In normal foveal vision, the critical distance (in minutes) is more or less proportional to target size, falling close to the line of unity slope for Gaussian Es (Figure 2) and for Gabor Es (
Figure 3). For a fixed-size Gaussian E target (
Figure 2), the critical distance is bigger in peripheral vision, and similar results are obtained when the flanks consist of 5 patches each, or just 2 appropriately placed patches. The results with Gaussian targets are similar to those of previous work: The stimuli are broadband; therefore, the increased extent of crowding may be a consequence of the peripheral visual system engaging large (low) spatial frequency filters. Note, however, that most previous studies used differently sized targets to test the fovea and periphery. Our results show that the extended crowding in peripheral vision is not simply a consequence of using larger peripheral targets. Interestingly, similar results are obtained with Gabor patches (
Figure 3). For very large target sizes (greater than about 150 minutes), the critical distance approaches (but is larger than) that of the normal fovea; however, for smaller targets, there appears to be a floor, so that the critical distance becomes a nearly constant (large) distance. The smallest critical distance depends on eccentricity (it is larger at 10 degrees than at 5 degrees). At both eccentricities, the smallest critical distance with Gabor patches is approximately 10% of the effective eccentricity (i.e., eccentricity, E + E
2, where E is the eccentricity and E
2 is the doubling eccentricity, is approximately 0.7 degrees [
Levi, Klein, & Aitsebaomo, 1985]); at an eccentricity of 5 degrees, it is about 0.5 degrees, and at an eccentricity of 10 degrees, it is about 1 degree. Note that the critical distance is roughly similar in size for the 4AFC task and the 2AFC task (which is discussed below). The gray symbols show the critical distances obtained with Gaussian Es (with 5 patches/flank, from
Figure 2). For D.L., the Gaussian data are consistent with the 10% floor; for M.F., they are somewhat lower. Thus, in peripheral vision, the extent of crowding is not proportional to target size; however, the extent of interaction is stimulus dependent. We note that the critical distance is very much larger (more than 20 times) than the resolution limit, but that it is similar to the critical distance for the crowding effect of flanks on a single Vernier target (
Levi, Klein, & Aitsebaomo, 1985). In foveal vision, crowding is scale invariant and is primarily determined by target size (SD). When replotted as threshold elevation (i.e., flanked threshold/unflanked threshold) versus target-to-flank distance expressed in standard deviation units (SDU, i.e., target-to-flank distance [in arc min], divided by patch SD [in arc min]), foveal performance over a wide range of pattern sizes collapses into a more or less unitary function (see Levi et al., 2002, Figure 7). In peripheral vision (
Figure 4, solid symbols), it is clear that crowding is not scale invariant. When plotted as threshold elevation versus target-to-flank distance (in SDU), it is clear that for small targets, the crowding does not scale to target size, but is disproportionately large—instead of the extent of crowding being ≈ 2.5 SDU as in the fovea, it may be much larger in the periphery (e.g., D.L. 5 degrees with Gaussian Es [not shown] is about 15 SDU). The extended crowding in peripheral vision is not a consequence of our choice of spatial frequency. The diamonds in Figure 4 show that in the periphery, as in the fovea, crowding is similar for patches of the same size (SD) with spatial frequencies that are one octave apart. However, in the periphery, it is the eccentricity, rather than the target size, that determines the extent of crowding.