Section III. Explaining the Moon Illusion, and
                    Evidence For The Visual Angle Illusion

The new theory first describes the basic relative visual angle illusion that characterizes the moon illusion suffered by at least 90% of the population. It then explains why changes in the moon's perceived visual angle correlate with changes in distance-cues, by proposing that the illusion is an example of oculomotor micropsia/macropsia.

Oculomotor micropsia described briefly.
Oculomotor micropsia is a visual angle illusion caused by changes in the activity of eye muscles. The muscles most involved in the illusion are the external ones that turn the eyes to aim both of them onto the same viewed point (the process called convergence for a point close to the face, and divergence for a very distant point). Also involved might be the muscle inside each eye which changes the shape of the lens in order to sharply focus the optical images on the retina (the process called accommodation). Since 1965, some researchers have claimed that the "size" illusion caused by changes in convergence and accommodation is primarily a visual angle illusion (McCready, 1965, 1983, 1985; Ono, 1970; Komoda & Ono, 1974). This visual angle illusion necessarily is accompanied, secondarily, either by a linear size illusion, or by a distance illusion, or else by both.

The illusion is described as follows:

While looking at a fixed object which subtends a constant visual angle, if one focuses and converges one's eyes to a distance closer than the object, the visual angle of that object looks smaller than it did, as micropsia. Four outcomes commonly have been found for the accompanying linear size and distance perceptions.
     1.  The object appears at about the same distance as before (an equidistance outcome) in which case its linear size necessarily looks smaller than it did (off-size).
     2.  The object's linear size continues to appear the same (linear size constancy) in which case the object necessarily looks farther away than it did (the relative perceived angular size cue to distance).
     3.  The object looks both linearly smaller and farther away than it did (an intermediate outcome).
     4.  The object appears closer than it did (in agreement with the oculomotor change) so its linear size necessarily looks very much smaller than it did (off-size).

Historically, the simple term micropsia ("looking small") has had two quite different meanings, and that has created much confusion. To avoid confusion, I use the term micropsia only for a visual angle illusion, and the term, off-size, for the linear size illusion.

All the outcomes listed above have been found among observers in experiments on oculomotor micropsia, but the 4th outcome has been found less often that the others (Komoda & Ono, 1974; Ono, Muter, & Mitson, 1974).

     Tech Note: Because of the oculomotor micropsia data (and much other evidence) vision scientists have known for a long time that neurological afferent "feedback" from contractions of the eye muscles involved in accommodation and convergence does not provide a strong cue to perceived distance. Instead, the 'distance-cue' that controls micropsia seems to be the neurological brain activity (the efferent "motor command") being sent to (or about to be sent to) the muscles in order to make the eyes move (whether or not those muscles contract). End of Tech Note.]

The converse of oculomotor micropsia is oculomotor macropsia. It can be witnessed when one shifts the focus and convergence of one's eyes from a nearby viewed object to a much greater distance. In that case, the viewed object's visual angle looks larger than it did, and the object looks either a larger linear size (off-size) or closer, or else both of those secondary illusions accompany the macropsia. (I'll use the term, oculomotor micropsia, as a general term both for micropsia and for macropsia, unless otherwise specified.)

Oculomotor micropsia is perhaps the largest visual angle illusion, and it occurs during everyday viewing whenever convergence and accommodation change, which, of course, is quite often. Amazingly, this omnipresent illusion is rarely mentioned in conventional discussions of "size" illusions.

Although oculomotor micropsia is a very dramatic illusion, it is limited: For instance, in micropsia the visual angle for an object rarely looks smaller than half its true value. And, in macropsia the object's visual angle rarely looks larger than twice its true value. Those limits are sufficiently broad, however, to encompass the small visual angle illusions that are the basic illusions in many of the best-known "size" illusions. Why oculomotor micropsia occurs is explained in Section IV. How it becomes the basis of the moon illusion is discussed below.

Eye Adjustments in the Moon Illusion.
When one is looking toward the horizon moon, the distance-cue patterns in the typical horizon vista usually make one's eyes adjust, as expected, for "very far" (optical infinity). Consequently, to illustrate oculomotor macropsia, the horizon moon's visual angle looks large. But how large? At this time no measures of the perceived visual angle for the horizon moon have been published. (As previously noted, it would be extremely difficult to measure perceived visual angles as small as one or two degrees.) The best guess is merely that for most observers the perceived visual angle for the horizon moon is greater than 0.52 degrees.

On the other hand, the zenith moon's visible context typically has few distance-cues that indicate great depth: And, as vision researchers found long ago, when there are few distance-cues the eyes tend to adjust to a resting focus position about 1 or 2 meters from the face. A closely related phenomenon is that in relatively dark surroundings, the eyes tend to adjust to a nearby dark focus position, also about 1 meter from the eyes. Indeed, many of us become slightly nearsighted in relative darkness, a phenomenon known as night myopia.

These eye adjustments to "near" typically occur while one is viewing the zenith moon, therefore they can induce micropsia, and the zenith moon looks angularly small. But how small? One guess is that its perceived visual angle is less than 0.52 degrees. [However, evidence from some other illusions indicates that the perceived visual angle may equal the visual angle when the eyes are adjusted to the resting focus position; therefore, the perceived visual angle for the zenith moon might equal 1/2 degree.]

It should be noted that, although the eyes' adjustments to a relatively near position during natural viewing of the zenith moon undoubtedly would create imperfect optical imagery, the viewer usually is unaware of these "faulty" adjustments because they are involuntary and not quite large enough to cause double-vision or obvious blurring.
Likewise, it has been shown that when people look to a very far distance the eyes often will focus beyond optical infinity, and the resulting blurring is not noticed.

Enright (1975, 1987a, 1987b, 1989a, 1989b) and Roscoe (1979, 1984, 1985, 1989) have published evidence for all of the above descriptions. They also measured the changes in eye adjustments while observers viewed artificial, surrogate 'moons' at different distances, and also measured the accompanying changes in the perceived visual angle for those 'moons' when they were optically placed in horizon and zenith settings. Those measured changes in the perceived visual angle that accompanied a given change in eye adjustments, turned out to be about the same magnitude as the relative changes commonly found in laboratory studies of oculomotor micropsia. Essentially the same results have been obtained for objects and images in other laboratory setups that imitated viewing of the moon

The experiments by Enright and by Roscoe have provided the most significant data on the moon illusion offered since the researches of Rock & Kaufman (1962a, Kaufman & Rock, 1962a) revealed the major role of distance-cues.

The oculomotor micropsia illusion thus can explain why changes in distance cues induce the moon illusion. However, while you were reading the new descriptions of the moon illusion presented so far, you undoubtedly noticed that the distance-cues which initiate the magnification of the horizon moon's perceived visual angle typically do not make the horizon moon look farther away than the zenith moon.
After all, the many details in the landscape or cityscape extending toward the horizon moon form the distance-cue patterns which indicate that terrestrial objects near the horizon are much farther away than nearby objects. Those distance-cues for great depth are the ones that make the eyes adjust for "very far," and that evokes the macropsia illusion. Those distance-cues certainly could also establish a greater perceived distance for the horizon moon than for the zenith moon, but they usually don't. Why they don't is examined next.

Seeming Contradictions and Cue Conflicts.
The horizon moon most often looks either about the same distance away as the zenith moon or closer. These results are not paradoxes because they do not require a revision of the new theory. Instead, they merely reveal that the viewing conditions include several different sets of distance-cues that compete with each other for determination of the relative perceived distance for the moon.
Reviewed below are the two determiners of perceived distance that most often conflict with the changes in the vista distance-cues, and with the changes in eye adjustments.

The Equidistance Tendency.
Suppose this pair of letters, O o, is a picture of two spheres. One easy perception is to see them as pictured spheres at the same distance from the eye. In that case, the sphere that looks angularly larger also looks linearly larger. Let's say they look like a pictured baseball and a pictured golf ball at the same distance from you. That percept can be attributed to an equidistance tendency (Gogel, 1965) or an equidistance assumption (McCready, 1965).
By analogy, for people who say that the horizon moon "looks larger and about the same distance away" as the zenith moon, the equidistance tendency has won the competition between the different determiners of the moon's apparent distance.
Factors that can establish equal perceived distances for the two moons include one's knowledge that the moon's distance from the earth remains essentially constant from dusk to daybreak.

The Relative Perceived Visual Angle Cue to Distance.
For most people, the larger perceived visual angle for the horizon moon than for the zenith moon makes the horizon moon look closer than the zenith moon. This relative perceived visual angle cue to distance is one of the strongest monocular cues, and here it overrules the equidistance tendency, overrules the patterns of distance-cues which are evoking the changes in eye adjustments, and overrules the eye adjustments themselves as distance-cues. This strong distance-cue logically depends upon the occurrence of linear size constancy.

Linear size constancy.
At base, linear size constancy refers to the tendency for an object to look the same linear size from one moment to the next when other things change. It certainly dominates everyday viewing of objects; especially those we know don't change their size arbitrarily.  That is, linear size constancy is an aspect of  identity constancy, our tendency to assume that an object remains the same object from one moment to the next (Piaget, 1954).

Linear size constancy also refers to a perception that two viewed objects look the same linear size (or nearly so). For example, let this pair of letters, O o, again be a picture of two spheres: Another easy perception is to see two pictured spheres which are the same linear size (say two baseballs): And in this case the one that looks angularly larger necessarily looks closer. That example illustrates the relative perceived visual angle distance-cue.

Relative perceived visual angle distance-cue.
As discussed earlier, the relative perceived visual angle distance-cue is the basic element in linear perspective and texture gradients, two powerful distance-cue patterns.
For instance, as illustrated again by the picture of a cropped cornfield, both of those cue patterns offer objects of similar shapes arranged in a series in which the objects appear to subtend decreasing visual angles: therefore, if those objects appear to be about the same linear size (linear size constancy) they necessarily appear to recede from the viewer as their perceived visual angles decrease.

As Gibson (1979) emphasized, this perception of increasing distance with decreasing perceived visual angles has become a more-or-less automatic response in most adults. It is a response to the overall pattern of changing visual angles (the ecological display), which pattern is a texture gradient and a linear perspective pattern. In other words, the resulting perception of increasing distance with decreasing perceived visual angles for similar-shaped objects does not necessarily require adults to first consciously perceive equal linear sizes for those objects.

Getting back to the moon illusion, consider that in the typical vista for the horizon moon, the linear perspective and texture gradient patterns formed by the terrain are the distance-cues primarily responsible for making the eyes adjust for "very far." Therefore, the fact that most people say the horizon moon "looks larger and closer" than the zenith moon clearly means that the larger perceived visual angle for the horizon moon is a distance-cue strong enough to prevail over the other potential determiners of its perceived distance.

Ubiquitous 'Moon Illusion.'
The term 'moon illusion' has become a generic term. The same illusion occurs for the sun and for the constellations when they are seen in a horizon position compared with a zenith position.
And, again, the 'moon illusion' occurs for objects other than just celestial bodies. So, many researchers have measured the 'moon illusion' in experiments conducted indoors, as well as outdoors, using spheres (including golf balls) or other kinds of target objects presented in fabricated displays which offer distance-cue patterns that are changed in order to imitate the changes typically found between horizon moon viewing and zenith moon viewing. The "size" and distance perceptions obtained with these surrogate moons have been essentially the same as those obtained for the real moon.

Evidence That The Moon Illusion Begins As A Visual Angle Illusion.

One obvious indication that the visual angle looks larger for the horizon moon than for the zenith moon is, again, that people initially expect a photo of the two moons would look something like the picture at the right.

Another indication is that some people initially believe the horizon moon is closer to the earth than is the zenith moon, which, if true, would make the visual angle larger for the horizon moon than for the zenith moon. Actually, during the same evening the visual angle for the horizon moon is about 2 percent smaller than that for the zenith moon, because the distance to the moon from one's observation point is greater for the horizon moon than for the zenith moon by almost the distance of the earth's radius.

Another indication is the very popular initial belief that some physical phenomenon (say atmospheric refraction) is optically magnifying the horizon moon (that is, increasing its visual angle). But, no such magnification occurs. Instead, refraction by the atmosphere temporarily reduces the visual angle of the vertical diameter of the just rising full horizon moon, which makes it look a bit "squashed down," like an oval. The setting sun likewise appears that oval shape.

Retinal Image Size Constant.
When people first realize the moon's visual angle remains constant, some may think the cause of the illusion lies in the optical system of the eye. After all, the illusion certainly is as if the horizon moon's retinal image were larger than the zenith moon's. So, some people initially suppose that there probably are changes in the lens or in the size of the pupil opening which make the retinal image larger for the horizon moon than for the zenith moon. However, experts on the eye's optics agree that, when the moon's retinal image is sharply focused, it is an illuminated disk about 0.15 mm in diameter, and, although changes typically do occur in the lens and in the pupil size during normal viewing of the rising moon, such changes either would not change the retinal image's size or would change it so little that such a change certainly could not be responsible for an illusion ratio as large as 1.5, or even 1.1. Besides, older adults with presbyopia (whose lens cannot change) experience the moon illusion in full.

A related analogy, of course, is that the illusions of oculomotor micropsia occur in full while the lens and the iris muscles are temporarily paralyzed (by eye drops) and in that condition the retinal image cannot change size (Heinemann, Tulving & Nachmias, 1959). Therefore, it seems certain that the moon illusion also would occur in full under that paralysis condition which deliberately keeps the retinal image size constant.

Additional evidence that the moon illusion begins as a relative visual angle illusion for most people derives from the methods used to measure it.

Perceived Visual Angle for the Moon.
As discussed in Section I, if one pointed one's nose from one edge of the moon to the opposite edge, the angle of the head rotation would be an appropriate measure of the perceived visual angle, V' deg: But it would be too small to measure reliably. Even smaller would be the angle of an eye rotation when one looked from edge to edge.
So, no measures of the absolute perceived visual angle have been published for the moon.

Instead, researchers have measured only how the perceived visual angles compare for the horizon moon and the zenith moon. A popular method for making those relative measures is discussed next.

Surrogate Moon Method.
Nearly all measures of the moon illusion have been made using comparison methods that resemble the following example. These methods provide further evidence that the moon illusion is basically a visual angle illusion.

An observer views the full moon, just risen above the horizon, and also looks upward into the zenith sky at an optical image of an illuminated disk (a virtual image) seen there by means of a special optical apparatus. (See Kaufman & Rock, 1962a, 1962b.) That disk image serves as a surrogate zenith moon, and when it subtends 0.52 degrees, it typically looks smaller than the horizon moon: So, the disk's visual angle is increased until the observer says it looks the same as the horizon moon's. In general, among a large group of observers many different disk sizes would be chosen, and if the average of those choices happened to be a disk subtending 0.78 degree, it would illustrate a moon illusion with an average magnitude of 1.5.

Without doubt, when comparison methods like that are used, the "size" the observers are matching is the perceived visual angle. Recent measures obtained using a similar technique have been published by Reed & Krupinski (1992).

That concludes the presentation of the new theory except for an explanation of oculomotor micropsia. So, let's summarize what has been discussed so far.

Summary of the New Theory.
The 'moon illusion' in all its forms clearly illustrates the following:

When a pattern of distance-cues indicates a much greater distance for a viewed object than for nearby objects, one's eyes adjust to a far position when one views that far object, and, in turn, that makes its visual angle look slightly larger than its true value, to illustrate oculomotor macropsia. That describes the condition typically found during viewing of the horizon moon. It also is the condition found for all the other objects on or near the horizon seen over an extended terrain pattern that offers abundant distance-cues to great depths

On the other hand, a relative absence of distance-cue patterns which would indicate great distances (depth) between the nearest and farthest viewed objects typically makes the eyes adjust to a relatively near, resting focus position; so a viewed object's visual angle looks slightly smaller than its actual value, to illustrate oculomotor micropsia. That situation exists for a relatively "empty" field of view and also in dim light. It typically occurs during viewing of the zenith moon.

Of course, the 'moon illusion' in all its forms clearly illustrates that the truly ubiquitous illusion is oculomotor micropsia. So, to claim that the moon illusion is merely an example of the less famous illusion of oculomotor micropsia only partly explains it. In order to complete the theory it is necessary to explain (in Section IV) why oculomotor micropsia occurs.

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