Fixation disparity

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Fixation disparity is a tendency of the eyes to drift in the direction of the heterophoria. While the heterophoria refers to a fusion-free vergence state, the fixation disparity refers to a small misalignment of the visual axes when both eyes are open in an observer with normal fusion and binocular vision. [1] The misalignment may be vertical, horizontal or both. The misalignment (a few minutes of arc) is much smaller than that of strabismus. While strabismus prevents binocular vision, fixation disparity keeps binocular vision, however it may reduce a patient's level of stereopsis. A patient may or may not have fixation disparity and a patient may have a different fixation disparity at distance than near. Observers with a fixation disparity are more likely to report eye strain in demanding visual tasks; therefore, tests of fixation disparity belong to the diagnostic tools used by eye care professionals: [2] [3] [4] [5] [6] remediation includes vision therapy, prism eye glasses, or visual ergonomics at the workplace.

Contents

Fig.1: Visual axes of the two eyes in optimal binocular vision (blue) and in exo and eso fixation disparity (black and red, respectively). Fixation Disparity Visual Axes.png
Fig.1: Visual axes of the two eyes in optimal binocular vision (blue) and in exo and eso fixation disparity (black and red, respectively).

Optimal binocular vision

In Fig. 1, the blue lines and characters illustrate the situation of optimal binocular vision: the extra-ocular muscles adjust the vergence angle between the two visual axes so that the fixation target X is projected in each eye onto the centre of the fovea, i.e. the location on the retina with the highest spatial resolution. The fixation point is projected in the two eyes onto retinal points that correspond to the same visual direction in space so that single vision is provided. This means that the visual axes intersect at the fixation target X. On the level of the visual cortex there is a perfect spatial overlap, i.e. the binocular disparity is zero and best binocular summation is possible. Such an optimal state occurs only in a minority of observers. [1]

Sub-optimal condition of fixation disparity (FD)

Most observers have a so-called “normal” binocular vision in the sense that they are able to view stereoscopically, but still many of these observers can have a sub-optimal condition in terms of a fixation disparity (FD). The vergence angle is slightly misadjusted so that the fixation point is projected slightly apart from the centre of the fovea. The visual axes may intersect in front (red lines) of the target plane, or behind (black line); these states of over- or under-convergence are referred to as eso- or exo FD, respectively (see Fig.1). In the visual cortex, a binocular disparity between the two retinal images remains. If this disparity is small enough, sensory and neural mechanisms in binocular neurons still attribute the same visual direction to these slightly disparate images and single vision is provided. This mechanism of sensory fusion with normal retinal correspondence operates within a certain limit of disparity, referred to as Panum’s area. If the disparity is larger, the normal Panum’s fusion mechanism is not sufficient; rather, in order to achieve fusion, a neural remapping of retinal correspondence can occur, which - however - prevents a high quality stereo vision. [7]

Thus, in order to achieve single vision, two physiological mechanisms operate hand in hand: [8] [7]

1.)   The motor mechanism of the extra-ocular eye muscles adjusts the vergence angle as precisely as possible for the individual, but a small vergence error may remain.

2.)   Sensory (neural) mechanisms provide single vision by means of fusion within normal Panum’s area or remapping of retinal correspondence (extended Panum’s areas).

Methods for measuring fixation disparity

The methods can be explained based on the study of Hofmann and Bielschowsky [9] in 1900, who applied a modified Maddox wing: the right eye is presented with a horizontal scale and the left eye with an arrow. The observer perceives that the arrow points onto one of the numbers on the scale which indicates a possible vergence mis-adjustment. The Maddox wing, however, does not test binocular vision since no fusion target is present. For testing the state of binocular vision, Hofmann and Bielschowsky [9] included an additional fusion stimulus to the two eyes and still found a perceived offset of scale and arrow; they referred to this offset as “Disparitätsrest” (in German), which means “residual disparity”. Later, Ogle [10] [11] coined the term "fixation disparity".

More generally, this traditional vergence test is a subjective test in the sense that the observer reports his/her perception of the relative position of two test targets that are presented separately to the two eyes, i.e. dichoptic targets. This test relies on the assumption that retinal points are associated with visual directions in space. If physically aligned dichoptic targets appear subjectively aligned, they are projected onto corresponding retinal points and the visual axes intersect at the test target; thus, the vergence angle agrees with the viewing distance. In case of a deviating vergence state, the dichoptic targets need to have a certain physical horizontal offset in order to be perceived in line. These subjective measures agree with objective recordings with eye trackers, [12] if no fusion stimulus is involved.

For measuring subjective fixation disparity, researchers as Ogle, [11] Sheedy and Saladin, [13] Mallett, [14] Wesson [15] constructed test instrumentation including fusion targets and dichoptic targets using cross-polarized filters in front of the eyes; some of these devices are commercially available. If the dichoptic targets are presented to the observer in physical alignment, the angular amount (in the unit minutes of arc) of subjective fixation disparity is indicated by the perceived misalignment of the two dichoptic targets. This can be compensated by the patient's individual amount of a prism eye glass (in the unit prism dioptre) so that the patient perceives alignment. The latter prism needed to reduce the fixation disparity to zero is referred to as aligning prism [4] (earlier called associated phoria). Instrumentations as the Disparometer, the Mallett-unit, or the Wesson Card differ in the type of fusion target: some use small central fixation letters, others use more peripheral fusion targets. The instruments can be swung through 90° to measure any vertical fixation disparity. The test devices can also be used to detect suppression.

The above studies of subjective fixation disparity assumed - partly implicitly - that the dichoptic targets would indicate the vergence misalignment of the visual axes muscles, i.e. the vergence error, as it can be measured with eye tracking methods. This seemed to be justified by the first objective recording of fixation disparity made in 1960 by Hebbard [16] with an eye tracking method based on small mirrors fixed onto contact lenses: he found agreement between the two measures (in the one observer tested). However, subsequent studies [17] [18] [19] [8] [20] found that the objective recordings with eye trackers can differ substantially from the subjective test results with dichoptic targets: with central fusion targets and closely adjacent dichoptic targets, the subjective measure can be about 10 times smaller than the objective measure. When the dichoptic targets are gradually shifted by some degree away from the fusion target, then the two measures become more and more similar. [8] This was interpreted as a change in retinal correspondence in the sense that the visual direction associated with the dichoptic targets is modified in the vicinity of the fusion target.

Fig. 2: Definition of the two types of fixation disparity Figure 2 Fixation disparity.png
Fig. 2: Definition of the two types of fixation disparity

Definition of objective and subjective fixation disparity

Given the discrepancy between objective measures with eye trackers and subjective measures with dichoptic targets, different definitions should be applied (see Fig. 2): [21] [22]

·      Objective fixation disparity (oFD) is defined as the oculomotor vergence error that can only be measured with eye trackers, i.e. oFD = V – V0 . This is the difference between the vergence angle in binocular vision (V, red line in Fig. 2a) and the optimal vergence state when a target is projected in each eye onto the center of the foveola (V0=2 arc tan ((pd)/2)/D), blue line in Fig. 2a). V0 is estimated from the monocular calibration [23] of the eye tracker, i.e. the left eye is covered when the right eye calibration is made and vice versa; this procedure assumes that in monocular vision a target is projected onto the centre of the foveola.

·      Subjective fixation disparity (sFD) is defined as the angular amount of the offset between dichoptic targets that need to be adjusted to a certain offset d so that the observer perceives the dichoptic targets in alignment (see the pair of nonius lines in Fig. 2b). Note that this definition of sFD = arctan (d/D) does not refer to the current vergence angle. The resulting subjective fixation disparity may depend on the spatial arrangement of dichoptic targets and fusion targets.

The discrepancy between oFD and sFD is shown in Fig. 2 in that the disparity ∆ between the two visual axes is typically larger than angular amount of the nonius offset d.

Physiological properties of both types of fixation disparity

A fixation disparity is not constant within a certain observer, but can vary depending on the viewing conditions. If test prisms with increasing amount are placed in front of the observer’s eyes, the fixation disparity changes in the eso direction with base-in prisms and in the exo direction with base-out prisms (Fig. 3). These prisms force the eyes to change the vergence angle while the viewing distance remains unchanged. Prism-induced fixation disparity curves (prism FD-curves) can be characterized by the following parameters: [8] [13] [11]

Fig. 3: Fixation disparity as a function of the forced vergence angle which is induced by base-in prisms and base-out prisms in front of the eyes. Figure 3 FIxation disparity.png
Fig. 3: Fixation disparity as a function of the forced vergence angle which is induced by base-in prisms and base-out prisms in front of the eyes.

These prism FD-curves have widely been used for subjective fixation disparity [13] [11] and the clinical implications are described below. Only more recently, subjective and objective prism FD-curves have been measured simultaneously: [17] [8] In principle both measures have a similar form of these curves, but they can differ quantitatively; typically, oFD is much larger than sFD. A comparison of subjective versus objective measures revealed a significant correlation (about  r = 0.5 – 0.7) for the y-intercept (sFD0 versus oFD0), but not for the slope. [24]

In natural vision without prisms, the vergence state varies as a function of the viewing distance of the target: the subjective fixation disparity may shift towards more exo states from far-vision to near-vision. [25] The effect of proximity is different for objective and subjective fixation disparity. [26]

During reading of text material, the objective fixation disparity can be measured with eye trackers in the moments of fixation. [27] [28] This reading fixation disparity has the following properties:

Clinical diagnostic criteria

Fixation disparity can differ considerably between observers with normal binocular vision. The following conditions of subjective fixation disparity tend to be more prevalent in observers with eye strain.

Near-vision subjective fixation disparity (sFD0) tends to be larger in the exo direction and the aligning prisms (sP0) tends to be more base-in, suggesting that the eyes tend to under-converge. [34] [35] [36] [37] Most of these studies used the Mallett-unit, which consists of a small central fixation letter X surrounded by two letters O, one on each side of X. [38]

The prism FD-curve (measured subjectively in near vision) tends to have a steeper slope (see Fig. 3b), meaning that the binocular system is not able to reach a small fixation disparity when vergence is forced by prisms in the base-in and base-out direction. [13] This evidence came predominantly from studies with the Disparometer, an instrument that allows presenting dichoptic nonius lines with different amounts of offset to find a particular physical offset that leads to perceived alignment. These nonius lines are presented within a circular contour of 1.5 deg diameter that is viewed binocularly. [13]

The proximity FD-curve (measured subjectively as a function of viewing distance) tends to be steeper, meaning that the binocular system is not able to keep the fixation disparity small, if a target is shifted closer in the range of about 100 to 20 cm. This evidence came from studies using a computer-controlled test stimulus including a central fusion stimulus. [39] [6]

All the above measures in studies of eye strain refer to the subjective fixation disparity, because the procedure with dichoptic targets is technically easy and therefore can conveniently be applied in the clinical setting with some commercial test devices. Some of the cited studies found, that measures of subjective fixation disparity are a better diagnostic criterion for eye strain than the heterophoria, i.e. the vergence state without a fusion stimulus. [34] [35] [36] [13] The technically more complex eye tracking technology for measuring objective fixation disparity has not yet been investigated in relation to eye strain.

Remediation of fixation disparity in observers with eye strain

Given that an observer has a certain fixation disparity and suffers from eye strain, one may consider some of the following ways of remediation.  

Eye glasses with an included prism power is the optical method to reduce a fixation disparity. Different procedures have been proposed to determine the required amount of prism for the individual. Based on prism-FD curves (Fig. 3b), one can find the aligning prism sP0 that nullifies the naturally prevailing fixation disparity sFD0. This test procedure is typically made in near vision of 40 cm, e.g. with the Mallett-unit, the Disparometer, or the Wesson card (see above). Experimental evidence for the effectiveness of the aligning prism came from a study of reading speed and corresponding preferences of prism eye glasses. [40] A different approach was suggested by H.-J. Haase [5] [41] who proposed a set of dichoptic target tests with both central and more peripheral fusion targets and additional stereo tests that were predominantly used in far vision. Such prisms alleviated eye strain and remained stable over time. [42] [43] The usefulness of prism eye glasses has been criticized since the initial fixation disparity may reappear again after some time due to the adaptability of the vergence system. [44] One may consider, however, that vergence tends to be less adaptive in observers with eye strain so that in these observers the prisms may permanently reduce a naturally prevailing fixation disparity. [45] [46]

Visual ergonomics of a computer workstation may take into account the individual proximity FD-curve: [6] [39] individuals with a larger exo fixation disparity at near may prefer a longer viewing distance where the fixation disparity is smaller.

Visual vergence training (also referred to as orthoptic exercises or vision therapy) aims to improve the physiological condition of binocular vision with eye movement exercises, including e.g. frequent dynamic vergence changes between near and far vision. The effectiveness has been confirmed both in terms of alleviation of visual symptoms and in better physiological conditions, e.g. the prism-FD curves became more flat. [47] The physiological effect of visual vergence training has also been confirmed for other vergence functions. [48] [49] [50]

See also

Related Research Articles

<span class="mw-page-title-main">Saccade</span> Eye movement

A saccade is a quick, simultaneous movement of both eyes between two or more phases of fixation in the same direction. In contrast, in smooth pursuit movements, the eyes move smoothly instead of in jumps. The phenomenon can be associated with a shift in frequency of an emitted signal or a movement of a body part or device. Controlled cortically by the frontal eye fields (FEF), or subcortically by the superior colliculus, saccades serve as a mechanism for fixation, rapid eye movement, and the fast phase of optokinetic nystagmus. The word appears to have been coined in the 1880s by French ophthalmologist Émile Javal, who used a mirror on one side of a page to observe eye movement in silent reading, and found that it involves a succession of discontinuous individual movements.

<span class="mw-page-title-main">Binocular vision</span> Type of vision with two eyes facing the same direction

In biology, binocular vision is a type of vision in which an animal has two eyes capable of facing the same direction to perceive a single three-dimensional image of its surroundings. Binocular vision does not typically refer to vision where an animal has eyes on opposite sides of its head and shares no field of view between them, like in some animals.

<span class="mw-page-title-main">Eye examination</span> Series of tests assessing vision and pertaining to the eyes

An eye examination is a series of tests performed to assess vision and ability to focus on and discern objects. It also includes other tests and examinations pertaining to the eyes. Eye examinations are primarily performed by an optometrist, ophthalmologist, or an orthoptist. Health care professionals often recommend that all people should have periodic and thorough eye examinations as part of routine primary care, especially since many eye diseases are asymptomatic.

Ocular dominance, sometimes called eye preference or eyedness, is the tendency to prefer visual input from one eye to the other. It is somewhat analogous to the laterality of right- or left-handedness; however, the side of the dominant eye and the dominant hand do not always match. This is because both hemispheres control both eyes, but each one takes charge of a different half of the field of vision, and therefore a different half of both retinas. There is thus no direct analogy between "handedness" and "eyedness" as lateral phenomena.

Stereopsis is the component of depth perception retrieved through binocular vision. Stereopsis is not the only contributor to depth perception, but it is a major one. Binocular vision happens because each eye receives a different image because they are in slightly different positions on one's head. These positional differences are referred to as "horizontal disparities" or, more generally, "binocular disparities". Disparities are processed in the visual cortex of the brain to yield depth perception. While binocular disparities are naturally present when viewing a real three-dimensional scene with two eyes, they can also be simulated by artificially presenting two different images separately to each eye using a method called stereoscopy. The perception of depth in such cases is also referred to as "stereoscopic depth".

<span class="mw-page-title-main">Horopter</span>

The horopter was originally defined in geometric terms as the locus of points in space that make the same angle at each eye with the fixation point, although more recently in studies of binocular vision it is taken to be the locus of points in space that have the same disparity as fixation. This can be defined theoretically as the points in space that project on corresponding points in the two retinas, that is, on anatomically identical points. The horopter can be measured empirically in which it is defined using some criterion.

Vision therapy (VT), or behavioral optometry, is an umbrella term for alternative medicine treatments using eye exercises, based around the scientific evidences that vision problems are the true underlying cause of learning difficulties, particularly in children. Vision therapy has not been shown to be effective according to modern evidence-based medicine. Most claims—for example that the therapy can address neurological, educational, and spatial difficulties—lack supporting evidence. Neither the American Academy of Pediatrics nor the American Academy of Ophthalmology support the use of vision therapy.

Microsaccades are a kind of fixational eye movement. They are small, jerk-like, involuntary eye movements, similar to miniature versions of voluntary saccades. They typically occur during prolonged visual fixation, not only in humans, but also in animals with foveal vision. Microsaccade amplitudes vary from 2 to 120 arcminutes. The first empirical evidence for their existence was provided by Robert Darwin, the father of Charles Darwin.

<span class="mw-page-title-main">Vergence</span> Simultaneous movement of eyes in binocular vision

A vergence is the simultaneous movement of both eyes in opposite directions to obtain or maintain single binocular vision.

Convergence insufficiency is a sensory and neuromuscular anomaly of the binocular vision system, characterized by a reduced ability of the eyes to turn towards each other, or sustain convergence.

<span class="mw-page-title-main">Fixation (visual)</span> Maintaining ones gaze on a single location

Fixation or visual fixation is the maintaining of the gaze on a single location. An animal can exhibit visual fixation if it possess a fovea in the anatomy of their eye. The fovea is typically located at the center of the retina and is the point of clearest vision. The species in which fixational eye movement has been verified thus far include humans, primates, cats, rabbits, turtles, salamanders, and owls. Regular eye movement alternates between saccades and visual fixations, the notable exception being in smooth pursuit, controlled by a different neural substrate that appears to have developed for hunting prey. The term "fixation" can either be used to refer to the point in time and space of focus or the act of fixating. Fixation, in the act of fixating, is the point between any two saccades, during which the eyes are relatively stationary and virtually all visual input occurs. In the absence of retinal jitter, a laboratory condition known as retinal stabilization, perceptions tend to rapidly fade away. To maintain visibility, the nervous system carries out a procedure called fixational eye movement, which continuously stimulates neurons in the early visual areas of the brain responding to transient stimuli. There are three categories of fixational eye movement: microsaccades, ocular drifts, and ocular microtremor. At small amplitudes the boundaries between categories become unclear, particularly between drift and tremor.

Heterophoria is an eye condition in which the directions that the eyes are pointing at rest position, when not performing binocular fusion, are not the same as each other, or, "not straight". This condition can be esophoria, where the eyes tend to cross inward in the absence of fusion; exophoria, in which they diverge; or hyperphoria, in which one eye points up or down relative to the other. Phorias are known as 'latent squint' because the tendency of the eyes to deviate is kept latent by fusion. A person with two normal eyes has single vision (usually) because of the combined use of the sensory and motor systems. The motor system acts to point both eyes at the target of interest; any offset is detected visually. Heterophoria only occurs during dissociation of the left eye and right eye, when fusion of the eyes is absent. If you cover one eye you remove the sensory information about the eye's position in the orbit. Without this, there is no stimulus to binocular fusion, and the eye will move to a position of "rest". The difference between this position, and where it would be were the eye uncovered, is the heterophoria. The opposite of heterophoria, where the eyes are straight when relaxed and not fusing, is called orthophoria.

<span class="mw-page-title-main">Chromostereopsis</span> Visual illusion whereby the impression of depth is conveyed in two-dimensional color images

Chromostereopsis is a visual illusion whereby the impression of depth is conveyed in two-dimensional color images, usually of red–blue or red–green colors, but can also be perceived with red–grey or blue–grey images. Such illusions have been reported for over a century and have generally been attributed to some form of chromatic aberration.

Cyclovergence is the simultaneous occurring cyclorotation of both eyes which is performed in opposite directions to obtain or maintain single binocular vision.

Cyclotropia is a form of strabismus in which, compared to the correct positioning of the eyes, there is a torsion of one eye about the eye's visual axis. Consequently, the visual fields of the two eyes appear tilted relative to each other. The corresponding latent condition – a condition in which torsion occurs only in the absence of appropriate visual stimuli – is called cyclophoria.

<span class="mw-page-title-main">Stereopsis recovery</span>

Stereopsis recovery, also recovery from stereoblindness, is the phenomenon of a stereoblind person gaining partial or full ability of stereo vision (stereopsis).

Binocular neurons are neurons in the visual system that assist in the creation of stereopsis from binocular disparity. They have been found in the primary visual cortex where the initial stage of binocular convergence begins. Binocular neurons receive inputs from both the right and left eyes and integrate the signals together to create a perception of depth.

Stereoscopic motion, as introduced by Béla Julesz in his book Foundations of Cyclopean Perception of 1971, is a translational motion of figure boundaries defined by changes in binocular disparity over time in a real-life 3D scene, a 3D film or other stereoscopic scene. This translational motion gives rise to a mental representation of three dimensional motion created in the brain on the basis of the binocular motion stimuli. Whereas the motion stimuli as presented to the eyes have a different direction for each eye, the stereoscopic motion is perceived as yet another direction on the basis of the views of both eyes taken together. Stereoscopic motion, as it is perceived by the brain, is also referred to as cyclopean motion, and the processing of visual input that takes place in the visual system relating to stereoscopic motion is called stereoscopic motion processing.

<span class="mw-page-title-main">Prism fusion range</span>

The prism fusion range (PFR) or fusional vergence amplitude is a clinical eye test performed by orthoptists, optometrists, and ophthalmologists to assess motor fusion, specifically the extent to which a patient can maintain binocular single vision (BSV) in the presence of increasing vergence demands. Motor fusion is largely accounted to amplitudes of fusional vergences and relative fusional vergences. Fusional vergence is the maximum vergence movement enabling BSV and the limit is at the point of diplopia. Relative fusional vergence is the maximum vergence movement enabling a patient to see a comfortable clear image and the limit is represented by the first point of blur. These motor fusion functions should fall within average values so that BSV can be comfortably achieved. Excessive stress on the vergence system or inability to converge or diverge adequately can lead to asthenopic symptoms, which generally result from decompensation of latent deviations (heterophoria) or loss of control of ocular misalignments. Motor anomalies can be managed in various ways, however, in order to commence treatment, motor fusion testing such as the PFR is required.

The FourPrism Dioptre Reflex Test is an objective, non-dissociative test used to prove the alignment of both eyes by assessing motor fusion. Through the use of a 4 dioptre base out prism, diplopia is induced which is the driving force for the eyes to change fixation and therefore re-gain bifoveal fixation meaning, they overcome that amount of power.

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