Deviations from strict M scaling

It has been hypothesized that the visibility of stimuli can be made independent of location in the visual field if they are scaled according to the cortical magnification factor M (M scaling) [Exp. Brain Res. 37, 495 (1979); J. Opt. Soc. Am. A 4, 1568 (1987)]. Although the predictions of this hypothesis are quite good with regard to contrast sensitivity for sine wave gratings, they are inaccurate with regard to the detection of circular disks: the visual field contains large regions where diameter-threshold curves for these stimuli are independent of retinal location [Am. J. Optom. 49, 748 (1970); Vision Res. 20, 967 (1980)], although M varies by a factor of 3 over these regions. We measured diameter-threshold functions for circular symmetric stimuli with a Gaussian luminance profile and Gaussian temporal modulation at various eccentricities (as high as 420) along both sides of the horizontal meridian. Along the temporal side the results are similar to those for disks: between 120 and 420 the curves are largely independent of eccentricity. In addition a strong nasotemporal asymmetry is found: for the nasal side the thresholds are considerably higher than for the temporal side. The results suggest both scale and gain differences over the visual field. Reanalysis of data for gratings shows that M scaling holds only for high spatial frequencies at which the slope of the contrast sensitivity function is steep (acuity); if the slope is less steep, the results are similar to those for localized stimuli. The results can be explained if we assume that (i) the spatial scale varies proportionally to the diameter of the smallest receptive field center and (ii) the gain is a function of the overlap factor, i.e., the number of retinal ganglion cells covering a single point in visual space