Section IV.  Explaining Oculomotor Micropsia

Describing Oculomotor Micropsia Again
While one is looking at an object that subtends a constant visual angle, V deg, if one then accommodates and converges one's eyes to a distance much closer than the object's distance, the object's perceived visual angle, V' , decreases. As described earlier, this micropsia typically is accompanied by one of three outcomes: In a same distance and off-size outcome, the object's perceived linear size, S' decreases in proportion to the decrease in V': In a same linear size and increased distance outcome, the perceived distance D' increases in inverse proportion to the decrease in V'. In an intermediate outcome, D' increases and S' decreases, as V' decreases.
In a less common, decreased distance, off-size outcome, the object looks closer than it did (in at least partial agreement with change in accommodation and convergence) so S' looks considerably smaller than it did (very much off-size).

All those outcomes have been found in micropsia experiments (Komoda & Ono, 1974; Ono, Muter, and Mitson, 1974).

A macropsia illusion ("looks angularly larger") is obtained by shifting accommodation and convergence to a distance beyond the viewed object.

Explanations for the illusion can be divided into the "old" and the "new," as follows.

Old Explanations
Some researchers long ago recognized that oculomotor micropsia is as if the viewed object's retinal image size, R mm, had decreased, so they sought reasons why that physical change might actually happen, even though optical calculations predicted that a change in accommodation or pupil size would not change R for a constant visual angle V deg. But, Heinemann, Tulving, & Nachmias (1959) showed that the illusion occurs in full with accommodation and the pupil paralyzed by atropine drops.
And, Smith, Meehan & Day, (1992) recently confirmed that, as predicted, R remains constant for a constant visual angle, V, when accommodation changes.
So there is no optical basis for that visual angle illusion.

Apparent Distance Theory Unsatisfactory
In 1960 the apparent distance theory was the most popular explanation.
It proposed that accommodation and convergence to a closer distance act as distance-cues that make the object look closer than it did, so it must look a smaller linear size (off-size) in order to keep the visual angle the same. But very few people say the object "looks smaller and closer. " This unresolved "size-distance paradox" led most researchers to reject the apparent-distance theory.

Three New Theories
Since 1965, three "new" theories have been proposed.
The first (McCready, 1965; Ono, 1970) was based upon an analysis in terms of subjective experiences: The second, (McCready, 1983, 1985, 1994) is based upon an analysis in terms of the orienting reflex. It is the theory emphasized here. The third theory (Enright, 1989) is based upon an analysis in terms of a quite different reflex called the vestibular oculomotor reflex.

Observation 1.
The visual angle illusion of oculomotor micropsia is controlled by activity somewhere in the eye muscle systems responsible for routinely focusing and converging the eyes to the changing distances of objects.

Observation 2.
Abundant data from laboratory studies of oculomotor micropsia clearly indicate that the change in the perceived visual angle for an object away from the visual angle for it also occurs during normal everyday viewing whenever the eye adjustments change. The crucial question thus becomes, why would one's perception of directions, a vitally important visual function, become routinely distorted in this manner?

Observation 3.
All three theories propose that the continual adjustments and readjustments of visual angle perception during everyday viewing must be serving a useful purpose: They must be part of some kind of normal perceptual-motor adaptation. More specifically, it is proposed that these alterations of visually perceived directions serve the purpose of preventing or "correcting" errors in bodily responses that are guided by the directions in which objects appear.

Observation 4.
All three theories propose that the most likely reason why errors of that kind would occur is related to the fact that the eyes lie about 10 cm (four inches) in front of the center of the head. The three theories differ only in the choice of the visually guided response that would be affected by that displacement of 10 cm. In other words, each theory offers a different answer to the question, what bodily response, when guided by visually perceived directions, would become more accurate as a result of the direction illusions of oculomotor micropsia?
Consider how the first two theories answer that question.

First Theory: a Subjective Analysis.
The initial theory (McCready, 1965) was based upon an analysis of how one's visual perceptions of the angular size, distance and linear size for an object would relate to one's tangible (touch) perceptions (haptic perceptions) of the angular size, distance and linear size for the object when one looks at it while holding it. Without going into detail here, the analysis began with an assumption that the vertex of the perceived visual angle is the visual egocenter (or center of visual directions) a subjective locus which, according to some investigators, lies at about the center of one's body image of one's head, thus, in effect, about 10 cm behind the eyes.

Working from that assumption, it was shown that, if the perceived visual angle equaled the visual angle for an object being held as it approaches the eyes, the linear size and distance the object looked would begin to progressively disagree with how its linear size and distance felt. Then it was shown that this disagreement could be avoided if the perceived visual angle for the object (let's say one's own hand) equaled not the visual angle, but equaled, instead, the smaller angle the object subtended at about the center of the head. Accordingly, if that particular "correction" of visual angle perception occurred, and if it were appropriately linked to the distance to which the eyes are accommodated and converged, that would explain oculomotor micropsia.

A significant result of that analysis was a simple equation (see later) that specifies the amount by which the perceived visual angle should become less than the visual angle in order to bring about the appropriate correction for each viewing distance for an object. The equation furnishes numerical predictions that were shown to match, almost perfectly, the data of oculomotor micropsia published up until 1963. No other theory had come close to explaining the data that well.

Indeed, in 1970, Melvin Komoda and Hiroshi Ono ran experiments to test that theory and its equation. (Komoda & Ono, 1974; Ono, Muter, & Mitson, 1974). They concluded that it was the only available theory of oculomotor micropsia that could account for their numerical results and, as well, the published results of other investigators.

Second Theory: the Orienting Reflex Analysis.
Later, the theory was improved (McCready, 1983, 1985) by using a more behavioral analysis that restates the "correction" in terms of the head rotation component of the orienting reflex. Simply put, the theory proposes that the alterations of visual angle perception that show up as oculomotor micropsia improve the speed and accuracy with which one can turn one's head toward a nearby object that demands attention. This theory furnishes the same equation provided by the first theory.

The privately published article, "Toward the Distance Cue Theory of Visual Angle Illusions" (McCready, 1994a) elaborated the theory and showed how well the simple equation also fits micropsia data published after 1963. The following review begins by describing the orienting reflex.

Orienting reflex.
If an object suddenly captures or demands one's attention, one's head and eyes usually turn quickly, and more or less automatically, in the direction of that object. These involuntary movements are part of the well-known orienting reflex.

For instance, when one is looking at a given object, and a "new" object suddenly appears at a different place in the field of view, one's head usually will turn toward the "new" object: A successful rotation of the head aims the face directly toward the attention-grabbing object. This outcome thus places both ears and both eyes squarely into their "straight ahead" position, a position that can improve one's ability to assess, binocularly and binaurally, any threat the "new" object might introduce. The angle the head will rotate through is gauged by the difference one sees between the old object's direction and the direction of the new object. In other words, the visual perception that predicts the angle of the initial head rotation from one seen object to the other is the perceived angular separation between them.

If the head's initial ballistic turn toward the "new" object misses the mark, a corrective rotation occurs, but only after a brief delay. In order to enhance one's safety, it thus would seem quite important to correctly see the angular separation (the visual angle) between the objects, so that the perceived visual angle can predict and gauge an accurate initial turn of the head. Therefore, a visual angle illusion, such as oculomotor micropsia, would seem to be maladaptive. However, as explained below, it isn't that simple: The illusions of oculomotor micropsia actually can be quite adaptive for objects near the face. To illustrate that idea, let's consider how head rotation angles relate to visual angles.

Horizontal (side to side) rotations of the head take place around a vertical axis, here called the Y-axis. It is located behind the eyes by a distance that averages about 10 cm in adults. That displacement of 10 cm would be expected to create some errors in visually initiated orientations of the head, as illustrated by the following example.

An Example.
Suppose, first of all, that two viewed objects are at a very great distance and separated, left to right, by a visual angle of 18 degrees. Because they are very far away, the angle they subtend at the head's Y-axis also essentially equals 18 degrees. So, the angle of an accurate rotation of the head, to aim the face from one object to the other, would equal the visual angle. Thus, it would be most appropriate to have the perceived visual angle equal the visual angle, which for this example is 18 degrees.

For two nearby viewed objects, however, it is quite a different story.

For instance, to pick an extreme example, suppose two objects are only 10 cm (4 inches) from the eye, and separated, left to right, by a visual angle of 18 degrees: They thus are about 20 cm from the head's Y-axis, so the angle they subtend there is only 9 degrees. Accordingly, the angle of an appropriate head orienting response aimed from one to the other would be half the value of the visual angle. In this example, if the initial turn of the head from one object to the other equaled the visual angle of 18 degrees, the head would dramatically overshoot its mark. Therefore, that initial turn would be more accurate if the angular separation of the two nearby objects looked half of the visual angle they subtend. Of course, having the perceived visual angle equal to half of the visual angle is a very dramatic illusion, but in this case it would serve a useful purpose for objects sitting 10 cm from the eyes.

The correction also would improve non-emergency, "voluntary" rotations of the head intended merely to aim one's eyes and ears and critical attention from one viewed object to another.

What the theory proposes, of course, is that this useful modification of visual direction perception occurs as a normal perceptual adaptation during everyday viewing. And, in order to be appropriate, the magnitude of the corrective change in the perceived visual angle away from the visual angle value must somehow be linked to the distance of the objects from the eyes. As discussed next, that necessary connection undoubtedly is mediated by eye muscle factors.

Micropsia Controlled By Eye Muscle Factors..
The corrective changes in perceived visual angles are linked to the viewing distance primarily by means of the activity in the neurological system that controls the muscles responsible for changing accommodation and convergence. That is, the distance to which the eyes have just been adjusted, or are about to be adjusted, determines the magnitude of the correction of a perceived visual angle value.

Efference Readiness.
Without going into detail here, it turns out that the key factor is not an overt adjustment of the eyes, but the covert brain activity that is the precursor to such muscle activity. Such physiological activity aimed at moving the eye(s) has been called "motor efference readiness." Loosely speaking, one's mere "intention" to move one's eye alters one's perception of the direction of a viewed object. This concept has a long history in visual science [See the review and experiments by Festinger, Burnham, Ono, & Bamber (1967)].

For micropsia, the present proposal is that the intention (readiness) to converge and focus the eyes to some given distance is what "signals" or "controls" the change in the perceived visual angle appropriate for objects at that distance, whether or not that efference readiness leads to actual motor efference activity that changes the eyes' adjustments, see Enright (1989).
Foley (1980) refers to this particular factor as the egocentric distance signal

An Equation for Oculomotor Micropsia.
The orienting reflex theory leads to the following general equation, which specifies by how much the perceived visual angle, V', should change away from the target extent's visual angle, V, in order to yield the appropriate 'correction' for a given target distance.

V' /V = Dc / (Dc + T )

Dc is the convergence distance. It theoretically would equal the distance being signaled by the efference readiness for the viewed target, which currently can't be measured.
So, Dc nominally can be, instead, the distance to which the eyes are accommodated and converged. And, lacking that measure, one has to let Dc equal the target extent's distance, D, from the eye pupil, and assume that the eyes were appropriately adjusted (which can be a mistake).

T is the turn correction factor . It nominally equals the distance from the center of the eye pupil back to the Y-axis for rotations of the head, about 10 cm in adults. However, for body rotations, bending over, and other such large orienting movements, T could be much greater than 10 cm.

Again, predictions made by that equation fit the early published data on micropsia almost perfectly (McCready, 1965) and also fit the data published after 1963 quite well (McCready, 1994a). As may be expected, however, the results for a few observers in some viewing conditions in some studies are not fit well by the equation. But, as yet, no other theory can explain the micropsia data that well.

Moreover, the equation perfectly fits published data for some other visual angle illusions that previous theories could not fully explain, but which now can be explained as examples of oculomotor micropsia (McCready, 1994b) especially the classic illusion of curvature of the apparent fronto-parallel plane (McCready, 1995).

[How well the equation, and the concept of efference readiness fit many classic flat-pattern illusions and the data of Murray, et al. is shown in Appendix B.]

Micropsia for objects.
The proposed correction alters, of course, the perceived visual angle (V' ) for a viewed object's frontal width (or height or diameter). As a rule, the closer a viewed object is to the face, the more V'   becomes less than V deg, if the eyes properly focus and converge upon the object as it moves closer.

What may seem confusing here is the fact that, as an object of fixed linear size approaches the eye, the V for it increases, so V' also increases. The effect of the micropsia correction is merely that the increase in V' does not quite keep up with the increase in V deg. Again, even for an object very close to the eyes, V' rarely becomes less than half of V deg.
It is important to point out that the correction never keeps the perceived visual angle "constant" when V deg (hence the retinal image size, R mm) changes, as is unwittingly suggested by the popular (and illogical) definitions of "size constancy."

As discussed next, some obvious revisions of the theory are needed in order to describe macropsia illusions.

As it stands, the orienting reflex theory describes only micropsia: It does not describe macropsia, with V' deg greater than V deg. Yet, as indicated earlier, macropsia seems to be a common outcome for objects at great distances in complex landscapes or other scenes rich in distance-cues that indicate great depth between the nearest and farthest objects (see Higashiyama, 1992; Higashiyama & Shimono, 1994).

Indeed, macropsia for distant objects was revealed by the moon illusion researches of Roscoe and his colleagues (Roscoe, 1985, 1989) and also by Enright (1975, 1989a). A significant finding has been that the perceived visual angle usually equals the visual angle not when the eyes are adjusted to a great distance, but when they are adjusted, instead, to their resting focus (dark focus) position, let's say at a distance of about 1 meter.

For instance, recall that inverted viewing of objects seen near the horizon, including the moon, causes their visual angles to appear to shrink: That viewing condition reduces the efficacy of distance-cues to a great depth, so, like the viewing condition for the zenith moon, it apparently makes the eyes adjust to a resting focus position. What the data indicate is that, for this resting focus condition, the "smaller" perceived visual angles for objects actually may equal their visual angles. If so, then "true" micropsia (the perceived visual angle less than the visual angle) would occur when the eyes are adjusted to a distance closer than, say, 1 meter.

Micropsia versus Macropsia.
It therefore seems that, during everyday viewing when the eyes accommodate and converge upon objects at various distances, there is a general macropsia illusion when one views objects farther away than a meter, and a general micropsia illusion when one views objects less than a meter away.
In terms of the proposed orienting reflex "correction," it thus seems that V ' deg is kept "correct" for objects just beyond reach, while micropsia corrects for closer objects that might pose a threat, and the macropsia found for distant objects, although it is an illusion, does not create a safety problem because distant objects don't pose a threat as immediate as those within one meter of the face.

One line of speculation, however, has been that the macropsia illusion for objects seen near a distant horizon might be adaptive if it were equivalent to having a "built-in" telescope that slightly magnifies distant terrestrial objects (Higashiyama, 1992). Indeed, there is evidence that visual acuity is slightly better for distant targets than for near ones, and also slightly better for a target when it is undergoing oculomotor macropsia (McCready, 1963). Those two phenomena might be related to each other, but that is not certain.

The simple equation obviously must be rewritten in order to describe both micropsia and macropsia. In its present form it does not predict a visual angle illusion as large as the moon illusion. However, that problem with the simple equation does not mean that the moon illusion is not an example of oculomotor micropsia/macropsia.

Half-Angle of the Sky Illusion.
Macropsia for distant horizon objects also seems to be revealed by the illusion known as the half-angle of the sky. For instance, while observers are viewing an "empty" sky and asked to indicate the point which looks halfway between the horizon and the zenith pole (at 90 deg elevation) they typically indicate a place only about 30 deg above the horizon. In other words, the direction difference (visual angle) from the horizon up to 30 degrees appears to be about 45 degrees, for a macropsia illusion of magnitude about 1.5. An explanation for that absolute visual angle illusion could go a long way toward explaining why the horizon moon's small visual angle would look 1.5 times larger than 0.52 deg. The present 'new' theory for oculomotor micropsia can explain a macropsia magnitude as large as 1.5 for a small visual angle, but it cannot easily account for an absolute visual angle illusion as large as 1.5 for a target subtending 30 degrees.

This brief review now must mention some other puzzling "size" and distance illusions that also can be explained as examples of oculomotor micropsia.

Oculomotor Micropsia for Flat Patterns.
During everyday viewing, the shifts of accommodation and convergence among viewed objects invariably are a response to the distance-cues in the viewing situation that specify the distances of the objects from the eyes. The role of changes in distance-cues in the moon illusion, in all its forms, was discussed earlier.

An additional fact is that distance-cue patterns in flat pictures also can evoke slight changes in accommodation and convergence, which, of course, create micropsia.

To understand how flat patterns induce oculomotor micropsia, consider what happens when one views pictures like the one below (discussed earlier). The texture gradient and linear perspective distance-cues create the pictorial illusion of a winter cornfield extending toward a very distant horizon.

Visual Angle Illusion
Consider first just the middle and lower circles. As previously noted, observers can say both circles correctly appear on the same page, so they have the same perceived distance, and the middle circle looks slightly larger than the lower circle, let's say 10% larger, to reveal the underlying visual angle illusion that has been of greatest interest.

Again, the apparent distance theory cannot explain that small visual angle illusion for the two equal circles on the page.
How the angular size contrast theory may explain it was discussed in the earlier analysis of the 'paradoxical' Ponzo illusion.
How the oculomotor micropsia/macropsia theory can explain it is discussed below.

Perspective Vergence
Many researchers have clearly shown that this kind of "size" illusion in flat pictures is controlled by changes in the monocular distance-cue patterns: Indeed, the more effective the distance-cue patterns are in creating a great pictorial depth illusion, the greater is the "size" illusion (Kilbride & Leibowitz, 1972; Rock, Shallo, & Schwartz, 1978).

Moreover, researchers found, long ago, that when one views the image of a 'far' object in a flat picture, the eyes tend to converge and focus to a farther distance than they do when one views the image on the page of a 'nearby' object. This common effect is called perspective vergence (for recent reviews see Enright, 1987a, 1987b, 1989).

Of course, for a flat picture held perpendicular to the line of sight, the viewing distance is essentially the same for all the images, therefore those changes in eye adjustments caused by changes in distance-cues are optically inappropriate: However, they usually are small enough to prevent double vision and noticeable blurring. Nevertheless, they are large enough to induce a slight degree of oculomotor micropsia: Therefore, in response to the change in distance-cues in the flat pattern above, when the lower "near" circle and "far" middle circle are viewed successively, the eye adjustments change, and the perceived visual angle becomes slightly larger for the middle one than for the lower one. (Why it also occurs for simultaneous viewing is presently discussed.)

'Moon Illusion' In Pictures
Enright (1987a, 1987b, 1989) measured the small visual angle illusion obtained using pictures similar to the picture above (without the lowest circle). The "horizon" circle typically looks slightly larger than the equal "zenith circle" because the eyes adjust for a farther distance for the horizon one than for the zenith one.
That result thus imitates the moon illusion in a small way. (Also, the crude picture used here may not yield as large an illusion as those used in research studies.)
Similar measures of that "moon illusion in pictures" were made by Coren & Ax (1990) but they did not distinguish between the linear size illusion (which they measured) and the underlying visual angle illusion.

In general, the oculomotor micropsia explanation outlined above applies to all the flat pattern illusions to which researchers previously have applied the apparent-distance theory without success. Well-known examples discussed earlier are the Ponzo illusion and Ebbinghaus Illusion (McCready, 1983, 1985). It seems clear that the very famous Mueller-Lyer illusion also can be explained that way.

In short, many of the classic flat-pattern illusions that have defied explanation now can be explained as visual angle illusions that illustrate oculomotor micropsia induced by changes in monocular distance-cues in the flat pattern.

These illusions for flat patterns are more complicated than that, however, because the relative visual angle illusion also may exist even when the eyes are fixed upon one place in the pattern and not shifting their focus or convergence. In order to explain how changes in distance-cues induce these simultaneous relative visual angle illusions, the theory of oculomotor micropsia must be taken a step beyond what has been described so far, as follows.

Conditioned Micropsia.
Changes in distance-cue patterns evidently have acquired the power to induce a visual angle illusion more or less directly, without first causing a change in the eye muscle adjustments as an intermediate event. It is as if the changes in distance-cues anticipate the adaptive corrections of oculomotor micropsia.
After all, oculomotor micropsia constantly occurs during everyday viewing, and the changes in oculomotor adjustments that induce these changes in perceived visual angles away from the visual angle values typically are caused by changes in distance-cues. So, it seems reasonable to suggest that, due to this constant association, those changes in perceived visual angles have become conditioned to the distance-cue changes. Consequently, when similar changes in distance-cues occur, even in flat patterns, they can evoke illusory changes in perceived visual angles directly (McCready, 1985, 1986, 1994a).

As discussed in Appendix B, the present idea is that cues to distance establish the efference readiness, expressed by Dc in the equation, which controls the micropsia (McCready, 1994a). This proposal is discussed more fully in Appendix B.

For that reason it also is possible for the moon illusion to occur as a direct response to distance-cue patterns without necessarily involving overt eye muscle changes.

Before closing, it is necessary to mention the third "new" theory of oculomotor micropsia.

Theory 3: Enright's VOR Theory.
Enright (1989) also considers oculomotor micropsia to be a normal perceptual adaptation that "corrects" for problems that would arise because head rotation centers lie about 10 cm posterior to the eyes. But he has proposed a different explanation for it. His theory appeals not to the orienting reflex, but to a quite different 'normal' physiological reflex known as the vestibular oculomotor reflex, or VOR.
My review of that VOR theory (in McCready, 1994a) indicates that it might provide an equation identical to the one provided by the orienting reflex analysis. However, I'm not certain about that, because it is not yet clear how the VOR reflex would apply to perceived visual angles. The needed clarification undoubtedly will be offered by Enright.

Oculomotor micropsia is a ubiquitous illusion.
It provides an explanation for the moon illusion in all its forms.
It also can explain many other "size" and distance illusions to which researchers have applied the apparent-distance theory, without success. In short, the new theory wholly replaces the apparent-distance theory of illusions.

How oculomotor micropsia can explain many of the best known flat pattern "size" illusions is shown in Appendix B.

The new theory is supplemented by the "size"-contrast theory that obviously is an angular size-contrast theory. However, for the moon illusion, this angular size-contrast seems to add very little to the overall illusion.

A promising explanation for oculomotor micropsia is the present theory based upon the orienting reflex. As shown elsewhere (McCready, 1965, 1994a, 1995) it offers numerical predictions that match published measurements of micropsia amazingly well.

The key to understanding the new theory is to understand the distinction between visual angle perception and linear size perception, and to accept the idea that both "sizes" are perceived at the same time. That idea is unconventional, so it is reviewed in more detail in Appendix A.

Index Page.
Introduction and Summary.
Section I. New Description of the Moon Illusion
Section II. Conventional Versus New Descriptions
Section III. Explaining the Moon Illusion
Section IV. Explaining Oculomotor Micropsia
Bibliography and McCready VITA
Appendix A. The (New) Theory)
Appendix B. Analysis of the Murray, Boyaci & Kersten (2006) Experiment