Moon illusion appears when the rising or setting moon appears larger than when it's high in the sky. The moon illusion has been noted for hundreds of years. Is it caused by a magnifying effect from the Earth's atmosphere or is the moon actually closer when it's rising or setting?

Turns out it's neither. Photographs taken of a rising moon and a moon high overhead on the same evening reveal identical size moon images.

Still, the rising moon appears much larger than the overhead moon. What's up?

It’s all about perspective, foreground objects and our brains trying to make sense of it all, according to a study by Dr. Lloyd Kaufman and his son, Dr. James H. Kaufman. Loyd Kaufman is professor emeritus at New York University, where for many years he was professor of psychology and neural science.

The Kaufman study confirms that the moon illusion is occurring not in the sky, but in our brains. The illusion happens when our brains attempt to compute the distances to the moon based on visual information. When the moon is rising or setting and near the horizon, foreground scenes (trees, buildings etc.) are included in our field of view. These known objects seen near the moon give the moon some relationship to terrestrial scenes, and the moon appears up to twice its normal size. Hours later when the moon is higher in the sky, our view of it is removed from these earthly scenes and the moon appears to have shrunk.

In 1960 as a young graduate student, the elder Kaufman and his mentor, Irvin Rock, first presented experimental results supporting the apparent-distance theory to explain the moon illusion. This theory says that the brain “computes” perceived distances to objects. When the moon is just above the horizon, the information presented by the intervening terrain affects the “computation” by indicating that the moon is at a vast distance.

By contrast, a view of the elevated moon contains weaker cues to distance, so the brain responds as if the moon were closer. Since information regarding an object’s apparent distance determines its perceived size, the more distant horizon moon is perceived as being up to twice as large as the elevated moon. This is similar to the classic Ponzo perspective illusion dating from 1913 in which two same-length lines are drawn between or across a pair of converging lines resembling railroad tracks going off into the distance. The upper line appears much larger because it spans a greater apparent distance between the rails, which our mind assumes are parallel.
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The Kaufmans then designed two experiments to measure directly the perceived distance to the moon. Both tests used an apparatus built at IBM Research to project stereoscopic images of artificial moons from an IBM ThinkPad computer display to optical infinity so viewers could see them against an actual sky. Professor Kaufman then took people to a Long Island hilltop, where he made hundreds of measurements of their perceptions of the distance to the moon.

Each person was first asked to position an artificial moon so it appeared to be halfway between themselves and a fixed moon that was either near the horizon or elevated. In every case, the viewers placed the halfway point to the horizon moon as being much farther away—on average four times more distant—than the halfway point to the elevated moon. This is entirely consistent with the apparent-distance theory.

In their second test, the viewer used the ThinkPad to adjust the apparent distance to a moon projected either on the horizon or elevated sky. In all cases, as the subjects moved the projected moon closer, they reported that it appeared to become smaller, not larger—a direct contradiction of the apparent-size theory. An animated simulation of this surprising but convincing second experiment can be viewed on the Web.

Before the tests, each of Kaufman’s subjects said they thought that the apparently larger moon would appear closer. But the opposite occurred. “A key element of a true illusion is that our conscious deductions and preconceptions do not necessarily reflect how our brains actually respond to the outside world,” Professor Kaufman said.

“Humans can accurately perceive an object’s size regardless of its distance,” Professor Kaufman says. “This effect—known as size constancy—is why we can discern the real size of a distant automobile, tree or building despite its small image size. Our brain automatically takes the apparent distance into account and compensates for the geometrical reality that the image we see of a distant object is smaller than the image of that same object nearby.”

In most cases, the terrain provides a rich set of cues that enable us to accurately perceive the sizes of objects at different distances, Professor Kaufman added. But apparently such large distances as those to the moon are beyond our brain’s capability. As an example, Professor Kaufman recommends viewing the moon through an aperture, such as pinching it between your thumb and forefinger or viewing it through a tube, which hides the the terrain leading up to the moon.

The moon suddenly appears to be small because our brain locates it at the nearby distance of the edges of the aperture. Removing the aperture restores the terrain’s distance cues and the moon springs back to its large, illusory size.

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