A comparison of threshold and suprathreshold appearance of gratings with components in the low and high spatial frequency range

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Abstract
The appearance of square gratings with some of their Fourier components missing was investigated for threshold and suprathreshold contrasts [in human vision]. If high frequency components are removed from a square grating there is only a very small effect on the detection threshold, or suprathreshold appearance, unless the components are visible by themselves. If the fundamental frequency is removed from a square-wave grating which has a spatial frequency lower than 1 cycle per degree (c/d) the contrast sensitivity is not altered. This is a generalization of the Craik-Cornsweet illusion. If the contrast is raised above the detection threshold the grating is indistinguishable from a square grating, unless the contrast is high enough to see the fundamental when it is presented alone. If the fundamental is removed from a square grating which has a spatial frequency higher than 1 c/d the contrast threshold and the appearance at all contrasts are changed. At threshold it appears as a sinusoidal grating of three times the fundamental frequency. The threshold is dictated solely by amplitude of the third harmonic. If the contrast is further raised, so that the 5th harmonic also reaches threshold, the periodicity of the fundamental is seen. Therefore, gratings of many different luminance profiles (including the Craik-Cornsweet profile) all produce the perception of a square grating simply because those missing components which would be required in each case to produce a perfect square are by themselves undetectable. The visual system responds as though hardwired to detect square gratings and edges by means of quasi-Fourier analysis. These results are analogous to the missing fundamental, or residue, effect in hearing.