Nonlinear visual distortion:An effective expansive nonlinearity from asymmetry in on and off pathways

Purpose Masking experiments with mixtures of spatial frequencies provide a challenge to the notion that there are independent mechanisms tuned to spatial frequency and orientation. Here, masks made of two high similar spatial frequencies produce unexpectedly large threshold elevations at the low difference, or beat, frequency. One explanation for the paradoxical masking is that an early nonlinear stimulus transformation has injected a real grating at the beat frequency (a distortion product) and this is responsible. Is this correct? If so, what is the nature of the early nonlinearity and how does it come about? Methods We measured masking of a 1cpd test grating of random phase by a mask composed of two, 20% contrast, 8 and 9 cpd gratings (this beats at 1 cpd). Masking was measured as a function of the contrast of another real grating which was added so as to cancel or reinforce the putative distortion product at 1cpd. Results Adding a 1 cpd grating, of 2% contrast, at a phase of 270° (with respect to the 8 and 9 cpd carriers), reduces the amount of masking - adding it in at 90° increased the amount of masking. Conclusions The phase of the 1cpd grating that results in minimal masking implies that the distortion product is generated by an expansive nonlinearity. An expansive receptoral luminance transformation is incompatible with the phenomenon of light adaptation. However, a simple asymmetry in the treatment of light increments and decrements can account for the results. For example, if both ON's and OFF's were nonlinearly compressed, but ON's were compressed less than OFF's an 'effective expansion' would result. It can be shown that this simple model accounts for physiological and psychophysical data on nonlinearity that was thought to be due to an early compressive nonlinearity - including the observation that the bright bars of sine wave gratings appear wider than the dark bars (Pelli, ARVO, 1986).