The attenuation surface for contrast sensitivity has the form of a witch’s hat within the central visual field

Over the full visual field, contrast sensitivity is fairly well described by a linear decline in log sensitivity as a function of eccentricity (expressed in grating cycles). However, many psychophysical studies of spatial visual function concentrate on the central ±4.5 deg (or so) of the visual field. As the details of the variation in sensitivity have not been well documented in this region we did so for small patches of target contrast at several spatial frequencies (0.7–4 c/deg), meridians (horizontal, vertical, and oblique), orientations (horizontal, vertical, and oblique), and eccentricities (0–18 cycles). To reduce the potential effects of stimulus uncertainty, circular markers surrounded the targets. Our analysis shows that the decline in binocular log sensitivity within the central visual field is bilinear: The initial decline is steep, whereas the later decline is shallow and much closer to the classical results. The bilinear decline was approximately symmetrical in the horizontal meridian and declined most steeply in the superior visual field. Further analyses showed our results to be scale-invariant and that this property could not be predicted from cone densities. We used the results from the cardinal meridians to radially interpolate an attenuation surface with the shape of a witch's hat that provided good predictions for the results from the oblique meridians. The witch's hat provides a convenient starting point from which to build models of contrast sensitivity, including those designed to investigate signal summation and neuronal convergence of the image contrast signal. Finally, we provide Matlab code for constructing the witch's hat.