Objects presented in the plane of fixation can be aligned with great precision. For example, the threshold for perceiving an offset between vertical Vernier 1 lines lies in the order of 500 (Westheimer & McKee, 1977). This high precision qualifies Vernier acuity as a variant of hyperacuity (Westheimer & McKee, 1977). At high contrast, binocular judgements are about as precise as