The role of separation and eccentricity in encoding position.

We measured two- and three-line spatial interval and alignment thresholds for a wide range of separations and eccentricities. In order to avoid confounding the role of separation and eccentricity, the test lines were presented on iso-eccentric arcs, with radii between 0.625 and 10 deg. The iso-eccentric paradigm allows separation to be varied over a large range while holding eccentricity constant. Our main finding is that for all tasks, at all eccentricities, Weber's law fails at large separations. Our results are consistent with the hypothesis that distance judgements are limited by at least two factors: (1) when the separation of the iso-eccentric test lines is small with respect to the eccentricity position thresholds are proportional to the separation of the features, and show little dependence on eccentricity. This is Weber's law for position, and the threshold is approx. 0.03-0.05 times the stimulus separation; (2) when the separation of the iso-eccentric test lines is comparable in size to the eccentricity, position thresholds are proportional to the target eccentricity, and are essentially independent of separation. In this "eccentricity regime", position discrimination thresholds are = ECC * k where ECC is the stimulus eccentricity in degrees, and k is a fraction of the eccentricity (approximately 0.01-0.03). The observer uses whichever mechanism is more sensitive to the stimulus. Under the conditions of our experiments, the observers perform a Weber computation when the separation, S, between the pair of iso-eccentric test lines is less than about 0.5 * ECC, and apply a "cortical ruler" when S is greater than about 0.5 * ECC. If the angle subtended by the fixation point and the pair of iso-eccentric test lines is considered, then for both the two-line and the three-line tasks, when the angle is less than approx. 30 deg, thresholds are proportional to separation, and when it is between 30 and 180 deg, thresholds are proportional to eccentricity.