Abstract
Vertical vergence eye movements (Vg) were elicited in 3 human subjects by applying vertical disparities to horizontal square-wave gratings lacking the fundamental (“Missing Fundamental” stimulus, MF). Viewing was dichoptic by Wheatstone stereoscope and eye movements were recorded with the search coil. Stimuli were large (46 deg wide × 30 deg high; spatial frequency: 0.04–1 c/deg) and presented only briefly (200ms). To avoid spatial aliasing, stimuli were synthesized by summing the odd harmonics only up to the Nyquist Frequency (16 c/deg for our display). Disparities were ¼ of the fundamental wavelength so that the overall pattern and its luminance features (peaks, troughs), together with the 4n+1 harmonics (n=integer), had left-hyper (or right-hyper) disparity, whereas the 4n-1 harmonics, including the strongest Fourier component (3rd harmonic), had the reverse disparity. The earliest Vg had short latency (70–80ms) and were always in the direction of the 3rd harmonic, but their magnitude fell short of those that were elicited when the same disparities were applied to pure sinusoids whose spatial frequency and contrast (32%) matched those of the 3rd harmonic. This shortfall (on average, about 20%) was approximately halved when the MF stimulus lacked the 5th harmonic (“MF-5” stimulus)—indicating a contribution from the next most powerful harmonic—and was completely eliminated when the contrast of the MF-5 stimulus was reduced so that its 3rd harmonic had a contrast of 16% or less—consistent with a contribution from distortion products, which are dominated by the even harmonics (2nd, 4th, 6th, etc) that have zero disparity. In sum, the direction and magnitude of the earliest vertical disparity vergence responses could be attributed entirely to the major Fourier components of the binocular image, consistent with current disparity-energy models in which the monocular visual inputs undergo spatial filtering prior to their binocular matching.
Supported by the Intramural Program of the National Eye Institute (USA) and AIST (Japan)