Retinal inhomogeneity and the witch's hat: contrast sensitivity declines as a bi-linear function of eccentricity in each direction

The logarithm of contrast sensitivity has been described as a linear function of retinal eccentricity for a visual field of 120 deg (Pointer and Hess, 1989 Vision Research 29 1133-1151). Here we ask whether this is a suitable account for the central 9 deg of the visual field where most contrast sensitivity experiments are performed. We measured contrast detection thresholds for oriented cosine-phase log-Gabor stimuli with a spatial frequency of 4 cycles deg¹ and bandwidths of 1.6 octaves and 25. Four meridians were tested (-45º, 0º, 45º, and 90º), each with four stimulus orientations (-45º, 0º, 45º, and 90º). Eccentricity was sampled in steps of 6 cycles, and 1.5 cycles in a subsample of conditions. In almost every case, we found that the initial sensitivity loss with eccentricity was steep (average = 1.1 dB cycle¹), becoming shallower (average = 0.4 dB cycle¹,similar to previous reports) after a critical point: a behaviour that was nicely described by a bilinear equation. This equation also improved the fit to the Pointer and Hess results. Sensitivity to the entire central visual field was estimated by elliptical interpolation between bi-linear fits to each of the four cardinal half-meridians. This produced a sensitivity surface shaped like a 'witch's hat', and made good predictions for the results for the oblique meridians. By testing other spatial frequencies, we aim to determine whether the location of the hat's brim is a fixed visual angle(as might be expected on anatomical grounds) or a fixed number of stimulus cycles.