Nonlinearity in human visual responses to two-dimensional patterns, and a limitation of Fourier methods

Subjects viewed a pattern consisting of two superimposed gratings: a vertical grating that was counterphase-modulated at Fl Hz and a variable-orientation grafting modulated at F2 Hz. A nonlinear orientation-tuned cross-modulation term of frequency (2F1 + 2K2)Hz in the evoked potential was large when the gratings were parallel and had a half-height full bandwidth of about 12 deg. But a strong (2F1 + 2F2) term was also produced by orthogonal gratings. The application of Fourier methods to analyzing human visual processing of patterns modulated in two dimensions assumes that there is no nonlinear interaction between visual responses to orthogonal gratings. The existence of a strong cross-modulation term in the orthogonal-grating response violates this crucial requirement. Our findings could not result from the stimulation of independent, linear, orientation-selective mechanisms.