Abstract

A periodic moving stimulus can appear to move in the reverse direction if it is under-sampled in time, as in the case of the "wagon wheel" effect caused by an inadequate frame rate in motion pictures. Sampling by a spatial array of sensors or pixels can produce a similar motion reversal for periodic patterns moving at any velocity, if the spatial sampling frequency is too low. These artifacts are well-known to engineers who design discrete imaging systems. The artifact resulting from spatial under-sampling has been demonstrated in biological imaging systems (Goetz, 1965, Coletta and Williams, 1987). For example, insects tethered at the center of a rotating drum containing low spatial frequency vertical stripes exhibit an optomotor response: they rotate in the same direction as the stripes. However, these insects reverse their direction of motion when confronted with spatial frequencies that exceed the Nyquist frequency of their ommatidial array. This is just what one would expect from spatial aliasing by the regular array of insect ommatidia. Nancy Coletta and I have demonstrated a similar effect in the human with drifting interference fringes whose contrast is immune to optical degradation. In the parafoveal retina, high spatial frequency (but not low) gratings look like two-dimensional spatial noise and can appear to move in the opposite direction from their true direction of motion. This motion reversal can be demonstrated with a forced-choice technique. Subjects guessed the direction of motion of vertical, unity contrast fringes whose direction was randomly determined on each trial. No feedback was provided. Percent correct falls significantly below chance performance at high spatial frequencies, indicating a reversal in the perceived direction of motion. At higher frequencies, the perceived direction of motion reverses a second time, and at even higher frequencies performance settles to chance.

© 1989 Optical Society of America