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CHAPTER 2 Binocular Vision and Space Perception W ithout an understanding of the physiology of binocular vision it becomes difficult, if not impossible, to appreciate its anomalies. The reader is well advised to study this chapter thor- oughly since important basic concepts and termi- nology used throughout the remainder of this book are introduced and defined. It is of historical inter- est that most of these concepts and terms have only been with us since the nineteenth century when they were introduced by three men who may be considered among the fathers of modern visual physiology: Johannes Mu ¨ller, Hermann von Helm- holtz, and Ewald Hering. The basic laws of binoc- ular vision and spatial localization that were laid down by these giants of the past form the very foundation on which our current understanding of strabismus and its symptoms and sensory conse- quences is based. Fusion, Diplopia, and the Law of Sensory Correspondence Let us position an object at a convenient distance in front of an observer at eye level and in the midplane of the head. If the eyes are properly aligned and if the object is fixated binocularly, an image will be received on matching areas of the two retinas. If the eyes are functioning normally and equally, the two images will be the same in size, illuminance, and color. In spite of the pres- ence of the two separate physical (retinal) images, 7 only one visual object is perceived by the ob- server. This phenomenon is so natural to us that the naive observer is not surprised by it; he is surprised only if he sees double. Yet the opposite—single binocular vision from two dis- tinct retinal images—is the truly remarkable phe- nomenon that requires an explanation. Relative Subjective Visual Directions Whenever a retinal area is stimulated by light entering the eye, the stimulus is perceived not only as being of a certain brightness and color and of a certain form but also as always being localized in a certain direction in visual space. One cannot have a visual impression without seeing it somewhere. If the stimulated retinal area is located to the left of the fovea, it is seen in the right half of the field; if it is located to the right of the fovea, it is seen in the left half of the field. The direction in which a visual object is local- ized is determined by the directional, or spatial, values of the stimulated retinal elements. These directional values (the local signs of Lotze) are an intrinsic property inherent to the retinal elements, as are all the properties that lead to sensations of brightness, color, and form of a percept. That the directional values are intrinsic proper- ties of the retinal elements and are not caused by the location of the light stimulus in external space or by some other properties of the light stimulus
Transcript
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C H A P T E R 2Binocular Vision andSpace Perception

Without an understanding of the physiologyof binocular vision it becomes difficult, if

not impossible, to appreciate its anomalies. Thereader is well advised to study this chapter thor-oughly since important basic concepts and termi-nology used throughout the remainder of this bookare introduced and defined. It is of historical inter-est that most of these concepts and terms haveonly been with us since the nineteenth centurywhen they were introduced by three men who maybe considered among the fathers of modern visualphysiology: Johannes Muller, Hermann von Helm-holtz, and Ewald Hering. The basic laws of binoc-ular vision and spatial localization that were laiddown by these giants of the past form the veryfoundation on which our current understanding ofstrabismus and its symptoms and sensory conse-quences is based.

Fusion, Diplopia, and the Lawof Sensory Correspondence

Let us position an object at a convenient distancein front of an observer at eye level and in themidplane of the head. If the eyes are properlyaligned and if the object is fixated binocularly, animage will be received on matching areas of thetwo retinas. If the eyes are functioning normallyand equally, the two images will be the same insize, illuminance, and color. In spite of the pres-ence of the two separate physical (retinal) images,

7

only one visual object is perceived by the ob-server. This phenomenon is so natural to us thatthe naive observer is not surprised by it; he issurprised only if he sees double. Yet theopposite—single binocular vision from two dis-tinct retinal images—is the truly remarkable phe-nomenon that requires an explanation.

Relative Subjective VisualDirections

Whenever a retinal area is stimulated by lightentering the eye, the stimulus is perceived notonly as being of a certain brightness and colorand of a certain form but also as always beinglocalized in a certain direction in visual space.One cannot have a visual impression withoutseeing it somewhere. If the stimulated retinal areais located to the left of the fovea, it is seen in theright half of the field; if it is located to the rightof the fovea, it is seen in the left half of the field.

The direction in which a visual object is local-ized is determined by the directional, or spatial,values of the stimulated retinal elements. Thesedirectional values (the local signs of Lotze) are anintrinsic property inherent to the retinal elements,as are all the properties that lead to sensations ofbrightness, color, and form of a percept.

That the directional values are intrinsic proper-ties of the retinal elements and are not caused bythe location of the light stimulus in external spaceor by some other properties of the light stimulus

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8 Physiology of the Sensorimotor Cooperation of the Eyes

can be shown by using inadequate stimuli. If theretina is stimulated mechanically (pressure) orelectrically, the resulting sensation is localized inthe same specific direction in which it would belocalized if the retinal elements had been stimu-lated by light. For instance, if we apply fingerpressure near the temporal canthus through thelids of one eye, we will become aware of a posi-tive scotoma in the nasal periphery of that eye.

It must be made clear at this point that when-ever retinal elements, retinal points, or retinalareas are spoken of in this book, they are to beunderstood in the sense in which Sherrington85

used them. He defined these terms to mean ‘‘theretinocerebral apparatus engaged in elaborating asensation in response to excitation of a unit areaof retinal surface.’’ None of the ‘‘properties’’ spo-ken of ‘‘belong’’ to the retinal elements per se.Anatomical, physiological, biophysical, and bio-chemical arrangements and mechanisms withinthe retina give rise to excitations that ultimatelyresult in what we know as ‘‘vision.’’ We ‘‘see’’with our brain, not with our retina, but the firststep in elaboration of information received by theeye takes place in the retina. Without the retina,there is no vision. Since it is vastly easier for usto visualize the retina than the totality of theretinocerebral apparatus, retinal terminology is ad-hered to throughout this book.

Each retinal element, then, localizes the stimu-lus as a visual percept in a specific direction, avisual direction, but this direction is not absolute.It is relative to the visual direction of the fovea.The fovea, the area of highest visual acuity, isalso the carrier of the principal visual directionand the center to which the secondary visual direc-tions of all other retinal elements relate. This rela-tionship is stable, and this stability is what makesan orderly visual field possible. Since the localiza-tion of the secondary visual direction is not abso-lutely fixed in visual space but is fixed only asrelated to the visual direction of the fovea, itsdirection shifts together with the principal visualdirection with changes in the position of the eye.Strictly speaking, visual directions are subjectivesensations and cannot be drawn in a geometricconstruct. The objective correlates to visual direc-tions for the use in such drawings are the principaland secondary lines of directions. A line of direc-tion is defined as a line that connects an objectpoint with its image on the retina. Helmholtz44, vol.

1, p. 97 defined it (the direction ray) also as a linefrom the posterior nodal point to the retina. All

FIGURE 2–1. Relative lines of direction. A, Eye instraight-ahead position. F, principal line of direction; N andP, secondary lines of direction. B, Eye turned to right.The sheath of lines of directions shifts with the positionof the eyes, but F� remains the principal line of directionand N� and P� remain the secondary lines of direction.

lines of direction therefore should meet in theanterior nodal point. For simplicity, the lines ofdirection are represented as straight lines in sche-matic drawings (Fig. 2–1).

Retinomotor Values

There is a further important result of this stableand orderly arrangement of the relative visual di-rections. The appearance of an object in the pe-riphery of the visual field attracts attention, andthe eye is turned toward the object so that itmay be imaged on the fovea. The resulting eyemovement, also called a saccade, is extraordi-narily precise. It is initiated by a signal from theretinal periphery that transmits to the brain thevisual direction, relative to the foveal visual direc-tion, where the peripherally seen object has ap-peared. Corresponding impulses are then sent tothe extraocular muscles to perform the necessaryocular rotation, mediated and controlled in a man-ner discussed in Chapter 4. This function of theretinal elements may be characterized by sayingthat they have a retinomotor value. This retinomo-tor value of the retinal elements increases fromthe center toward the periphery. The retinomotorvalue of the fovea itself is zero. Once an image ison the fovea, there is no incentive for ocularrotation. The fovea, then, in addition to its otherfunctions, is also the retinomotor center or retino-motor zero point. The retinal organization de-scribed here has an important clinical application:it makes it possible to measure ocular deviationsby means of the prism and cover test (see prismand cover test in Chapter 12).

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Binocular Vision and Space Perception 9

FIGURE 2–2. A, The fixation point, F, and the objects L and R all lie on the geometric lines ofdirection Ffl and Ffr of the two foveae. F, L, and R therefore are seen behind each other in subjectivespace in the common relative subjective visual direction of the two foveae, f, as shown in B. Theimaginary ‘‘third’’ eye, the cyclopean eye, is indicated by dashed lines in A.

Common Relative Subjective VisualDirections

Thus far, only the single eye has been discussed.How do the relative subjective visual directions ofthe two eyes relate to each other?

Let a person with head erect fixate an object,F (Fig. 2–2), called the fixation point. Ffl and Ffr

are the lines of direction of the two foveae and assuch are of special importance. They are alsocalled principal lines of direction or visual axes.Other synonyms are line of gaze, line of vision,and line of regard. If the two principal lines ofdirection intersect at the fixation point, it is saidthat there is binocular fixation. If only one princi-pal line of direction goes through the fixationpoint, fixation is monocular.

As we have seen, F, fixated binocularly (seeFig. 2–2), is seen not in the direction of theprincipal line of direction of either eye but in adirection that more or less coincides with themedian plane of the head. This holds true not onlyfor the fixation point but also for any object pointin the principal line of direction. L and R in Figure2–2, which lie on the principal lines of directionof the left and right eyes, therefore will appear tobe behind each other and in front of F, althoughall three are widely separated in physical space.All object points that simultaneously stimulate thetwo foveae appear in one and the same subjectivevisual direction. This direction belongs to both the

right and left foveae and therefore is called thecommon subjective visual direction of the foveae.

The two foveae have more than just a commonvisual direction; if an observer fixates F binocu-larly (Fig. 2–3), the object points, N and N�, ifproperly positioned, will be seen behind eachother, since the peripheral retinal points nl and nhave a common visual direction represented by b.What applied to nl and n applies to all other retinalelements. Every retinal point or area has a partner

FIGURE 2–3. A, Stimulating corresponding retinal ele-ments, objects N and N�, are localized in visual space inthe common relative subjective visual direction of nl andn�r and despite their horizontal separation are seen behindeach other in B, subjective visual space. F, fixation point.

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10 Physiology of the Sensorimotor Cooperation of the Eyes

in the fellow retina with which it shares a commonrelative subjective visual direction.

Retinal Correspondence

Retinal elements of the two eyes that share acommon subjective visual direction are called cor-responding retinal points. All other retinal ele-ments are noncorresponding or disparate with re-spect to a given retinal element in the fellow eye.This definition also may be stated in the followingway: corresponding retinal elements are those ele-ments of the two retinas that give rise in binocularvision to the localization of sensations in one andthe same subjective visual direction. It does notmatter whether a stimulus reaches the retinal ele-ment in one eye alone or its corresponding partnerin the other eye alone or whether it reaches bothsimultaneously (see Figs. 2–2 and 2–3).

The common visual direction of the foveae isagain of special importance. All visual directions,as has been seen, have a relative value in subjec-tive space. The common subjective visual direc-tions, too, have a fixed position relative only tothe principal common visual direction. They deter-mine the orientation of visual objects relative toeach other with the principal visual direction asthe direction of reference.

All common subjective visual directions can berepresented in a drawing as intersecting at onepoint with the principal visual direction. Thus,they form a sheaf that is the subjective equivalentof the two physical eyes and may be thought ofas the third central imaginary eye46, p. 348 or thebinoculus, or cyclopean eye44, vol. 3, p. 258 (see Fig.2–2). If the principal subjective visual directionlies in the median plane of the head, the physicalcorrelate of the point of intersection of the visualdirections, their origin, would be approximately inthe area of the root of the nose (whence ‘‘cyclo-pean’’ eye).

Corresponding retinal elements arranged in ho-rizontal and vertical rows provide the subjectivevertical and horizontal meridians. Meridians thatinclude the visual direction of the fovea are theprincipal corresponding horizontal and verticalmeridians.

The existence of corresponding retinal elementswith their common relative subjective visual direc-tions is the essence of binocular vision. It may becalled the law of sensory correspondence in anal-ogy with the law of motor correspondence, whichis discussed in Chapter 4.

The oneness of the directional sensory re-sponses originating in each eye is impressivelydemonstrated by means of afterimages. If one cre-ates an afterimage on the retina of one eye, it willappear in the binocular field of view in the com-mon visual direction of the stimulated retinal areaand in its nonstimulated partner in the other eye.It is difficult, indeed almost impossible, for theobserver to judge which eye carries the afterim-ages. It will continue to be seen and localized inthe same direction, whether the eyes are open orclosed or whether the stimulated eye is closed andthe other eye held open. In this latter situationsome authors19, 55 have spoken of an afterimagetransfer. This term is a misnomer as nothing isbeing transferred.43

If a horizontal afterimage is formed in one eyeby a strong horizontal light stimulus, leaving thefovea unstimulated, and if a similar verticalafterimage is created in the other eye, the resultingvisual percept is an afterimage in the form of across with a gap in its center.10, 49, p. 158 The gap isseen because of the lack of stimulation in thefoveae. The center of the horizontal and verticalafterimages is consequently a single spot localizedin the principal common visual direction. Thehorizontal and vertical legs of the afterimagesare oriented accordingly (Fig. 2–4). It is of greatimportance to understand clearly that the appear-ance of the afterimage cross is independent of theposition of the eyes. Once a lasting stimulus, suchas an afterimage, has been imparted, its localiza-tion in subjective space depends solely on thevisual direction of the retinal elements involved.One may topically anesthetize one eye and moveit passively with a forceps or push it in any direc-tion with one’s finger—the cross remains a cross.No change in the relative localization of the verti-cal and horizontal afterimage will occur. The useof afterimages has an important place in the diag-nosis of anomalous retinal correspondence (seeChapter 13). The principles underlying afterimagetesting must be fully understood to guard againstgross errors in interpretation.

Sensory Fusion

Sensory correspondence explains binocular singlevision or sensory fusion. The term is defined asthe unification of visual excitations from corres-ponding retinal images into a single visual per-cept, a single visual image. An object localized inone and the same visual direction by stimulation

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Binocular Vision and Space Perception 11

FIGURE 2–4. A, Afterimages produced in the right and left eye, respectively. The fovea is repre-sented by the break in the afterimage. B, The combined binocular afterimage forms a cross. Thetwo gaps appear single.

of the two retinas can only appear as one. Anindividual cannot see double with correspondingretinal elements. Single vision is the hallmark ofretinal correspondence. Put otherwise, the stimu-lus to sensory fusion is the excitation of corre-sponding retinal elements.

Since both the central and peripheral parts ofthe retina contribute fusible material, it is mis-leading to equate sensory fusion with ‘‘central’’fusion (as opposed to ‘‘peripheral’’ or motor fu-sion). Fusion, whether sensory or motor, is alwaysa central process (i.e., it takes place in the visualcenters of the brain).

For sensory fusion to occur, the images notonly must be located on corresponding retinalareas but also must be sufficiently similar in size,brightness, and sharpness. Unequal images are asevere sensory obstacle to fusion. Obstacles tofusion may become important factors in the etiol-ogy of strabismus (see Chapter 9). Differences incolor and contours may lead to retinal rivalry.

The simultaneous stimulation of noncorres-ponding or disparate retinal elements by an objectpoint causes this point to be localized in twodifferent subjective visual directions. An objectpoint seen simultaneously in two directions ap-pears double or in diplopia. Double vision is thehallmark of retinal disparity. Anyone with twonormal eyes can readily be convinced of this factby fixating binocularly an object point and thendisplacing one eye slightly by pressure from afinger. The object point, which appeared singlebefore pressure was applied to the globe, is nowseen in diplopia because it is no longer imagedon corresponding retinal areas. Qualifications thatmust be made about equating disparate retinalelements and diplopia are discussed on page 20.Paradoxical diplopia with ordinarily correspond-

ing elements in cases of strabismus is discussedin Chapter 13.

Motor Fusion

The term motor fusion refers to the ability to alignthe eyes in such a manner that sensory fusion canbe maintained. The stimulus for these fusional eyemovements is retinal disparity outside Panum’sarea and the two eyes are moving in oppositedirections (vergences; see Chapter 4). Unlike sen-sory fusion, which occurs between correspondingretinal elements in the fovea and the retinal pe-riphery, motor fusion is the exclusive function ofthe extrafoveal retinal periphery. No stimulus formotor fusion exists when the images of a fixatedvisual object fall on the fovea of each eye.

Retinal Rivalry

When dissimilar contours are presented to corres-ponding retinal areas, fusion becomes impossible.Instead, retinal rivalry may be observed. This phe-nomenon, also termed binocular rivalry, must beclearly distinguished from local adaptation, orTroxler’s phenomenon.67

If a person looks into a stereoscope at twodissimilar targets with overlapping nonfusible con-tours, first one contour, then the other will beseen, or mosaics of one and the other, but notboth contours simultaneously. In Figure 2–5, takenfrom Panum,78 each eye sees a set of oblique lines,one going from above left to below right, seen bythe left eye, and another set going from aboveright to below left, seen by the right eye. Whenobserved in a stereoscope, these lines are not seenas crossing lines but as a changing pattern of

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12 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–5. Rivalry pattern. A, Pattern seen by theleft eye. B, Pattern seen by the right eye. C, Binocularimpression. (From Panum PL. Physiologische Untersu-chungen uber das Sehen mit zwei Augen. Kiels. Ger-many, Schwerssche Buchhandlung, 1858, pp. 52 ff. )

patches of oblique lines going in one or the otherdirection.

Binocular rivalry may also be produced byuniform surfaces of different color (color rivalry)and unequal luminances of the two targets. Manycombinations of contours, colors, and luminanceshave been studied exhaustively since the daysof Panum,78 Fechner,41 Helmholtz,44 and Hering.45

Review of the literature may be found in thereports of Hofmann,49 Ogle,76, p. 409 and Levelt.67

It is of interest that it takes a certain buildupof time (150 ms) before dissimilar visual input tothe eyes causes binocular rivalry. Dichoptic stim-uli were perceived as ‘‘fused’’ when presented forshorter periods.63

The phenomenon of retinal rivalry is basic tobinocular vision and may be explained as follows.Simultaneous excitation of corresponding retinalareas by dissimilar stimuli does not permit fusion;but since such excitations are localized in the samevisual direction and since two objects localized inthe same place give rise to conflict and confusion,one or the other is temporarily suppressed. Whichof the two is suppressed more depends on thegreater or lesser dominance of one eye rather thanon the attention value of the visual object seen byeach eye.17 In other words, it is the eye and notthe stimulus that competes for dominance under awide range of conditions. Stimulus rivalry occurs

only within a limited range of spatial and temporalparameters.59

The extent to which true fusion or monocularalternation in the binocular field governs normalvisual activity—in other words, the significance ofthe rivalry phenomena for the theory of binocularvision—is considered on page 31.

It is at once clear that rivalry phenomena, orrather their absence, must in some fashion berelated to what is known as suppression in strabis-mic patients. Suppression is discussed in detail inChapter 13. Here we state only that constant fo-veal suppression of one eye with cessation ofrivalry leads to complete sensory dominance ofthe other eye, which is a major obstacle to binocu-lar vision. Return of retinal rivalry is a requisitefor reestablishment of binocular vision.

The retinal rivalry phenomenon has been ex-plained in neurophysiologic terms by the presenceof separate channels for the right and left eyesthat compete for access to the visual cortex. Athird binocular channel is activated only by fusibleinput.27, 102 Because of this competition and theinhibition elicited, only fragments of the imageseen by each eye are transmitted to the striatecortex in the case of nonfusible binocular input.Competitive interaction occurs not only in theprimary visual cortex14 but continues at severalafferent levels of the visual pathway, well afterthe inputs to the two eyes have converged.64

Objective (Physical) andSubjective (Visual) Space

Certain terminological differentiations made ear-lier in this chapter will not have escaped the noticeof the attentive reader. For example, location ofan object point in physical (objective) space wasseparated from its localization in visual (subjec-tive) space. The (objective) lines of direction de-termine which retinal area will be stimulated; their(subjective) counterpart, the visual directions, de-termine the direction in which the object will beseen in visual space.

Clear distinctions between physical space andits subjective counterpart are essential both inthinking about spatial orientation and in the ex-pression of that thinking. Failure to do so has beenthe source of much confusion and error in thedescription of normal and abnormal binocular vi-sion. The naive observer gives little thought tovision. His thoughts are for the things he sees. Hetakes it for granted that he sees things as they are

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Binocular Vision and Space Perception 13

and where they are. This instinctive approach isdeeply ingrained in all of us, and we act in accor-dance with it in practical life. In fact, however,we do not see physical objects. What takes placeis that energy in the form of light waves is ab-sorbed by photosensitive receptors in the retinaand is transformed into other forms of energy.Eventually this process leads in some manner toevents occurring in our consciousness; we callthis seeing. Thus, vision results from the activetransformation of the excitations produced initiallyin our retinas by energy emanating from a narrowband within the electromagnetic spectrum. In con-sciousness this builds up our world of light, color,and spatial orientation.

This view of vision is not shared by everyone.Some maintain that events in certain parts of thebrain are synonymous with vision and that whatwe experience in consciousness is an epiphenome-non. Others state that vision is nothing more thanan overt response of the organism to stimulation,a form of behavior, but all concede that we do notsee physical objects. What occurs in our brain arephysicochemical and electrical events. What weexperience in our consciousness are sense data. Injoining one sense datum to other sense data de-rived from the same or from different receptororgans, we proceed from sensation to perception.Relating these sense data to past experience isenormously complex, and each new sense datumbecomes either meaningful or not meaningful.

The sense datum is qualitatively different fromand is not commensurate with the physical processto which it is correlated. This is immediately clearwhen speaking of colors. Neither radiant energyof 640 mm nor the processes evoked by thisradiant energy in the retina, the optic nerve, or thebrain cells is ‘‘red.’’ Red is a sensation. It isnot immediately clear that similar considerationsapply to the perception of space. That they indeeddo apply will be evident throughout this book.

The scientific or philosophical validity of thevarious concepts of the nature of sensation andperception and of ‘‘reality’’ will not be arguedhere. The question under consideration is notwhich view is ‘‘true’’ or ‘‘correct’’—that is,verifiable—but which one gives the best descrip-tion of the phenomena and is most likely to helpin furthering the understanding and the advance-ment of clinical work. In this respect, the mostuseful view is that incorporated into the methodol-ogy termed exact subjectivism by Tschermak-Seysenegg.94 This view recognizes objective and

subjective factors in vision, that physical space,of which we and our visual system are a part, andsubjective space are built up from sense data.

The subjective space is private to each one ofus. A color-normal person can understand butnever experience how a color-blind person seesthe world, nor can a color-blind person ever expe-rience colors as a color-normal person does. Simi-larly, a person with a normal sensorimotor systemof the eyes may be able to understand but cannever experience certain phenomena that peoplewith abnormal sensorimotor systems may experi-ence in their subjective space (see Chapter 13).

The sensations of color and spatial localizationare not anarchic, however. Certain physical pro-cesses are always correlated with certain sensa-tions and perceptions. Known changes introducedinto the environment produce regular changes insensations and perceptions. These lawful relationsallow us to make quantitative determinations. Wehave no yardstick for the sensation ‘‘red,’’ and wehave no yardstick for subjective space; but we cancharacterize them quantitatively by changes in theenvironment with which they are correlated.

Each stimulus has certain characteristics: lumi-nance, wavelength, extent, and location in physicalspace. All these parameters, singly and combined,have an effect on the visual system; but how acolored object appears does not depend solely onthe wavelength it emits or reflects but also on thestate of the eye, particularly on the color to whichit has been previously adapted. The brightness ofa percept depends not only on the luminance ofthe stimulus but also on the state of the eye andits responsiveness. For instance, a stimulus that isbelow threshold for an eye adapted to bright lightmay appear very bright if the eye is adapted todarkness.

The ability of the eye to adapt to varying levelsof illumination is involved also in one of theconstancy phenomena. A white sheet of paperappears to be white not only at noon but also attwilight, although it reflects much more light intothe eye at noon. The smaller amount of light is aseffective in the dark-adapted eye as is the greateramount of light in the light-adapted eye. Up to acertain distance the size of a man remains constantas he walks away from us, although the retinalimage grows smaller (size constancy). Eventually,however, he will appear smaller, and as he recedesfarther he shrinks to a point and finally disappearsaltogether.

Most important, no stimulus is ever isolated. It

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14 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–6. Retinal discrepancies.Subjective appearance of circles (bro-ken lines) contrasts with objectivecircle (solid lines). (From Tschermak-Seysenegg A Von: Der exacte Sub-jectivismus in der neueren Sinnes-physiologie, ed 2, Vienna, Emil, Haim,1932.)

has a surround, and this surround also has stimulusqualities. The effects of the surround, especiallyat the borders, lead to the phenomena of inductionand physiologic contrast, which play a great rolein visual discrimination and color vision.

Where a visual object is localized in subjectivespace relative to other objects does not depend onthe position of that object in physical space. Itdepends on the visual direction of the retinal area

FIGURE 2–7. Discrepancies between subjective vertical meridian, SVM, and plumb line in the twoeyes. No discrepancy exists between the subjective horizontal, SHM, and the objective horizontalmeridians. (From Tschermak-Seysenegg A Von: Der exacte Subjectivismus in der neueren Sinnesphy-siologie, ed. 2, Vienna, Emil Haim, 1932.)

that it stimulates. An object may be located inphysical space at any place. So long as it stimu-lates the foveae it is seen in their common subjec-tive visual direction.

Discrepancies of Objective andSubjective Metrics

The difference between the metric of physicalspace and the metric of the eye is emphasized by

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Binocular Vision and Space Perception 15

the existence of so-called visual discrepancies. Ifone attempts to bisect a monocularly fixated linein an arrangement that excludes other visual cluesfrom the field, a constant error is detected. Theline is not divided into two objectively equal linesegments. If placed horizontally, the line segmentimaged on the nasal side of the retina, that is, theone appearing in the temporal half of the field, islarger than the temporally imaged retinonasal linesegment. This is the famous partition experimentof Kundt, a German physicist of the mid nine-teenth century.95, p. 137 The opposite phenomenon,described by Munsterberg,73 occurs only rarely.Similarly, the lower line segment (imaged retino-superiorly) is shorter than the upper (retinoinfer-ior) segment. In subjective space, therefore, theequivalent of a true circle fixated centrally is asomewhat irregular round figure, the smallest ra-dius of which points outward. Accordingly, a sub-jectively true circle does not correspond to a truecircle in physical space (Fig. 2–6). In general, thediscrepancies in the two eyes are symmetrical.They compensate each other, and the partition ofa line into two equal segments is more nearlycorrect in binocular fixation.

There are also directional discrepancies thatresult in a deviation of the subjective verticalfrom the objective vertical. A monocularly fixatedplumb line shows a definite disclination with thetop tilted templeward. This disclination is, as arule, approximately symmetrical in the two eyes(Fig. 2–7). In general, the angle of disclination isnot greater than 4� to 5�, but it has been reportedin isolated cases to be as high as 14�.

The discrepancies described are evidence thatthe retinal elements that physically have the sameeccentricity in the two eyes are not equivalentfunctionally. This is the basis of the Hering-Hille-brand horopter deviation (see p. 18).

Distribution of CorrespondingRetinal Elements

The Foveae as CorrespondingElements

That the foveae have a common subjective visualdirection is demonstrated by Hering’s fundamentalexperiment,46, p. 343 which in its classic simplicityis reminiscent of a bygone day when basic discov-eries in physiologic optics could be made with acandle, some cardboard, and a few strings and pul-leys.

Place yourself in front of a closed window withan open view. Close the right eye and look for anoutstanding, somewhat isolated object, say, a tree.Make an ink mark on the window pane at aboutthe midline of your head that will cover a spot onthe tree. Now close your left eye, open the righteye without moving your head, and fixate the inkspot. Observe what object it covers in the land-scape, say, a chimney on a house. Open both eyesand fixate the ink spot binocularly. You will notethat the chimney, the tree, and the ink spot appearin a line behind each other, approximately in themidline of your head. All those objects are seenin the common visual direction of the two foveae,even though they may actually be widely sepa-rated in physical space (Fig. 2–8). If you nowplace the point of a fine object (e.g., the tip of apencil) between one eye and the ink spot, it willalso appear in line with the objects seen outside

FIGURE 2–8. Hering’s fundamental experiment. (Modi-fied from Ogle KN: Researches in Binocular Vision. Phila-delphia, WB Saunders, 1950.)

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16 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–9. A, Title page of the volume by Francis Aguilonius, S.J., Six Books on Optics Useful toPhilosophers and Mathematicians, published in Antwerp, 1613. B, First page of book II of Aguilonius’volume, which deals with the horopter � 30.

the window. This simple experiment shows con-vincingly the discrepancies that may exist betweensubjective and objective physical space.

The Horopter

Determining the distribution of the correspondingretinal elements throughout the retina is lessreadily achieved. For a long time the idea pre-vailed that the distribution of the correspondingretinal elements was strictly geometric. If thiswere indeed true, then corresponding points wouldbe retinal elements having the same horizontaland vertical distance from the fovea in the rightand left halves of the retinas. The following men-tal experiment clarifies the concept. Place the tworetinas one on the other so that the two foveae andthe geometric horizontal and vertical meridianscoincide. Imagine a needle placed through the tworetinas anywhere within the area subserving thefield of binocular vision. The needle should strike

corresponding points in the two retinas. On theassumption that this is in fact the case, the horo-pter was determined theoretically.

Horopter is a very old term, introduced in 1613by Aguilonius1 in his book on optics (Fig. 2–9)even though the basic concept of the horopter hadbeen known since the times of Ptolemy.36 In mod-ern usage it is defined as the locus of all objectpoints that are imaged on corresponding retinalelements at a given fixation distance.

The determination of the total horopter surfacewas approached mathematically by Helmholtz44,

vol. 3, pp. 460 ff, on the basis of assumptions about thegeometric distribution of the corresponding retinalelements and about the position of the subjectivevertical meridians. For our purpose, we need beconcerned only with the horizontal distribution ofcorresponding retinal elements and to consider thelongitudinal horopter curve. This is the lineformed by the intersection of the visual plane(with head erect and eyes fixating a point straight

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Binocular Vision and Space Perception 17

FIGURE 2–9 Continued. C, Pages 110 and 111 of the volume of Aguilonius in which he introducesthe term horopter and defines it as the line that delimits and bounds binocular vision. The pertinentparagraph is indicated by a box. (From the copy of the book of Aguilonius at Dartmouth College’sBaker Library. Courtesy Dartmouth College Photographic Service, Hanover, NH.)

ahead in symmetrical convergence) with the ho-ropter surface.

The term longitudinal horopter is an inadequatetranslation of the German term Langshoropter.Boeder, in his 1952 translation of Tschermak-Seysenegg’s Einfuhrung zur physiologischen Op-tik (Introduction to Physiological Optics), sug-gested the term horopter of horizontal correspon-dence.95, p. 134 This much better but somewhatcumbersome term has not found general accep-tance. The term longitudinal horopter refers tothe locus in space of object points imaged on‘‘subjective longitudes’’ of the retina.

VIETH-MULLER CIRCLE. If corresponding pointshave a geometrically regular horizontal distancefrom the two retinas, the longitudinal horoptercurve would be a circle passing through the centerof rotation of the two eyes and the fixation point(Fig. 2–10). This would be true because by thetheorem of inscribed circles any lines drawn from

two points on a circle to any other pair of pointson its circumference include equal angles, asshown in the insert (see Fig. 2–10). This wasfirst pointed out by Vieth99 and later taken up byMuller,72 and this circle, which is the theoreticalor mathematical horopter curve, is also known asthe Vieth-Muller circle (see Fig. 2–10).

EMPIRICAL HOROPTER CURVE. By actual exper-imental determinations of the horopter curve, He-ring45, 46 and his pupil Hillebrand47 could showthat the Vieth-Muller circle does not describe thelongitudinal horopter. The empirical horoptercurve is flatter than the Vieth-Muller circle (seeFig. 2–10). This means that the distribution of theelements that correspond to each other is not thesame in the nasal and temporal parts of the tworetinas (e.g., the right half of each retina). Thecharacteristics of the horopter for each individualvary within certain limits; each person has hispersonal horopter.

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18 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–10. Vieth-Muller circle. VMC, empirical horopter; EH, objective frontoparallel plane; OFPP,fixation point; F, inset, law of inscribed circles. Object P on EH is seen singly, but object PO onVMC elicits double vision because of discrepancies between the empirical and theoretical horopter(see text).

The discrepancy between the theoretical ho-ropter (the Vieth-Muller circle) and the empiricallyestablished horopter curve (the so-called Hering-Hillebrand horopter deviation) might be attributedto disturbing optical properties of the ocular media.However, Tschermak-Seysenegg95 has shown con-clusively that this is not the case.

A great deal of work has been expended onexperimental studies of the horopter. Interestedreaders are referred to the books by Tschermak-Seysenegg95 and Ogle.75 Only the broad outlinesof the information resulting from this work andthe experimental techniques are discussed on page28, but first other phenomena of binocular visionmust be presented.

Physiologic Diplopia

All object points lying on the horopter curve stim-ulate corresponding retinal elements. By defini-tion, all points on the horopter curve are seensingly. Also by definition, all points not lying onthe horopter curve are imaged disparately and,with certain qualifications, are seen double. Thediplopia elicited by object points off the horopteris called physiologic diplopia.

Physiologic diplopia can be readily demon-strated to anyone with normal binocular vision.

Hold a pencil at reading distance in front of yourhead in its midplane and select a conspicuous,somewhat isolated object on the wall in line withthe pencil. Fixate the more distant object, and thepencil will be seen double. Shut alternately oneeye and then the other. The contralateral doubleimage of the pencil will disappear; that is, theimage on the left will disappear if the right eye isshut, and the one on the right will disappear if theleft eye is shut. In other words, when fixating adistant object, a nearer object is seen in crossed(heteronymous) diplopia. Crossed diplopia is ex-plained by the fact that the nearer object is seenin temporal (crossed) disparity with reference toits fovea (or to a corresponding element in periph-eral vision if the nearer object is located in theperiphery of the visual field). This is shown inFigure 2–11, A.

If one now fixates the pencil binocularly it willbe seen singly, but the more distant object doublesup. By again alternately closing each eye, onefinds that the ipsilateral double image vanishes.There is uncrossed (homonymous) diplopia be-cause the more distant object is imaged in nasal(uncrossed) disparity (Fig. 2–11, B).

Clinical Significance

Physiologic diplopia, a fundamental property ofbinocular vision, has a twofold clinical significance.

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Binocular Vision and Space Perception 19

FIGURE 2–11. Physiologic diplo-pia. A, Crossed (heteronymous)diplopia of the object p�, closerthan the fixation point F, imagedin temporal disparity. B, Un-crossed (homonymous) diplopiaof the object P, more distant thanthe fixation point F and imaged innasal disparity.

Occasionally a person accidentally will becomeaware of physiologic diplopia. Since double visionmust appear as an abnormal situation, the individ-ual likely will seek the help of an ophthalmologist.If the ophthalmologist cannot establish the pres-ence of an acute paresis of an extraocular muscleor any of the other causes of diplopia mentionedin this book, one must conclude that all the patienthas experienced is physiologic double vision. Theophthalmologist must attempt to explain to thepatient that physiologic diplopia is a characteristicof normal binocular vision and evidence that thepatient enjoys normal cooperation of the two eyes.This is not always easy. Apprehensive, neuroticpatients may not accept the explanation and willreinforce the annoyance by constantly looking fora second image ‘‘that should not be there.’’ Manypatients have spent considerable amounts ofmoney looking for an ophthalmologist who willfinally rid them of their diplopia.

This is the undesirable clinical aspect of physi-ologic diplopia. The desirable use that can bemade of physiologic diplopia is both diagnosticand therapeutic. In diagnosing binocular coopera-tion, the presence of physiologic diplopia indicatesthat the patient is capable of using both eyes incasual seeing and presumably does so. In orthoptictreatment of comitant strabismus, physiologic di-plopia is an important tool (see Chapter 24).

Suppression

Physiologic diplopia is not just a trick producedin vision laboratories. It is a phenomenon inherent

to normal binocular vision. The question arises,why are we not always aware of diplopia?

From the first moment in which binocular vi-sion is established, we become accustomed orconditioned to the arrangements provided for bin-ocular seeing and hence to physiologic diplopia.We learn how to disregard it, and unless someabnormal process interferes we are never awareof diplopia.

If a patient acquires an acute lateral rectusparesis in one eye, the eye turns in. An objectpoint fixated by the other eye is now imaged on anasally disparate area in the deviated eye. Conse-quently, the patient experiences uncrossed diplo-pia. If he or she has acquired a medial rectusparalysis, the eye turns out and the fixation pointis imaged in temporal disparity. The patient hascrossed diplopia. These forms of diplopia in pa-tients with acute paralytic strabismus are to beexpected from what is known about physiologicdiplopia and are a normal response of the sensorysystem to an abnormal motor situation.

As a rule, patients with comitant strabismus ofearly onset do not see double in spite of therelative deviation of the visual lines. Visual im-pressions that should be transmitted to the brainby one eye may be suppressed. The ability todisregard physiologic diplopia must be distin-guished from suppression, an active, inhibitorymechanism. The former is a psychological, thelatter a neurophysiologic process. The ability toselectively exclude certain unwanted visual im-pulses from entering consciousness (the ability todisregard or suppress them) is important in normal

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20 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–12. Panum’s area as determined on the horopter instrument. F, fixation point; OFPP,objective frontoparallel plane; SFPP, subjective frontoparallel plane (horopter).

and abnormal vision and is given a good deal ofattention in the clinical parts of this book.

Panum’s Area of SingleBinocular Vision

The statement has been made that object pointslying on the horopter are seen singly, whereaspoints off the horopter are seen double. The firstpart of this statement always holds true; the sec-ond part needs qualification.

If under appropriate experimental conditions,one fixates a fixed vertical wire with a number ofmovable vertical wires arranged to each side ofthe fixation wire (p. 28), all wires are seen singlyif they are placed on the horopter. If one of thewires seen in peripheral vision is moved, one willnotice that this wire can be displaced a certainshort distance, forward or backward, away fromthe horopter position without being seen double.Since the wires must be imaged on disparate reti-nal meridians as soon as they are displaced fromthe horopter, it follows that within a narrow bandaround the horopter stimulation of disparate retinalelements transmits the impression of single vision.Panum,78 the Danish physiologist, first reportedthis phenomenon, and the region in front and backof the horopter in which single vision is presentis known as Panum’s area of single binocular

vision or Panum’s fusional area (Fig. 2–12). Notonly is single vision possible in Panum’s area butvisual objects are seen stereoscopically, that is,in depth.

According to classic views the horizontal ex-tent of these areas is small at the center (6 to 10minutes near the fovea) and increases toward theperiphery (around 30 to 40 minutes at 12� fromthe fovea). The vertical extent has been variouslyassessed by different observers.75, p. 66 However,more recent research suggests that Panum’s areais considerably larger. Moving random-dot stereo-grams, which are most effective in retaining fu-sion while the disparity is increased, have shownthat disparities of as much as 2� to 3� can befused.40, 54, 79

The increase of Panum’s area toward the pe-riphery may be related to anatomical and physio-logic differences known to exist between themonosynaptic foveal cone system and the rod andcone system of the periphery. It parallels the in-crease in size of the retinal receptive fields. Notealso the ability of summation of the retinal periph-ery, an ability that is virtually absent in the foveain the photopic state (see Chapter 13). The hori-zontal extent of Panum’s area can be reduced tosome degree by training.

The question is sometimes asked whether Pa-num’s area is in (physical) space outside the eyeor in the retina. This question is obviously mean-

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Binocular Vision and Space Perception 21

ingless. This ‘‘area’’ represents the subjective re-sponse to a specific stimulus situation elicitingsingle visual impressions. The areas in physicalspace (location of object points and their imageson the retinas) simply define operationally theregions within which binocular single vision maybe obtained with stimulation of disparate retinalareas.

Fixation Disparity

A physiologic variant of normal binocular visionexists when a minute image displacement, rarelyexceeding several minutes of arc of angle, occurswithin Panum’s area while fusion is maintained.Although this phenomenon was demonstrated inearlier experiments,4, 50 Ogle and coworkers77 werethe ones who clarified the nature of this conditionand coined the term fixation disparity.

Fixation disparity can be elicited experimen-tally by presenting in a haploscopic device visualtargets that appear as mostly similar and somedissimilar markings to the eyes. Such an experi-mental arrangement, from a paper by Martens andOgle,70 is shown in Figure 2–13. The periphery ofthe screen, seen by each eye, containing identicalvisual information is fused. At the center of thescreen two vertical test lines are arranged so thatthe lower one is seen only by the right eye andthe upper one only by the left eye. The positionof one of these lines can be varied so that duringthe test the lines can be adjusted until they appearaligned to the observer. The actual separation ofthe lines, expressed in minutes of arc of subtended

FIGURE 2–13. Testing arrange-ment to determine fixation dispar-ity. (From Martens TG, Ogle KN:Observations on accommodativeconvergence, especially its non-linear relationships. Am J Oph-thalmol. 47:455, 1959.)

angle, is the fixation disparity. Whether fixationdisparity is an interesting but clinically irrelevantlaboratory finding or whether it represents the firststep between orthophoria and microtropia is amatter of debate.32

The use of the fixation disparity method tomeasure the accommodative convergence–ac-commodation (AC/A) ratio is described in Chapter5, and its possible relationship to the etiology andpathophysiology of heterophoria is discussed inChapter 9.

Stereopsis

When the experiment using fixation wires is per-formed to determine Panum’s area and the wiresseen peripherally are moved backward and for-ward, they do not double up so long as theyremain within Panum’s area of single binocularvision. As soon as they are moved out of thehoropter position, however, they appear in frontor in back of the fixation wire and are then seenstereoscopically. Stereopsis is defined as the rela-tive ordering of visual objects in depth, that is, inthe third dimension. This extraordinarily intri-guing quality of the visual system requires a ratherdetailed analysis.

Relative localization in the third dimension indepth parallels that of visual objects in the hori-zontal and vertical dimensions. The ability to per-ceive relative depth allows one to localize theperipherally seen wires just alluded to in front orin back of the fixation wire, and it is this abilitythat permits one to perceive a cube as a solid.

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22 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–14. A solid object placedin the midline of the head createsslightly different or disparate retinalimages, the fusion of which resultsin a three-dimensional sensation. Thelowercase letters of the retinal imagecorrespond to the uppercase lettersof the object.

Physiologic Basis of Stereopsis

Wheatstone,101 by his invention of the stereoscopein 1838, was the first to recognize that stereopsisoccurs when horizontally disparate retinal ele-ments are stimulated simultaneously. The fusionof such disparate images results in a single visualimpression perceived in depth, provided the fusedimage lies within Panum’s area of single binocularvision, which provides the physiologic basis ofbinocular depth perception. Vertical displacementproduces no stereoscopic effect.

A solid object placed in the median plane ofthe head produces unequal images in the two eyes.Owing to the horizontal separation of the two eyes(the interpupillary distance), for geometric reasonseach eye receives a slightly different image (Fig.2–14), referred to as a parallactic angle by physi-cists. The sensory fusion of the two unequal reti-nal images results in a three-dimensional percept.

The object producing slightly unequal imagesin the two eyes need not be a solid one. A stereo-scopic effect can also be produced by two-dimen-sional pictures, some elements of which are im-aged on corresponding retinal elements to givethe frame of reference for the relative in-depthlocalization of other elements of figures con-structed to provide horizontally disparate imagery.Such figures must be viewed separately but binoc-ularly in a stereoscope or some haploscopic device(see Chapter 4). This is another example of adifference between physical and subjective space.Neither figure seen by each eye has depth; each

provides only the appropriate stimulus situationthat, when elaborated by the visual system, pro-duces a three-dimensional percept in visual space.

A simple example will make this clear. If onepresents to each eye in a stereoscope or haplo-scope a set of three concentric circles, they willbe fused into a single set of three flat concentriccircles. Each circle is imaged on correspondingretinal elements. To ensure that each eye has in-deed viewed the circles, a black dot, a so-calledcheck mark, is placed to the left of the circlesseen by the left eye and to the right of the circlesseen by the right eye. In the fused image a dotwill be seen on each side of the three circles(Fig. 2–15A).

FIGURE 2–15. A, Two sets of concentric circles to beviewed in a stereoscope. B, Two sets of eccentric circlesto be similarly viewed.

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Binocular Vision and Space Perception 23

The circles may be drawn so that they are notconcentric, but eccentric, by shifting the center ofthe two inner circles on the horizontal diameterof the outer circle (Fig. 2–15B). If viewed in astereoscope, the outer circles imaged on corres-ponding retinal elements will be fused and servethe viewer as a frame of reference for the othertwo circles, which are also fused. However, theywill appear in front or in back of the outer circle,depending on the direction in which their centershave been shifted. If they are displaced towardeach other (i.e., toward the inner side of the cir-cumference of the outer circles), they create atemporal disparity and therefore are seen in frontof the outer circle. If they are displaced awayfrom each other (toward the outer side of the largecircles), they are imaged in nasal disparity andtherefore are seen in back of the outer circle. Thegreater the displacement of the inner circles, thefarther away from the outer circle they are local-ized. The greater the depth effect, the greater thehorizontal disparity.

The inner circles are seen not only in depthrelative to the outer circle in the fused image butthey also appear concentric with it, although theimage in each eye appears as eccentric circles.This most startling phenomenon of a shift in visualdirection of the fused image is the very essenceof stereopsis, and without it there is no stereopsis.It has implications for the clinical use of stereo-scopic targets (see Chapter 15).

Stereopsis is a response to disparate stimulationof the retinal elements. It is this highest form ofbinocular cooperation that adds a new quality tovision, but it is not a ‘‘higher’’ form of fusion asis implied in the term third degree of fusion, usedin the older literature to denote stereopsis.

FIGURE 2–16. Random-dot stereogram. The central square will appear behind the plane of the pagewhen the eyes overconverge and in front of the paper when they underconverge. (From Julesz B:The Foundations of Cyclopean Perception. Chicago, University of Chicago Press, 1971.)

The question arose whether the brain mustcompare the images formed on each retina beforeit can use the disparity of the visual input toconvey the sense of depth. The answer to thisquestion was provided by Julesz’s invention57 ofrandom-dot stereograms. Random-dot stereo-grams, when monocularly inspected, convey novisual information other than random noise (Fig.2–16); however, when binocularly fused by con-vergence or prisms, a square pattern appears invivid depth above or below the level of the page.It follows that stereopsis does not depend on mon-ocular clues to spatial orientation or shape recog-nition, since each monocularly viewed figure con-tains no information about the contour of thestereoscopic image. Binocularly imaged informa-tion is independent of the monocular information.Moreover, since the square is seen only because itis perceived in depth, monocular pattern recogni-tion is not necessary for stereopsis. Julesz58 con-cluded from a series of elegantly designed experi-ments that form perception must occur afterstereopsis in the functional hierarchy of visualprocessing and not before, as was once assumed.

The principle on which random-dot stereo-grams is based is shown in Figure 2–17. The dotdistributions seen by the right and left eyes areidentical (0 and 1 squares) except for the centralsquares of each figure, which are shifted in ahorizontal direction relative to each other (A andB squares). The retinal disparity of the centralsquares when both images are fused elicits stere-opsis.

Local vs. Global Stereopsis

The rather startling finding that random-dot stere-opsis is not preceded by form recognition directed

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24 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–17. Principle of gener-ating a random-dot stereogram.(From Julesz B: The Foundationsof Cyclopean Perception, Chicago,University of Chicago Press,1971.)

attention to the dot-by-dot or square-by-squarematching process that must occur between theright and left stereogram to elicit stereopsis.Julesz58 applied the term local stereopsis to thiscorrelation and pointed out that the elements of arandom-dot stereogram (i.e., black and white dots)may give rise to many false matches within Pa-num’s area since ambiguity exists about whichelements in the two monocular fields are corres-ponding. There is less uncertainty about whichparts of the drawing are seen by correspondingretinal elements in a classic stereogram (see Fig.2–15). For random-dot stereopsis to occur theglobal neighborhood of each matching pair of dotsor lines that provide the stimulus for stereopsisand, ultimately, for form recognition must be takeninto account. This mechanism was termed globalstereopsis by Julesz.58

The clinician must ask how the recognition ofstereopsis in a random-dot stereogram relates tostereopsis under casual conditions of seeing. It isdisconcerting to learn, for instance, that 40% of162 normal children aged 4 1/2 to 5 1/2 yearswere found to have random-dot stereopsis of lessthan 40 seconds of arc.59 This finding casts doubtupon the value of random-dot testing in differenti-ating visually normal from abnormal subjects7 anddraws attention to the fact that testing for random-dot stereopsis is not the same as testing for stere-opsis under casual conditions of seeing. For in-stance, under ordinary visual conditions the recog-nition of form does not depend on intact stereopsisand the visual system is not challenged by the taskof having to unscramble a seemingly meaninglesspattern of black and white dots without the avail-ability of nonstereoscopic clues to depth percep-tion.

This should not distract from advantages ofusing tests that exclude contamination of testing

results by monocular clues and permit the objec-tive testing of infants5 or experimental animals31

for stereopsis Other clinical features of stereopsistesting are discussed in Chapter 15.

Stereopsis and Fusion

Although it is true that sensory fusion is essentialfor the highest degree of stereopsis, lower degreesof stereopsis may occur in the absence of sensoryfusion and even in the presence of heterotropia.Examples are microtropia and small angle esotro-pia. Moreover, it has been shown experimentallythat binocular depth discrimination may occurwith diplopia.20 For instance, if a peripherally seenwire is located to the left and at some distance infront of a binocularly fixated wire, as in a horopterapparatus (see p. 28), the peripheral wire appearsin (physiologic) diplopia. One can now attempt toplace a second peripheral wire, located in the righthalf of the field, in line with the left peripheralwire. The closer the left peripheral wire is to thecentrally fixated wire, the more accurate is thesetting of the wire on the right. The accuracydecreases with increasing distance from the centralwire, and eventually the settings are made by purechance, indicating that the wire on the right isno longer placed by the criterion of stereopsis;stereopsis has broken down. These observationsare important for the theory of stereopsis. Whereasthis experiment shows that sensory fusion of dis-parate retinal images is not absolutely essentialfor binocular depth discrimination, it must be em-phasized that to obtain higher degrees of stereop-sis the similar parts of a stereogram must be fusedto obtain a frame of reference (see Fig. 2–17).

On the other hand, sensory fusion (i.e., theability to unify images falling on correspondingretinal areas) in itself does not guarantee the pres-

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Binocular Vision and Space Perception 25

ence of stereopsis. There are patients who readilyfuse similar targets and who may have normalfusional amplitudes but who have no stereopsis.Such patients suppress selectively the disparatelyimaged elements of a stereogram seen by one eye.This behavior is of clinical importance and isdiscussed in Chapter 15.

Stereoscopic Acuity

The responsiveness to disparate stimulations hasits limits. There is a minimal disparity beyondwhich no stereoscopic effect is produced. Thislimiting disparity characterizes a person’s stereo-scopic acuity.

Stereoscopic acuity depends on many factorsand is influenced greatly by the method used indetermining it. In refined laboratory examinationsand with highly trained subjects, stereoscopic acu-ities as low as 2 to 7 seconds of arc have beenfound. There are no standardized clinical stereo-scopic acuity tests comparable to visual acuitytests, and no results of mass examinations. Gener-ally speaking, a threshold of 15 to 30 secondsobtained in clinical tests may be regarded as excel-lent.

It is clear that visual acuity has some relationto stereoscopic acuity. Stereoscopic acuity cannotbe greater than the Vernier acuity of the stimulatedretinal area. Stereoscopic acuity decreases, as doesvisual acuity, from the center to the periphery ofthe retina.21 However, despite this relationship,stereopsis is a function not linearly correlated withvisual acuity. It has been shown, for instance, thatreduction of visual acuity with neutral filters overone eye does not raise the stereoscopic threshold,even if the acuity was lowered to as low as 0.3.A further decrease in vision to 0.2 greatly in-creased the threshold and with a decrease in acuityof the covered eye to 0.1, stereopsis was absent.71

Colenbrander28 quotes Holthuis as stating that inexamining aviators he found that poor visual acu-ity was generally accompanied by reduced stereo-scopic acuity but that there was no correlationbetween the two functions. On the other hand,spectacle blur decreases stereoacuity more thanordinary visual acuity.100 Of special clinical inter-est is the fact that stereoacuity in patients withamblyopia may be better than what one wouldexpect from their visual acuity.7, 26 This observa-tion raises doubts about the value of stereoacuitytesting being advocated by many as a foolproofvisual screening method for preschool children.

Since there is a stereoscopic threshold, it fol-lows that stereopsis cannot work beyond a certaincritical distance. This distance has been computedsomewhere between 125 and 200 m by variousauthors, depending on the threshold used for com-putation.

Monocular (Nonstereoscopic)Clues to Spatial Orientation

Stereopsis—the relative localization of visual ob-jects in depth—can occur only in binocular visionand is based on a physiologic process derivedfrom the organization of the sensory visual sys-tem. It is not acquired through experience and isunequivocal and inescapable.

Stereopsis is restricted to relatively short visualdistances and is not the only means we havefor spatial orientation. A second set of clues, themonocular or experiential clues, are important inour estimation of the relative distance of visualobjects and are active in monocular as well asbinocular vision. The importance of monocularclues in judging the relative distance between re-mote objects is perhaps best exemplified by anoptical illusion known to every sailor and broughtabout by the paucity of such clues on the open sea:two ships approaching each other from oppositedirections may appear to be dead set on a collisioncourse when, in fact, they are separated by manyhundreds of yards of water as they pass each other.

Monocular clues are the result of experienceand are equivocal. Such clues are numerous, anddescriptions of the most important ones follow.

MOTION PARALLAX. When one looks at two ob-jects, one of which is closer than the other, andmoves either the eyes or the head in a planeparallel to the plane of one of these objects, move-ment of the objects becomes apparent. The fartherobject appears to make a larger excursion than thenear object. This behavior is learned by experi-ence, and one makes much use of it in daily life,for instance, in sighting monocularly. If there aredepressions or elevations in the fundus, one canobserve the apparent movement of the retinal ves-sels by moving the head from side to side. Theparallactic movement of the more distant vesselsgives a compelling picture of the different levelsof the retina.

LINEAR PERSPECTIVE. Object points having aconstant size appear to subtend smaller and

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26 Physiology of the Sensorimotor Cooperation of the Eyes

smaller angles as they recede from the subject.Railroad tracks, which are in fact parallel, seemto approach each other in the distance. Foreshort-ening of horizontal and vertical lines is one ofthe most powerful tools for creation of three-dimensional impressions on a two-dimensionalsurface (Fig. 2–18). Renaissance artists made ex-aggerated use of this ‘‘trick’’ to create depth intheir paintings.

OVERLAY OF CONTOURS. Configurations inwhich contours are interposed on the contoursof other configurations provide impelling distanceclues. An object that interrupts the contours ofanother object is generally seen as being in frontof the object with incomplete contours (Fig. 2–19); the second, farther object is also higher thanthe first one. This, too, is a clue made use of byearly painters to indicate relative distances.

DISTRIBUTION OF HIGHLIGHTS AND SHAD-

OWS. Highlights and shadows are among the mostpotent monocular clues. Since sunlight comesfrom above, we have learned that the position ofshadows is helpful in determining elevations and

FIGURE 2–18. This photograph of an airport corridorshows the strong depth effect created by the apparentlydecreasing width of the ceiling lights and the decreasingheight of the columns.

FIGURE 2–19. Effect of overlay of contours. The rectan-gle in incomplete outline generally seems farther backthan the one that is complete. The incomplete rectangleis also higher, which adds to this impression.

depressions, that is, the relative depth, of objects.This phenomenon is impressively shown in Figure2–20, taken from a paper by Burian22; a piece ofcloth, (Fig. 2–20C) is photographed by throwinglight on it in such a way that horizontal threads inthe tissue appear as ridges. In Figure 2–20D, theidentical photograph has been turned 180� and theridges appear as troughs.

The inversion can occur because nothing in ourexperience prevents it from happening. In Figure2–20A and B, a photograph of a sculptured headis shown. Here the inversion of the print does nothave the same effect. Some observers may note ageneral flattening in the inverted face, but a noseis a nose and can never be seen as a trough.

SIZE OF KNOWN OBJECTS. If the size of twoobjects is known, one can judge the relative dis-tance of these objects by their apparent size. If anobject known to be smaller appears to be largerthan the other, we judge it to be nearer.

AERIAL PERSPECTIVE. Aerial perspective is theterm used for the influence of the atmosphereon contrast conditions and colors of more distantobjects. The bluish haze of more distant mountainsis an example. Chinese painters are masters at

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FIGURE 2–20. Effect of highlights and shadows. A,Sculpture of human head illuminated from above. B, Pho-tograph A inverted. C, Piece of cloth illuminated fromabove. D, Photograph C inverted. (From Burian HM: Theobjective and subjective factors in visual perception. JAssoc Med Illustrators 9:4, 1957.)

creating extraordinary depth in landscapes by us-ing subtle variations of shading.

NATURE OF MONOCULAR CLUES. The impres-sion of three-dimensionality imparted by all theseclues is a judgment, an interpretation, and impliesthat false judgments are possible; indeed, such isthe case. It also implies that this impression de-pends on past experience, as does every judgment.The nature of the nonstereoscopic clues is thatthey are experiential and can be meaningful onlywhen they are capable of being related to pastexperience.

Interaction of Stereoscopic andMonocular Clues

All this does not mean that nonstereoscopic mon-ocular clues are less important in everyday lifethan stereoscopic clues. Normally the two functiontogether, one enhancing the effect of the other, butthis is not always the case. If one introduces intostereograms monocular clues that conflict withstereoscopic clues, fascinating observations canbe made.

Not everyone reacts in the same fashion to such

stereograms. Some people are more responsive todisparate stimulation, that is, stereoscopic clues,whereas others respond more readily to monocularclues. These differences are caused both by physi-ologic peculiarities or actual abnormalities of thevisual system and by past experience. A personstereoblind since infancy must rely exclusively onmonocular clues and will flawlessly perform mostordinary tasks requiring depth discrimination, suchas pouring milk into a glass or parallel parking.He or she will fail abysmally, however, when ahigher degree of stereopsis becomes essential andmonocular clues are no longer available, for in-stance, as occurs in the limited field of visionprovided by an operating microscope.

Humans, then, have at their disposal two setsof clues for their orientation in space. By meansof the monocular clues to spatial localization, in-terpretation of the depth relation of visual objectsis achieved on the basis of experience. The cluesprovided by fusion of disparate retinal imagesafford the direct perception of this relation on thebasis of intrinsic physiologic arrangements.

Clinical Significance of MonocularClues

All this is of considerable clinical importance inpatients with strabismus. For example, if there isdoubt about whether a patient actually does seestereoscopically, misleading monocular clues in-troduced purposely into stereograms may providethe answer. Heavy black figures (as in the circlesof Fig. 2–15) appear closer than lighter figures doto a person without stereopsis, even if the stereo-gram is so drawn that the black figures shouldappear in back of the lighter ones. Furthermore, ifit is not known if a patient can see stereoscopi-cally, again use the eccentric circles and ask thepatient to state whether the inner circle seems tobe closer to the right or left side of the outercircle. If the patient answers that it is closer toone side or the other, one can be sure that he orshe does not see stereoscopically, since the circleswould otherwise have to appear concentric. Inaddition, the patient’s answer allows one to deter-mine which eye the patient is suppressing. Forexample, if the two inner circles are displacedaway from each other and the patient reports thatthe heavier circle is to the left in the outer circle,he or she is suppressing the right eye (see Fig. 2–15).

A patient with binocular vision but who has

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28 Physiology of the Sensorimotor Cooperation of the Eyes

recently lost one eye and is looking across asquare will have no question that a lamppost is infront of a house. The continuous lines of thelamppost are interposed over the interrupted hori-zontal contours of the house. However, the patientmay have considerable difficulty in pouring creaminto a coffee cup and performing other tasks ofvisuomanual coordination. In time the patient mayovercome these difficulties and become as skillfulor almost as skillful as before the eye was lost.Fast-moving objects (such as a flying ball) maycontinue to give trouble, but as time passes mon-ocular clues to depth perception may be used,even in near vision where formerly stereoscopicclues were relied on entirely.

Experimental Determinationof the Longitudinal Horopterand the Criteria of RetinalCorrespondence

In preceding discussions in this chapter, referencehas been made repeatedly to wires placed in vari-ous positions relative to a binocularly and cen-trally fixated wire. Such an arrangement of wiresis used in the determination of the empirical horo-pter.

The horopter apparatus (Fig. 2–21) is operatedin the following manner. The observer’s head isfixed in a headrest, and a suitable aperture ex-cludes all extraneous elements from the observer’svisual field. Tracks are provided that converge ata point below the middle of the observer’s basal

FIGURE 2–21. Horopter apparatus. (From Ogle KN: Researches in Binocular Vision. Philadelphia,WB Saunders, 1950.)

line, that is, the line segment connecting the cen-ters of rotation of the two eyes. In these tracksrun carriers to which vertical wires are fastened.The observer fixates a vertical wire placed at achosen near vision distance in the median plane.The position of the central wire remains un-changed. To each side of the fixation wire aresituated movable wires that the observer sees at1�, 2�, 3�, 4�, 6�, 8�, 12�, and so on in peripheral vi-sion.

The purpose of the horopter apparatus is todetermine the distribution of corresponding retinalelements. Therefore the patient must be assigneda task in which the peripherally seen wires arearranged so that they stimulate corresponding reti-nal elements. The patient must strictly fixate thecentral wire, which may be equipped for this pur-pose with a small bead. A number of possiblecriteria of correspondence can now be evaluated.

Criterion of Single Vision

Double vision with corresponding retinal points isimpossible. One could instruct an observer to setthe peripheral wires in the horopter apparatus sothat they would all appear singly. This is not areliable criterion for correspondence because ofPanum’s area of single binocular vision.

Apparent Frontal Plane Criterion

As we have also seen, stereopsis depends on dis-parate stimulation. Simultaneous stimulation ofcorresponding retinal elements does not produce athree-dimensional effect. The stereoscopic value

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of corresponding retinal elements is zero. There-fore, if an observer is asked to place all peripheralwires in such a manner that they appear in a planeparallel with his or her forehead, the subjectivefrontoparallel plane, all wires presumably stimu-late corresponding retinal elements and their posi-tion determines the observer’s horopter.

For near vision distances, this horopter curvedoes not coincide with the objective frontoparallelplane. It is a curve that is slightly convex to theobserver but has less of a curvature than the Vieth-Muller circle (see Fig. 2–10). At times it is amus-ing to see a naive observer’s astonishment whenit is shown that he or she has set the horopterwires in a curve. The observer is so sure they arein a plane!

Criterion of Common VisualDirections

The criterion of frontoparallel appearance is con-venient and easy to use. This method is suffi-ciently reliable so that it has been used in almostall horopter studies, but it is indirect. In principle,the most reliable criterion would be direct determi-nation of the common visual directions, whichcan be done with a special arrangement of thehoropter wires.

If one of the peripheral wires is partially oc-cluded so that, for example, its upper part is seenby one eye and its lower part by the other, theline will be seen as continuous only when it comesto lie on corresponding meridians in the two reti-nas. This method presents considerable practicaldifficulty, mainly because the reduction in fusiblematerial in the field makes it difficult to maintainthe proper positioning of the eyes.

Criterion of Highest StereoscopicSensitivity

Although the stereoscopic value of correspondingretinal elements is zero, stereoscopic sensitivity ishighest in the immediate vicinity of correspondingretinal elements. This means that the smallestchanges in the position in front of or behind theperipherally seen wires are detected near the ho-ropter curve. By determining this position, an ap-proximation of the observer’s horopter curve canbe obtained. This procedure is tedious and doesnot approximate the horopter curve as well asthe much simpler determination of the subjectivefrontoparallel plane.

Egocentric (Absolute)Localization

Thus far this chapter has dealt with localization ofvisual objects relative to each other in the threedimensions. We must now turn to the absolute andegocentric localization of visual objects, that is, totheir orientation with respect to a coordinate sys-tem that has its origin in physical space (absolutelocalization), especially that part of physical spaceoccupied by a person’s body (egocentric localiza-tion).

The physical coordinates for egocentric local-ization are the median plane of the body (verticalin an upright position of the body, perpendicularto the baseline at its center), the horizontal planeof the body (containing the baseline and the twoprincipal lines of direction), and the frontal planeof the body (containing the baseline, which isperpendicular to the median and the horizontalplane). Subjective planes correspond to thesephysical planes: the subjective median plane trans-mits the impression ‘‘straight-ahead’’; the subjec-tive horizontal (visual) plane transmits the impres-sion ‘‘at eye level’’; and the subjective frontalplane transmits the impression ‘‘at a distance fromme.’’ In general, these subjective equivalents donot coincide with their physical counterparts.

Hering46, p. 417 made the assumption that theydid coincide since it happened to be true for him,and accordingly he placed the origin of the ego-centric coordinate system at the root of the nose.It need not be there. If a person has a markedlydominant eye, the absolute position of the com-mon visual direction of the foveae (and thereforeof the subjective median plane and the ‘‘straight-ahead’’ position) may not be in the objective me-dian plane but may be shifted toward the side ofthe dominant eye. Recent data suggest that thereference point for visual localization lies betweenthe midpoint of the interocular axis and the lineof sight of the dominant eye.84

Egocentric Localization andConvergence

Of special interest is in-depth egocentric localiza-tion. How do we judge the distance of an objectfrom us? Many factors cooperate in this function.The size of the retinal image could be one, sincethe retinal image of an object is smaller the fartherit is from the eye. For objects of known size (e.g.,a man) and relatively short distances, this clue is

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30 Physiology of the Sensorimotor Cooperation of the Eyes

of limited value because of the size-constancyphenomenon. Accommodation may provide an-other clue. Convergence is generally assumed tobe the most potent clue.

A simple experiment will demonstrate thispoint convincingly. Hold up one thumb in front ofyou at arm’s length and look at a window or doorat the end of the room. Then converge your eyeson your thumb and the distant objects will seemto shrink and to move closer. This is a compellingphenomenon that is not only of theoretical butalso of practical clinical significance in patientswith intermittent exotropia (see Chapter 17).

It was postulated in the older literature that anawareness of the impulses required to bring orkeep the eyes in a particular position was at theorigin of our perception of absolute distance. Thistheory is not satisfactory, and Tschermak-Seyse-negg95, p. 219 replaced it with the theory of an indi-rect sensory function of the ocular muscles. Itmakes the following assumption: Afferent nervefibers respond to the active tonus of ocular mus-cles, but not to passive relaxation. However, thereis no consciousness of the tension of single mus-cles or of the eye posture as such. The simple,preexisting sensation of the straight-ahead positionor the equally high position is related to a certaincomplicated tonus distribution of the oculomotorapparatus and, therefore, to a complex of afferentexcitation.

This somewhat awkwardly put explanation is,in fact, an anticipation of the way in which mod-ern models describe control of eye movementsand awareness of absolute depth. It contains theconcept of ‘‘space representation’’ and of negativeand, indeed, parametric feedback.

Egocentric Localization andProprioception

As mentioned earlier in this chapter, there are twosources of information from which the brain maydetermine eye position and receive spatial orienta-tion clues: visual input from the retina, (outflow)and proprioceptive information from the extraocu-lar muscles (inflow). While there can be littledoubt that efferent outflow is the dominant mecha-nism in supplying the most necessary spatial infor-mation to the brain, there is mounting evidencethat proprioceptive inflow may also play a role.The human extraocular muscle is certainly ade-quately equipped to provide proprioceptive input:there are abundant muscle spindles, Golgi tendon,

and palisade endings located at the musculotendi-nous junction (see Chapter 6). Skavenski86 wasfirst to show in a carefully designed experimentthat the human oculomotor system is capable ofprocessing nonvisual inflow information. His sub-jects were able to correct for passively appliedloads to the eyes with appropriate eye movementsin the dark. Experiments in cats42, 69, 93 stronglysuggested that the ophthalmic branch of the tri-geminal nerve carries proprioceptive afferents.That the same may hold true for humans wassuggested by Campos and coworkers25 who de-scribed faulty egocentric localization in patientswith herpes zoster ophthalmicus. Gauthier and co-workers42 (see also Bridgeman and Stark18)showed that passive deviation of one eye causedfaulty localization of objects seen by the othereye in the direction of the passive movement,suggesting the utilization of inflow informationfor egocentric localization.

Lewis and Zee65 reported that proprioceptiveafference may influence egocentric localization inthe absence of normal oculomotor innervation ina patient with trigeminal-oculomotor synkinesis.Lewis and coworkers66 showed also that proprio-ceptive deafferentation of the extraocular musclesdid not influence the accuracy of pointing andconcluded that inflow provides sufficient informa-tion about orbital eye position for correct egocen-tric localization.

Mechanical vibration of the inferior rectusmuscle to each eye simultaneously and undermonocular and binocular conditions caused an il-lusionary movement of a red light presented intotal darkness and induced past-pointing.97 Thisvisual illusion could also be elicited by vibrationof the horizontal rectus muscles and cannot beattributed to retinal motion of the image of thefixated target.96 Lennerstrand and coworkers62

showed that vibratory activation of the musclespindles in extraocular muscle affects eye positionand these signals are processed differently in nor-mals and in exotropic patients.

Steinbach and Smith91 found surprisingly accu-rate egocentric localization in patients after stra-bismus surgery who had been deprived of visualinput until the time of the experiment. Accordingto these authors, this information can only bederived from inflow (see also Dengis and cowork-ers33, 34). Myotomy of a muscle had a greater effectin deafferenting proprioception than a recession,presumably because of greater destruction of thepalisade endings by the former procedure.92 How-

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ever, Bock and Kommerell16 could not duplicateSteinbach’s finding and Campos and coworkers24

were unable to correlate pointing errors after stra-bismus surgery with a particular surgical proce-dure. They did, however, show changes in egocen-tric localization after exerting stretch on anextraocular muscle.23

While some of these data are contradictorythere is little doubt that inflow signals are avail-able to the visual system. However, it is not clearhow they are used by the brain and correlatedwith outflow information under casual conditionsof seeing when visual input is abundantly avail-able. Skavenski and coworkers87 showed thatwhen inflow and outflow signals conflict, the out-flow signal is, as one may expect, the strongerone. It has been proposed that inflow acts as along-term calibrator and is involved in main-taining the stability and conjugacy of gaze89 andof smooth pursuit movement.35 For reviews, seeSteinbach88, 90 and Lennerstrand.60, 61

Clinical Significance of Relative andEgocentric Localization

One need not go into experimental evaluationsof egocentric localization, but emphasis must beplaced on making a clear distinction between rela-tive and absolute (egocentric) localization becauserelative and egocentric localization may be inde-pendently affected in certain forms of strabismus.Confusion between the two forms of subjectivelocalization leads to misinterpretations of the ob-served phenomena. For instance, a patient with anacute paralysis of an extraocular muscle will past-point (see Chapter 20), which is evidence of ab-normal egocentric localization, but will have nor-mal relative localization (the double images arelocalized according to the laws of physiologicdiplopia). A patient with comitant strabismus doesnot, as a rule, past-point, although exceptions dooccur,3, 93, 94 but rather may experience abnormalrelative localization; that is, the patient does notlocalize the double images according to the lawof physiologic diplopia (anomalous retinal corre-spondence; see Chapter 13).

Theories of Binocular Vision

Correspondence and Disparity

According to the theory of binocular vision pre-sented in this chapter, sensory binocular coopera-

tion is based on a system of correspondence anddisparity.

A given retinal element in one retina shares acommon subjective visual direction with an ele-ment in the other retina. These corresponding ele-ments form the framework or zero system of bin-ocular vision. When stimulated simultaneously byone object point, they transmit single visual im-pressions that have no depth quality. When stimu-lated simultaneously by two object points thatdiffer in character, binocular rivalry results. Whendisparate elements are stimulated by one objectpoint, diplopia is experienced. However, if thehorizontal disparity remains within the limits ofPanum’s area, a single visual impression is elicitedthat has the quality of relative depth or stereopsis.The fused component, that is, the singly ap-pearing, disparately imaged component of thestimulus or target, is seen not only in depth butalso in the subjective visual direction of the rela-tive retinal element to which the stimulus is dispa-rate.

The perceived depth increases with increasingdisparity. With further increase in disparity, diplo-pia eventually occurs. Although stereopsis gener-ally occurs with fusion, it is still possible up to apoint to experience a true stereoscopic effect fromdouble images.20; 76, p. 281 However, increasing dis-parity causes the quality of stereopsis to decreaseuntil finally there is no longer any binocular ste-reoscopic effect. There is, then, no sharp delinea-tion between fusion with full stereopsis and diplo-pia without stereopsis, but only a gradualtransition. This is consistent with many other bio-logical processes, especially visual ones, none ofwhich change abruptly from function to nonfunc-tion.

One can think of each retinal element as beingthe center of attraction of a retinal unit, the at-traction diminishing as the distance from the ele-ment increases. In considering this simile, keep inmind that (1) the retinal units are overlapping, and(2) the stimulation of neighboring units may resultin inhibitory stimulation of surrounding units.

Neurophysiologic Theory ofBinocular Vision and Stereopsis

The correspondence theory has been built on thebasis of overwhelming evidence from psycho-physical data. Direct physiologic evidence for ithas emerged from the work of Hubel and Wie-sel.51–53 These authors have given us insight into

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32 Physiology of the Sensorimotor Cooperation of the Eyes

FIGURE 2–22. Receptive fields de-pendency on preferred directionand orientation of the stimulus.(Modified from Bishop P: Verticaldisparity, egocentric distance andstereoscopic depth consistency: Anew interpretation. Proc R SocLond B Biol Sci 237:1289, 1989.)

how visual stimuli from the retina to the visualcortex are modified and coded. In their microelec-trode studies of single-cell responses in the striatecortex of the cat, they have found that roughly80% of the neurons could be driven from eithereye. However, only 25% of these binocularlydriven cells are stimulated equally well from eacheye; the remaining 75% represent graded degreesof influence from the right or left eye. Ten percentof the cells are driven exclusively from the rightor left eye. Cells that can be driven by stimulationof either eye have receptive fields of nearly equalsize and in approximately corresponding positionsin the visual field. The receptive field of a visualneuron is defined as that part of the visual fieldthat can influence the firing of that cell.52 Theactivity of most striate neurons is maximal tomovement of a linear slit of light in front of theeye when the slit has a particular orientation andpreferred direction of movement (Fig. 2–22).

Similar experiments in monkeys yielded com-parable data8, 29 (Fig. 2–23). That this dominancein distribution of cortical neurons is easily upsetwhen animals are reared with experimental stra-bismus, anisometropia, or form vision deprivationby lid suture is discussed in Chapter 14.

A reasonable assumption is that neurons in thestriate cortex responding equally well to succes-sive stimulation, and especially those in whichthe response can be maximized with simultaneousstimulation, are somehow involved with binocularvisual processing. Indeed, Hubel and Wiesel52

showed response summation or inhibition, de-pending on the alignment or misalignment of thestimulus on the receptive field, concluding that

summation occurs whenever corresponding partsof the receptive field are stimulated.

The discovery of disparity-sensitive binocularcells in the striate cortex had to await the arrivalof precise receptive field mapping techniques thatexcluded all eye movements during the experi-ment. The chronological sequence of a series ofclassic experiments that led to the discovery of theneurophysiologic mechanisms of stereopsis wasreviewed by Bishop and Pettigrew.13 Barlow, Bla-kemore, and Pettigrew9 were the first to describehorizontal disparity sensitivity of binocular striateneurons in the cat and proposed that these cellsmay be responsible for stereopsis. Hubel and Wie-

FIGURE 2–23. Dominance distribution of striate neuronsfrom two normally reared monkeys. Categories 1 and 7contain neurons driven only through the left or right eye.The remaining categories represent greater degrees ofbinocular influence with neurons in 4 being equally influ-enced by both eyes. (From Crawford MLJ, Blake R, CoolSJ, Noorden GK von: Physiological consequences of uni-lateral and bilateral eye closure in macaque monkeys:Some further observations. Brain Res 84:150, 1975.)

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sel53 identified cells described as being sensitiveto binocular depth in area 18 of the macaquecortex. Poggio and coworkers80–83 discovered inrhesus monkeys neurons in cortical areas 17 and18 that responded to dynamic random-dot stereo-grams containing no depth clues other than dispar-ity. They identified two functional sets of stereo-scopic neurons, one tuned excitatory and the otherinhibitory. These cells responded differently, de-pending on whether visual objects were on, infront of, or behind the horopter.83 Bishop11, 12 pro-posed that binocularly activated cortical cells maynot only be selective for horizontal but for verticalstimulus disparities as well. However, in monkeysthe horizontal disparities are appreciably greaterthan the vertical disparities and in humans verticaldisparity produces no measurable stereoscopic ef-fect.

Crawford and coworkers29, 30 showed in behav-ioral and electrophysiologic experiments that in-fant monkeys with a severely reduced binocularstriate neuron population after a period of experi-mental strabismus become stereoblind (Fig. 2–24).Once binocular neurons are lost they do not re-cover, even with extensive binocular visual experi-ence.30 This may explain the markedly reducedstereoacuity in spite of early surgery in childrenwith essential infantile esotropia (see Chapter 16)and emphasizes the extraordinary vulnerability ofthe primate binocular system to abnormal visualexperience. Thus, stereopsis has been unequivo-cally linked with the so-called binocular cells inthe striate cortex, and there has been goodagreement between psychophysical data collected

FIGURE 2–24. Stereoblind monkeys (N � 3) had most cortical cells controlled exclusively by oneeye or the other (categories 1 and 7) with only 13% (N � 276) binocular innervation in cortex layersV1 and 30% (N � 108) in V2. The black bars represent the missing binocularly innervated neuronsordinarily found in control monkeys. (From Crawford MLJ, Smith EL, Harwerth RS, Noorden GK von:Stereoblind monkeys have few binocular neurons. Invest Ophthalmol Vis Sci 25:779, 1984.)

from humans and neurophysiologic research incats and primates.30, 31

Whether binocular striate cells subserve func-tions other than stereopsis is not known. The re-sponse summation depending on stimulus align-ment observed in animal experiments suggests thatbinocular cells may also be involved in the fusionprocess. On the other hand, the clinician knowsthat sensory fusion may occur in the absence ofstereopsis. The cortical centers for sensory andmotor fusion are yet to be identified.

Older Theories of Binocular Vision

Older theories of binocular vision still espousedin the second half of this century are mostly ofhistorical interest now. However, familiarity withthese concepts is indispensable for understandingthe older literature.

ALTERNATION THEORY OF BINOCULAR VI-

SION. Sensory fusion has been defined as theperceptual unification of the images received incorresponding locations in the two retinas. Thisdefinition is supported by the experience of singlevision, which is quite compelling, but it is notnecessarily the correct description of the process.Since 1760, when Du Tour39 claimed that rivalryphenomena gave evidence that the binocular vi-sual field is composed of a mosaic of monocularlyperceived patches, this theory has had many ad-herents. Verhoeff,98 in his replacement theory ofbinocular vision, assumed that corresponding reti-nal units were represented separately in the brain

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34 Physiology of the Sensorimotor Cooperation of the Eyes

but that each one of every pair was representedin consciousness by the same single unit. Thisconscious unit would receive the stimulus fromonly one retinal unit at a time; the other wasexcluded. Asher6 attempted to show that in binoc-ular stimulation one pair of corresponding ele-ments always suppressed the other. Hochberg48

presented a similar view. Levelt,67 although in-clined toward the same view, did not share this all-or-none assumption. He believed that it is better tothink of different levels of dominance of the eyesfor each point of the visual field.

The ‘‘mosaicist’’ concept of the binocular vi-sual field is supported by all its adherents withessentially the same evidence, largely based onthe phenomena of rivalry. They fail, however, toexplain many phenomena of binocular vision, par-ticularly stereopsis. Also, as Linksz68, p. 846 argued,the motor responses to the relative displacementof similar and dissimilar targets in a haploscopecould not be as different as they are if alternatesuppression were the basis of single binocularvision. Experiments in cats and monkeys haveshown that when receptive fields from correspond-ing points of the retina are superimposed in theplane of an optimal stimulus, firing is markedlyfacilitated. When these fields are out of register,they mutually inhibit one another.74 Moreover,‘‘moderate summation’’ of responses from corticalneurons in macaques have been described follow-ing simultaneous stimulation of both eyes.8, 53

These findings do not support the alternation the-ory of binocular vision.

PROJECTION THEORY OF BINOCULAR VISION.

A theory that has now been largely abandoned isthe projection theory, which contends that visualstimuli are exteriorized along the lines of direc-tion. If a person fixates binocularly, a ‘‘bicentric’’projection is supposed to occur that places theimpression of each eye at the point of intersectionof the lines of projection.

This theory is untenable for many reasons. Itfails to explain even such fundamental observa-tions as physiologic diplopia, not to mention thediscrepancies between stimulus distribution andperception, and breaks down completely when in-terpretation of the sensory phenomena observedin strabismus is attempted (see Chapter 13). Thebasic reason for the inadequacy of the projectiontheory is that the distinction between physical andsubjective space is disregarded and it attempts toreduce localization to a dioptic-geometric scheme.

Alexander Duane,36–38 among American oph-thalmologists, has most clearly presented the pro-jection theory, but he modified it to meet someobvious objections. According to Duane, in bothmonocular and binocular vision the visual impres-sions are projected or referred to a definite posi-tion in physical space outside the body. There is,however, an essential difference between monocu-lar and binocular ‘‘projection.’’ In monocular vi-sion each eye ‘‘projects with reference to its ownaxis’’ and in binocular vision with reference tothe midline or ‘‘bivisual axis.’’ In other words,‘‘binocular projection’’ may be conceived as per-formed by a single cyclopean ‘‘binoculus.’’ Duanestates that the change from monocular to binocularvision is proved by the fact that in physiologicdiplopia the double images are not ‘‘projected’’ tothe plane of the fixation point but to the plane inwhich the object lies, which is seen double. Thus,Duane showed that physiologic diplopia cannot beexplained by the projection theory and acceptedthe concept of the cyclopean eye. Nevertheless,he considered the projection theory to be valid.

It would not be necessary to go into the projec-tion theory in such detail if it were not for thefact that it continues to crop up in the literature,at least in the terminology. For example, one stillencounters such statements as ‘‘the functional sco-toma in strabismus projected into space for thepurpose of solving diplopia.’’ The term projectionshould be altogether avoided in connection withvisual orientation.

The projection theory, as espoused by Duane,38

is also responsible for binocular vision being de-scribed in terms of ‘‘oculocentric localization’’from each eye and for anomalous correspondencestill being termed ‘‘anomalous projection’’ bysome modern authors. Alperr2 states that ‘‘Thestimulus for stereopsis is a disparity in the oculo-centric localization of a given object in the fieldof one eye with respect to its oculocentric localiza-tion in the field of the other eye.’’ This gives—atleast terminologically—an independence to eacheye that it does not possess. Even less acceptableis ‘‘disparity of egocentric localization of the cen-ter of the visual fields of the two eyes’’ as thestimulus to motor fusion. Neither eye has an ‘‘ego-center.’’ Only the subject has an egocenter towhich the egocentric localization of visual objectsis referred. The persistent confusion between rela-tive and absolute (egocentric) localization hascaused many misunderstandings in the ophthalmicliterature.

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Binocular Vision and Space Perception 35

THEORY OF ISOMORPHISM. Linksz68, pp. 380 ff. de-veloped a theory of binocular vision based on arigid retinocortical relationship. He believed thatfusion is based on neuroanatomical features,which bring excitations from the two retinas intoclose proximity within the visual cortex. Thosefrom corresponding elements are ‘‘consummated’’in Gennari’s stripe, which he considers to be theanatomical counterpart of the horopter plane inobjective space and of the nuclear plane in subjec-tive space. ‘‘Nuclear plane’’ denotes the counter-part in subjective space of the horopter surface inphysical space. The term is derived from the Ger-man Kernpunkt (nuclear point, the subjective cor-relate of the fixation point) and Kernflache (nu-clear plane, the subjective correlate of theobjective frontal plane). Objects nearer to or far-ther from the fixation point stimulate disparateretinal elements, and the resultant excitations con-verge in front of or behind Gennari’s stripe instrict conformity with the distribution of objectsin space. In this way the sensation of stereopsis iscreated. The point-to-point relationship betweenretina and cortex and strict conformity or isomor-phism between the distribution of objects in spaceand cortical events form the basis of spatial orien-tation. Subjective visual directions as a propertyof the retinal elements do not exist. Retinal corre-spondence cannot change. There can be no ‘‘as-similation of visual directions’’ in stereopsis.Anomalous correspondence in patients with stra-bismus (see Chapter 13) has been misinterpreted.

Linksz extensively elaborated his fascinatingintellectual theory. There is, however, no evidencefor the physiologic rigidity of the retinocorticalrelationship or the convergence of the pathwayson which it is based.

Advantages of BinocularVision

The current tendency is to overemphasize stereop-sis as the only important reason for having binocu-lar vision. For instance, Bishop11 stated that ‘‘withthe exception of stereopsis, seeing with both eyesis marginally, if any, better than seeing withone—absolute threshold, differential threshold,and visual acuity being about the same.’’ Indeed,binocular summation experiments show no mon-ocular-binocular differences or at best give onlyequivocal results.15 On the other hand, there arecertain advantages to having binocular vision in

addition to stereopsis that are not readily appreci-ated by the nonclinician.

Parents of strabismic children whose eyes havebeen aligned surgically will often volunteer theinformation that the child’s visuomotor skills havesuddenly and vastly improved. This improvementdoes not seem to depend on the presence of stere-opsis. It is noted as long as gross binocular visionon the basis of normal or abnormal retinal corre-spondence is reestablished. Jones and Lee56 sub-stantiated this clinical observation by evaluatinghuman binocular and monocular performancethrough a variety of exteroceptive and visuomotortasks. The results indicated that binocular concor-dant information provides better exteroception ofform and color and better appreciation of the dy-namic relationship of the body to the environment,thereby facilitating control of manipulation, reach-ing, and balance. Also, the advantages of an intactbinocular field of vision, which is larger than amonocular field, and of central visual field overlapbecome obvious as soon as the function of oneeye becomes impaired by a disease process.

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