Spatial and temporal analysis of contrast-modulated sine-wave gratings reveals that the second-order motion stimulus contains two sidebands, with equal energy but moving in opposite directions, flanking a stationary carrier. Any early linear spatial filtering process in the visual system that attenuates one sideband more than the other will be detrimental to the balance between the two sidebands, so that the perceived direction of the carrier might be opposite to that of the envelope motion. We tested this hypothesis by using contrast-modulated gratings presented centrally or at 20 deg in the horizontal nasal field with a two-alternative forced-choice staircase paradigm. We found that when the envelope frequency was close to that of the carrier, a second-order stimulus whose envelope motion direction was correctly identified in the fovea appeared to drift in the opposite direction in the periphery. Further increasing the envelope spatial frequency resulted in a reversed motion percept in both central and peripheral viewing conditions. For subjects to identify correctly the direction of motion of the envelope, the spatial frequency ratio of the carrier to the envelope had to be more than 2 in the fovea and more than 6 in the periphery. These phenomena in second-order motion perception can be explained by a linear model of motion detection with an early spatial filtering process. Further experiments and computer simulation show that undersampling of the carrier has little effect on second-order motion perception in the periphery, as long as the carrier is detectable.
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