Keithan Ducre¹ (), Juliet Horenziak¹, Peter Xu¹, Kalanit Grill-Spector¹; ¹Stanford University

The full moon appears larger at the horizon than when elevated. Known as the moon illusion, its magnitude and mechanisms are debated. In experiment 1 (perceptual matching, n=175), participants were given circular probes and indicated which one matched the moon’s size for a lower and elevated moon. On the horizon, observers perceptually magnify the visual angle of the moon by 4.1x and magnification decreases with elevation (power law, exponent=-0.33). In experiment 2 (adjusted matching), the same observers were allowed to hold the probes against the moon and adjust until they found a match. Surprisingly, the illusion was abolished but perceptual magnification wasn’t: observers perceptually magnify the moon by 1.96x on the horizon, and magnification increases with elevation (power law, exponent=0.07). To determine the underlying factors, we conducted perceptual and adjusted matching experiments (n=140) in the Stanford Quad with objects that varied in distance (15.2[m]–151.9[m]), visual angle (0.35[deg]–7.34[deg]), and elevation (0.64[deg]–13.7[deg]). Observers magnify all objects, more in perceptual (1.71x) than adjusted (1.07x) matching and are generally unaware of their magnification. Perceptual magnification is predicted by a power law: PerceptualMagnification=C∙VisualAngle^a∙Distance^b∙(1+Elevation)^c. It is larger for smaller (a=-0.08) and farther (b_perceptual=0.37; b_adjusted=0.14) objects, and the elevation exponent varies across conditions. Since observers close one eye during adjusted matching, we tested if binocular disparity varies with moon (n=58) and disk (n=20) elevation. We find that when visual angle and distance are fixed, disparity increases with elevation and predicts the moon illusion. These data suggest that perceptual magnification of the moon is particularly large because of its small visual angle (~0.5 [deg]) and large distance (~384,400 [km]) and that binocular vision contributes to the illusion. Together, we not only elucidate the moon illusion, which was enigmatic for over two millennia, but also discover a new phenomenon of perceptual magnification and its underlying mechanisms.

Acknowledgements: Funding: NIH grant R01EY023915; Stanford VPUE grants to Keithan Ducre and Juliet Horenziak.