The stimuli in our experiments cons

The stimuli in our experiments consisted of a pair of
vertical ribbons (3% wide unless otherwise specified) of a
horizontal cosine grating with a vertical Vernier offset
between the ribbons. The ribbons were separated by a
gap of approximately 3%, which was at the mean luminance
of 100 cd:m2. Unless specified, the cosine ribbon
contrast was 40%. The cosine ribbons have two important
advantages for our purposes: first, they are well
tuned in vertical spatial frequency. This is important
because Vernier acuity depends strongly and nonmonotonically
on spatial frequency (see Fig. 1, see also,
e.g. Watt & Morgan, 1983; Bradley & Freeman, 1985;
Carney & Klein, 1991; Whitaker & MacVeigh, 1991;
Hu et al., 1993; Whitaker, 1993; Levi et al., 1994, 2000).
Second, the ribbons are localized in their horizontal
spatial extent1. This is important because the offset
information is highly localized, and with long gratings
(wide ribbons), it is not clear which part of the stimulus
is useful for the task (e.g. Whitaker, 1993). With elongated
gratings, there may be useful information for
contrast detection or discrimination along the entire
length of the grating; whereas, the useful information
for Vernier acuity may be restricted to a small region
near the offset. Indeed, Hu et al. (1993) found that at
high spatial frequencies, elongating the grating stimuli
improved contrast discrimination, but degraded Vernier
discrimination (also see Levi et al., 2000).