Retinal inhomogeneity. III. Circular-retina theory.

By introducing a local contrast-sensitivity function, defined as the Fourier transform of the local point-spread function, we have constructed a model of retinal inhomogeneity that predicts the contrast sensitivity for circular homogeneous or inhomogeneous sinusoidal targets up to 16 degrees in diameter. This model assumes that (1) contrast sensitivity is mediated by a standard, receptive-field-type filter function (one that fits our data somewhat better than available receptive-field models); (2) retinal inhomogeneity is circularly symmetric; i.e., receptive-field size varies only with eccentricity; (3) this size variation is governed by a linear scaling factor out to at least 8 degrees eccentricity; and (4) the local contrast sensitivities at different parts of the retina combine in accord with a fourth-power probability-summation rule. The parameters of the model were determined by fitting contrast-sensitivity data for a new class of stimulus patterns: locally sinusoidal, circularly symmetric targets with radially varying spatial frequency (but constant amplitude). The model also fits contrast thresholds for circular cosine disks and annuli of various sizes and eccentricities. (Predictions for noncircular patterns require a minor extension.) The results suggest that the uniform, homogeneous sinusoidal patterns used throughout the literature provide surprisingly little information about the form of receptive fields.