Equivalent intrinsic blur in spatial vision

We used Gaussian blurred stimuli to explore the effect of blur on three tasks: (i) 2-line “resolution”; (ii) line detection; and (iii) spatial interval discrimination, in both central and peripheral vision. The results of our experiments can be summarized as follows.

(i) 2-Line “resolution”: thresholds for pairs of unblurred, low contrast, stimuli are approx. 0.5min arc in the fovea. When the stimulus blur is small, it has little effect upon 2-line “resolution”; however, when the stimulus blur, σ, exceeds 0.5 min, thresholds are degraded. We operationally define this transition point as the equivalent intrinsic blur or B_i. When the standard deviation of the stimulus blur, σ, is greater than B_i, then the “ resolution” threshold is approximately equal to σ. Both the unblurred “resolution” threshold, and the equivalent intrinsic blur, B_i, vary with eccentricity in a manner consistent with the variation of cone separation within the central 10 deg. When the stimulus blur exceeds the equivalent intrinsic blur, “resolution” in the periphery is the same as in the fovea.

(ii) Line detection: when the standard deviation of the stimulus blur, σ, is less than B_i, then the line detection threshold is approximately inversely proportional to σ (it is≈ T_dB_i/gs) i.e. it obeys Ricco's law. When the standard deviation of the stimulus blur, σ, is greater than B_i, then the “resolution” threshold is approximately equal to σ and the detection threshold is approximately a fixed contrast (to be referred to as T_d).

According to (i) and (ii), the equivalent intrinsic blur, B_i, plays a dual role in determining both the “resolution” threshold and the detection threshold, B_i corresponds to the “Ricco's diameter” for spatial summation in a detection task, and it also corresponds to the “resolution” threshold for thin lines. This connection between detection and “resolution” is somewhat surprising.

(iii) Spatial interval discrimination: thresholds are proportional to the separation of the lines (i.e. Weber's law). At the optimal separation, the thresholds represent a “hyperacuity” (i.e. they are smaller than the “resolution” threshold). For unblurred lines, the optimal separation is approximately 2–3 times the “resolution” limit at all eccentricities, so the optimal separation varies with eccentricity at the same rate as the equivalent intrinsic blur, B_i. However, the optimal spatial interval threshold falls off with eccentricity about 3–4 times more rapidly, consistent with the rate of decline of other position acuity tasks. For Gaussian blurred lines, over a wide range of separations and eccentricities, spatial interval discrimination thresholds begin to rise when the stimulus blur exceeds between about? and ½ the separation of the lines. The strong elevation of the optimal spatial interval discrimination threshold in the periphery cannot be predicted on the basis of detectability of the lines, “resolution”, or on the basis of the equivalent intrinsic blur. We hypothesize that the increased spatial interval discrimination thresholds are a consequence of position uncertainty, perhaps due to sparse spatial sampling in the periphery.

Keywords: Resolution; Spatial interval discrimination; Hyperacuity; Blur; Gaussian blur; Intrinsic blur Spatial vision