thus, when the two eyes fixate objects to the left or right of the midline in asymmetric convergence, only the version, or conjugate, component of eye position contributes to perceived direction.
In addition to averaged eye positions, the subjective computation of egocentric directions of non-fixated objects involves a reconciliation of differences in oculocentric visual directions between the two eyes. For example, objects that are small distances in front or behind the plane of fixation are imaged at retinal locations with different angular distances from the visual axis and, therefore, have different oculocentric directions in each of the two eyes. When the retinal image disparity is small, the target still appears single, and the binocular egocentric direction is based upon the average oculocentric direction for the two eyes. In other words, the binocular egocentric direction deviates from either of the monocularly perceived directions by one-half of the angular disparity ( Fig. 36.2B ). However when the retinal images have unequal contrast, the average is biased or weighted toward the direction of the higher-contrast image.
As object distances from the plane of fixation increase, retinal image disparities become large, and an object appears diplopic with two separate egocentric directions. Egocentric directions of diplopic images are perceived as though both monocular components had paired images on corresponding points in the contralateral eye ( Fig. 36.2C ). The relative egocentric direction of each of the diplopic images depends on whether the object is nearer or farther than the plane of fixation. The example ( Fig. 36.2C ) illustrates that, for an object closer than the plane of fixation, the egocentric direction associated with the retinal image of the right eye is to the left of the egocentric direction produced by the image of the left eye. This form of diplopia, produced by near objects, is called “crossed” diplopia due to the right–left/left–right relationship between the eyes and perceived locations of the object. Conversely, objects farther than the plane of fixation will be perceived with uncrossed diplopia, where the right eye sees an object located on the right side and the left eye sees an object located on the left side.
In normal binocular vision, diplopia of non-fixated objects, classified as physiological diplopia, occurs as a natural consequence of the lateral separation of frontally located eyes and the topographical organization of visual directions across the retina. In contrast, patients with strabismus experience pathological diplopia, wherein objects in the plane of fixation are perceived as doubled. In pathological diplopia, the retinal image location caused by misalignment of the visual axis of the deviating eye causes a fixated target to be seen in different egocentric directions during binocular viewing, and yet, under monocular conditions each eye veridically perceives its direction. Under binocular viewing conditions, only one of the two visual directions seen in pathological diplopia can be veridical at any given moment. In addition to diplopia, a form of visual confusion confounds the space perception of strabismic patients. An object imaged on the fovea of the deviating eye has the same egocentric direction as another object imaged on the fovea of the fixating eye, even though their physical locations are much different. Diplopia and visual confusion create an intolerable visual environment that is typically alleviated during binocular vision by the development of suppression, which is a suspension of the vision in the deviating eye. Another solution to diplopia is anomalous retinal correspondence, which is an alteration of the normal topography of oculocentric directions.
Normal retinal correspondence
The perceptions of haplopia and diplopia arise from the sense of oculocentric visual directions of corresponding or non-corresponding retinal areas that are stimulated during binocular vision. Binocular retinal correspondence is defined by the set of retinal image locations that produces perceptions of identical visual directions when viewing with one eye, or with the other, or with both eyes simultaneously. Identical visual directions associated with corresponding points depend primarily on retinal image locations and their associated oculocentric directions, rather than on eye position and egocentric directions. This fundamental principle was demonstrated by Hering’s famous “window experiment” that illustrated the relationship between retinal image locations and perceived visual directions showed that objects imaged on the foveas have the same perceived visual direction regardless of their actual positions relative to the observer. Similarly, afterimages placed on the fovea of each eye always appear superimposed irrespective of the vergence or version positions of the two eyes. The identical visual directions of the afterimages show that normally corresponding retinal points are combined physiologically before eye position information is used to compute perceived egocentric direction.
These relationships for binocular visual directions are illustrated in Figure 36.3 , in which the two foveal images of a fixated object (diamond – panel A) share a common visual direction and are fused to produce the perception of a single haplopic object in subjective space (panel B). The specific pairs of retinal image locations in the two eyes that are perceived to have identical visual directions are called corresponding retinal points or areas. The foveas represent an important pair of corresponding retinal points, but there are many other pairs associated with secondary lines of sight and visual directions. For example, in Figure 36.3 the square represents the location of an object in the right visual field that falls on paired retinal areas with a common visual direction for the two eyes, thus defining another set of corresponding retinal areas. Similarly, the circle in the left visual field represents a location of an object in the left visual field that is imaged on corresponding retinal points. For an infinite fixation distance, a large number of potential object locations are imaged on corresponding retinal points. These object locations in space that are imaged onto corresponding retinal points can be imagined to define a surface that resembles a cylinder with an infinite radius of curvature. This surface of points stimulates the perception of identical visual directions for the two eyes and is called the horopter. At finite viewing distances, the surface is reduced to a horizontal line and a vertical line that pass through the intersections of the lines of sight when the eyes fixate in symmetrical convergence.
Points in tertiary locations (elevated and displaced laterally from the lines of sight) are closer to one eye than to the other and subtend larger visual angles at the more proximal eye. As a result, all physical points in tertiary locations at finite viewing distances are imaged with vertical disparities and, by definition; their images do not fall on corresponding points. At these finite viewing distances, only points imaged along the horizontal retinal meridian or along the vertical retinal meridian in the midsagittal plane can be formed on corresponding points without vertical disparities. The locations of object points that are imaged on corresponding points along horizontal meridians through the foveas define the longitudinal horopter, shown diagrammatically in Figure 36.3 by the arc passing through the fixated object and the two peripheral objects that stimulate corresponding retinal points. A vertical horopter is defined by the location of object points in the midsagittal plane that are imaged on corresponding points along the vertical meridian.
The relationship between object and image space for the longitudinal horopter is quantified by longitudinal visual angles, defined as the horizontal visual angles subtended by the primary and secondary lines of sight for each eye. The longitudinal visual angles for an object in the right visual field are illustrated by angles α 1 and α 2 in Figure 36.3 . Similarly, longitudinal visual angles can be defined for the object in the left visual field. The lateral separation of the eyes in the head results in each eye having a different perspective of objects not on the horopter, and these differences in perspective are used perceptually to reconstruct a three-dimensional space from the two-dimensional retinal images. The objects that are closer or farther than the horopter stimulate non-corresponding points, which is defined as a binocular disparity, retinal disparity, or simply, disparity of the retinal images. The horizontal component of binocular disparity is the unique stimulus for stereoscopic depth perception and is quantified by the difference in the longitudinal visual angles, also called horizontal disparity angles. The horopter serves as a zero disparity reference from which the magnitudes of non-zero disparities are computed. In the absence of other depth cues, the curvature and slant of the horopter will influence the perceived shape and orientation of surfaces seen in depth. Optical devices such as spectacle lenses that magnify and distort one of the two eyes’ retinal images will alter the horopter and produce predictable errors of space perception.
The empirical longitudinal horopter illustrated in Figure 36.3 is a smooth surface that is symmetrical about the fixation point, but the actual shape and curvature of the empirical horopter will depend on physiological and optical factors that affect the retinal images and their cortical representations. If the locations of corresponding retinal areas simply were determined by equal angular distances from the primary line of sight, then the horopter would be a circle passing through the fixation point and the entrance pupil of each eye (geometric or theoretical horopter or Vieth-Muller circle) ( Fig. 36.4 ). An analogy of “cover points” has been used to describe corresponding retinal locations determined by retinal distances. If the retina of one eye were to be translated and carefully aligned to cover the retina of the other eye, then a pin stuck into the retina would penetrate cover points, or corresponding retinal areas. Cover points, by simple geometry, would become corresponding points because the angles included by lines drawn from two points on the circumference of a circle to any other two points on the circle are equal. Consequently, the longitudinal visual angles will be equal (α 1 = α 2 ), and the theoretical horopter will be a section of a circle, specified as the Vieth-Muller circle (VMO), as illustrated in Figure 36.4 .
Except for rare cases, the empirically defined horopter does not actually coincide with the Vieth-Muller circle, but the theoretical longitudinal horopter is an important reference for zero disparity; in fact, clinical tests of stereopsis use the Vieth-Muller circle as the zero disparity reference. Another important reference in physical space is the objective fronto-parallel plane (OFPP), which is the plane at the fixation distance that is parallel to a line passing through the entrance pupils of the two eyes ( Fig. 36.4 ). Although, both the Vieth-Muller circle and the OFPP are used as reference surfaces to describe the empirical horopter, they are predicated on different perceptual correlates. The Vieth-Muller circle is based on a physical geometric assumption that identical visual directions are associated with retinal points that are equidistant from their respective foveas. The empirical longitudinal horopter, which is based primarily on identical visual directions, is the only pure measure of pairs of retinal corresponding points. On the other hand, the OFPP, which is a measure of perceived surface shape and orientation, depends on egocentric directions derived by combining oculocentric directions and information about absolute distance and direction. The OFPP can be used as a frame of reference for adjusting the depth of objects at different retinal eccentricities so that the objects appear to lie in a flat plane parallel to the face (apparent fronto-parallel plane, or AFPP). The location, shape, and slant of the AFPP is based on disparity, azimuth cues, and absolute distance cues. The AFPP is used to evaluate how disparity is scaled by absolute distance and how slant is influenced by azimuth estimates to enable subjects to estimate the depth of surface shapes and orientations. Both the empirical longitudinal horopter and the AFPP are used to evaluate the influence of optical distortions, such as magnification, on perceived space, since they usually yield similar results.
The empirical longitudinal horopter and the AFPP can be measured in several ways, based on different properties of visual directions and stereoscopic depth. The empirical longitudinal horopter can be determined by identical visual directions for the two eyes; by the highest stereoacuity for points at various eccentricities from fixation; by the center of the sensory fusion range known as Panum’s fusional area (see Fig. 36.7 below); and by object locations eccentric to fixation which result in a zero stimulus for disparity vergence. The vergence criterion assumes that horizontal version movements guide the intersection of the visual axes along the empirical horopter, even if this surface is curved in depth. The AFPP horopter can be measured by positioning eccentric objects so that they all appear to lie in the same plane, or by positioning eccentric objects so that they appear to be equidistant from the observer (i.e. equidistant from the egocenter).
Abnormal retinal correspondence
The properties of corresponding retinal areas underlying normal binocular vision provide a stable sensory organization of the two eyes consistent with the functional properties of neurons in primary visual cortex that are present in infancy (see Chapter 41 ). However, the normal sensory organization of binocular vision can be altered substantively in infantile strabismus by the development of anomalous retinal correspondence and/or suppression. Clinically, the type and extent of sensory adaptation is an important factor to be considered in treatments that are intended to reestablish functional binocular vision for a strabismic patient.
Sensory adaptations in strabismus are necessary to eliminate the constant diplopia (two egocentric directions for all objects) and common visual directions for fixated and non-fixated objects (visual confusion) that would otherwise prevail ( Fig. 36.5A ). Most strabismic patients do not experience diplopia and visual confusion, but their single vision is a result of suppression and/or anomalous retinal correspondence. Suppression causes the perception of objects normally visible to the deviating eye to be eliminated during simultaneous binocular viewing to provide single vision. Suppression in some exotropes may involve an entire hemi-field, but for esotropes the suppression is limited to a specific area (sometimes called a “suppression scotoma”), bounded by the fovea of the deviating eye and the area stimulated by the object that is fixated by the non-deviating eye (the diplopia point; Fig. 36.5B ).
Anomalous retinal correspondence ( Fig. 36.5C ) is an adapted shift in the visual directions of the deviated eye relative to the normal visual directions of the fixating eye. The result is that, during binocular viewing, a peripheral retinal area of the deviating eye acquires a common visual direction to that of the fovea of the fixating eye. This shift in retinal correspondence produces a difference in the visual directions between the two eyes for foveally imaged objects, which can be sometimes demonstrated clinically with the Hering-Bielschowsky test for anomalous correspondence. For this test, after-images are formed on the foveas of both eyes. Even with an interocular deviation from strabismus, a patient with normal correspondence will perceive the after-images in a common direction, but a patient with deep anomalous retinal correspondence will perceive the after-images in different visual directions. The subjective separation of the monocular after-images is referred to as the angle of anomaly, which represents the magnitude of the perceptual shift from the normal corresponding relationship between the two foveas. When the magnitude of the angle of anomaly is equal to the magnitude of the oculomotor misalignment (harmonious anomalous retinal correspondence), then objects in space can appear single even though one of the eyes is deviated. On the other hand, when the angle of anomaly is not equal to the angle of strabismic deviation (unharmonious anomalous retinal correspondence), the residual disparity will cause diplopia unless suppression is also present. The angular separation of the diplopic images is referred to as the subjective angle and in unharmonious anomalous retinal correspondence the subjective angle is usually smaller than the angle of strabismus (objective angle).
As illustrated by the data for a patient with infantile esotropia ( Box 36.1 ) tests for the sensory adaptations of a strabismic patient are variable and generally the diagnosis of anomalous retinal correspondence for a given strabismic patient is test dependent. Tests for anomalous retinal correspondence either locate the extra-foveal point in the deviating eye that has the same visual direction as fovea in the fixating eye, or quantify the angular separation of the visual directions of the foveas of the two eyes. Tests in the former category, e.g. Bagolini striated lenses or the Worth four-dot test, have a higher probability of being positive for anomalous retinal correspondence than tests in the latter category, such as the Hering-Beilschowsky after-image procedure. The dependence of the state of a patient’s retinal correspondence on the clinical procedure may be the result of variation in the angle of anomaly across the retina or some other property of the mechanisms underlying anomalous retinal correspondence. However, the practical consequence is illustrated by the patient with infantile esotropia ( Box 36.1 ) who demonstrated harmonious anomalous retinal correspondence with the Bagolini striated lens test and normal retinal correspondence with the major amblyoscope and after-image tests.
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College student, 26 years old
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Infantile strabismus
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Prior treatment
Surgery at age 2 years
Patching ages 2–4 years
Surgery at age 8 years
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Cover test: Constant, unilateral, right eye esotropia
Distance: 20 Δ ET
Near: 18 Δ ET
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Refractive errors and BVAs
OD: +2.00 −2.00 × 180 20/20
OS: +1.00 −0.5 × 180 20/20
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Lateral heterophoria: constant suppression of OD
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Bagolini striated lens test: Lines intersect at the fixation point – harmonious anomalous retinal correspondence.
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Amblyoscope: Equal objective and subjective angles – normal retinal correspondence.
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Hering-Bielschowsky afterimage test: Images intersect at the fixation point – normal retinal correspondence.
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Stereopsis with two-pencil test: Better accuracy with both eyes viewing.
Comment : The patient has a constant, unilateral esotropia without amblyopia. He demonstrates harmonious anomalous retinal correspondence under the fovea-to-extrafovea testing conditions of the Bagolini test and normal retinal correspondence with the more dissociating tests (amblyoscope) or the test that evaluates fovea-to-fovea correspondence (after-image test).
Three main theories on anomalous retinal correspondence have been proposed. The first theory states that, with anomalous correspondence the two eyes perceive space independently, much like the two hands explore space. Each eye computes egocentric visual direction from its own sense of eye position and oculocentric retinal image location. In effect, there is a lack of correspondence. The observation that the separation between foveal afterimages changes during spontaneous changes in the magnitude of the angle of strabismus supports this theory. This co-variation between the angle of anomaly and objective angle of strabismus results in a stable percept of space, even though the magnitude of the strabismus is unstable and varies in time. The second theory proposes that there is a shift in retinal correspondence so that retinal points that are normally disparate are shifted to acquire an anomalous coupling in the striate cortex, e.g. the fovea of the fixating eye is anomalously coupled with a peripheral area of the deviating eye. Measures of the identical visual directions horopter in strabismics reveal that correspondence is mainly shifted in the periphery, and the angle of anomaly decreases near the fovea in the region of space that lies between the visual axes that is projected to opposite cortical hemispheres. The third theory proposes that strabismics who have no suppression are able to perceive space singly due to enlarged Panum’s fusional areas. These three theories are not mutually exclusive and all of them can be expressed to some degree in the same strabismic patient, or different mechanisms may be present in different forms of strabismus, e.g. primary versus secondary microstrabismus.
Binocular (retinal) disparity
The empirical longitudinal horopter represents the specific locations of objects in physical space that have zero retinal image disparity. Objects not located on the horopter will have some amount of lateral binocular (retinal) disparity. With horizontal retinal disparity, an object is imaged on laterally separated non-corresponding retinal areas and, as the case for the empirical horopter, the longitudinal visual angles are not equal. Horizontal retinal disparity is a unique binocular stimulus for stereoscopic depth perception, horizontal disparity vergence eye movements, and diplopia, either physiological or pathological. In each case, the perceptual or motor response is a consequence of the relationship between the object’s disparate images and the horopter.
The following relationships concerning binocular disparities are important to the understanding of binocular vision.
1. Binocular disparities are classified as uncrossed (distal) or crossed (proximal), based on the relationship between the disparate object and the horopter, as illustrated in Figure 36.6 . For example, the square in the right visual field represents an object that is farther than the fixation point (represented by the diamond), and the secondary lines of sight for the square intersect behind the horopter. The binocular disparity produced by the square is classified as uncrossed and quantified by the difference between the longitudinal visual angles α 1 and α 2 . Perceptually, uncrossed disparities give rise to a sense of relative “far” stereoscopic depth or, if the disparity is large, to uncrossed diplopia (i.e. double vision with the right eye’s image seen to the right side of the left eye’s image). As oculomotor stimuli, uncrossed disparities evoke divergence eye movements. By a parallel classification, crossed disparities (illustrated by the circle in the left field, Fig. 36.6 ) give rise to a perception of “near” stereoscopic depth or crossed diplopia and elicit convergence eye movements.
2. Binocular disparities are classified as either relative or absolute. The absolute disparity of a target is the difference between the angle subtended by the target at the two entrance pupils of the eyes and the angle of convergence. A relative disparity is defined as the difference between two absolute disparities. Stereoscopic depth normally arises from discriminating relative disparities, wherein judgments are based on the perception of the depth of one object relative to another (e.g. the relative depth of the square with respect to the diamond, Fig. 36.6 ). Stereopsis with relative disparities, as measured by clinical testing, is quite fine compared to the perception of depth based solely on absolute disparities. In contrast, an absolute disparity is the optimal stimulus for motor fusion, such as occurs with prism-induced disparity vergence or with changes in fixation distances, which change disparity of all objects in the visual field by a constant amount.
3. For a person with normal binocular vision, there is a finite range of binocular disparities that provides a clear perception of relative depth with normal fusion (haplopia), and larger disparities produce diplopia. The disparity range for single vision, called Panum’s fusional area (PFA), is illustrated in Figure 36.7 . Panel A of the figure illustrates the measurement of Panum’s area. A test object is moved along the primary line of sight of the left eye while the two eyes maintain binocular fixation at one point in space. The crossed disparity limit for fusion is the greatest distance that the test-object can be moved toward the subject before it appears diplopic. Similarly, the object can be moved away from the subject to establish an uncrossed disparity limit for fusion. Thus, in subjective space (panel B) Panum’s fusional area (illustrated by the dashed oval) defines the disparity range for fused binocular vision, and objects subtending disparities outside this range will be diplopic unless one ocular image is suppressed. When the target is intersected by the primary line of sight of the left eye, the disparate image of the near target seen by the right eye is projected to the left visual field in crossed diplopia and the image of the far target is projected to the right visual field in uncrossed diplopia. In addition, there is also a vertical disparity range that is compatible with binocular sensory fusion, although it is generally smaller than the horizontal disparity range. Although the size and shape of PFAs depend on retinal eccentricity and spatio-temporal stimulus properties, the classical PFA for foveal vision is an oval with approximate horizontal and vertical dimensions of 15 × 6 arcmin.
4. Most individuals with normal binocular vision will have small vergence errors known as fixation disparities. Because the retinal images only need to fall within Panum’s fusional areas for single binocular vision to occur, a small residual misalignment of the visual axes (vergence error) can occur, resulting in a retinal disparity of a fixated object, i.e. a fixation disparity, without causing diplopia. This fixation disparity between the fixated object and the intersection of the primary lines of sight displaces the longitudinal horopter from the fixated object. An example illustrated in Figure 36.8 shows a small convergence error (eso-fixation disparity) for the object of fixation (diamond). The convergence error causes an inward shift of the horopter, (the locations of normal corresponding points), i.e. in normal binocular vision, identical primary visual directions result from bifoveal stimulation and, therefore, the horopter always passes through the intersection of the visual axes. Consequently, the fixated object lies beyond the horopter and, by definition, has an uncrossed retinal disparity, described clinically as an eso-fixation disparity. Conversely, an exo-fixation disparity causes a displacement of the horopter beyond the fixation distance, and crossed disparity of the fixated object. In any case, the magnitude of a fixation disparity cannot be larger than the width of Panum’s fusional area if the patient is to retain single binocular vision.
5. Clinically, fixation disparities have been considered a sign of stress on fusional vergence mechanisms. The clinical tests are based on the coincidence of the primary line of sight and the principal visual direction with normal retinal correspondence (see Fig. 36.8 ) and, therefore, the angular separation between dichoptic objects with a common visual direction is a measure of the convergence error (fixation disparity) at the given fixation distance. The assumption that clinically significant fixation disparity is caused by oculomotor stress is generally based on Ogle’s extensive investigations of fixation disparity – forced vergence functions, which demonstrated systematic changes in the direction and magnitude of fixation disparity with variation in the magnitude of the stimulus for disparity vergence (see Chapter 9 ). Three examples of fixation disparity – forced vergence functions are presented in Figure 36.9 . These data were obtained using subjective alignment of dichoptic nonius lines, i.e., alignment of two stimuli, one seen by each eye, to define corresponding retinal locations while the subject viewed a binocular fusion stimulus. The separate functions represent data for a patient with clinically normal binocular vision ( Fig. 36.9A ), a patient with esophoria ( Fig. 36.9B ), and a patient with an intermittent exotropia ( Fig. 36.9C ). The functions show that fixation disparities occur when a large fusional vergence component is required to correct a vergence error such as a heterophoria. The amount of base-out prism needed to eliminate the vergence effort is determined from the prismatic power at which the fixation disparity was zero. This occurs when the forced vergence function crosses the abscissa (i.e. the “associated” phoria). An example of the clinical application of these concepts is illustrated by the patient with asthenopia and esophoria with a base-out associated phoria for near-vision tasks that is presented in Box 36.2 . The fixation disparity can be a useful error with significant heterophorias because it provides a steady state stimulus to overcome the heterophoria and maintain ocular alignment with fusion. When large vergence responses are needed to overcome phoria they may be associated with asthenopia.
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19-year-old college student
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Visual complaints: Eye strain (burning and a “pulling” sensation) that she associates with reading and her other near work. Near-sighted, has worn glasses for 5 years and her vision is OK with a spectacle correction.
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Current spectacle correction & Vas
OD: −2.00 −0.50 × 075; 20/25
OS: −2.00 −0.25 × 090; 20/30
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Refractive errors & VAs
OD: −2.25 −0.75 × 070; 20/15
OS: −2.25 −0.75 × 105; 20/15
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Phorometric findings
Distance heterohoria: 1 Δ E(P)
Near phoria: 4 Δ E(P)
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Ductions at near: Base-in 5 Δ /12 Δ /4 Δ , Base out 8 Δ /14 Δ /7 Δ
Near associated phoria: 2 Δ Base out.
Comment: The patient’s asthenopia could be the result of astigmatism or oculomotor imbalance from an eso-fixation disparity caused by esophoria.
In summary, broad ranges of binocular disparities are present under all conditions of normal seeing and the utilization of disparity information by the visual sensory and motor systems is the most fundamental process of normal binocular vision. The clinical evaluation of a patient’s binocular vision includes tests of several aspects of retinal disparity, including relative disparities by measures of stereoacuity, absolute retinal disparities by measures of disparity-induced vergence eye movements, and fixation disparities.
Stereopsis
Stereopsis is the perception of relative distance, or the depth separation, between objects that occurs as a result of neural processing of the relative horizontal binocular disparities between the monocular retinal images. Binocular disparities are present because the lateral separation of the eyes in the head provides each eye with a slightly disparate view of a given object. Thus, as demonstrated by the seminal research of Wheatstone and Julesz, these horizontal (lateral) retinal image disparities produce stereoscopic depth. By themselves, vertical disparities do not result in depth perception; however, they are used to estimate azimuth and absolute distance in order to scale horizontal disparities into stereo-depth magnitudes.
Clinical measures of the smallest detectable stereoscopic depth (stereoacuities) are quantified by a stereo-angle (η) that is equal to the difference in the longitudinal visual angles (α 1 and α 2 ), or the parallax (convergence) angles (δ 1 and δ 2 ), as illustrated in Figure 36.10 . For a conventional stereogram (see Fig. 36.14 ), η can be derived directly from the angular differences in positions of common objects in the two half-views of the stereogram. The retinal disparity associated with the physical depth of an object in normal vision (illustrated in Fig. 36.10 ) can be determined by the relationship:
η = [ ( a * Δ b ) / d 2 ] * c
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