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F. W. Campbell, E. R. Howell^* and J. R. Johnstone

Physiological Laboratory, University of Cambridge, Cambridge CB2 3EG

1. The appearance of square gratings with some of their Fourier components missing has been investigated for both threshold and suprathreshold contrasts.

2. 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.

3. 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 generalisation 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.

4. 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 the amplitude of the third harmonic. If the contrast is further raised, so that the fifth harmonic also reaches threshold, the periodictiy of the fundamental is seen.

5. 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.

6. These results are analagous to the missing fundamental, or residue, effect in hearing.

Present address: Department of Physiology, University of Western Australia, Nedlands 6009, Western Australia.

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